A Virtual Coupling Strategy and Model Predictive Control Method for Train Operation

Abstract

This invention discloses a virtual coupling strategy and model predictive control method for train operation. By leveraging the predictive and multi-objective optimization characteristics of model predictive control, train control is combined with road information to achieve more precise and stable train speed control. The proposed method for calculating the minimum distance between trains can effectively improve the reliability and flexibility of train following and shorten the train spacing to within 100m, thereby effectively improving the utilization efficiency of the railway. At the same time, it solves the input delay problem of train control and enables more precise control of the train state when two trains are coupled and close together.

Description

Technical Field

[0001] This invention belongs to the field of train control technology, specifically relating to a virtual coupling strategy and model predictive control method for train operation. Background Technology

[0002] Rail transport is widely distributed in my country, including bullet trains, high-speed trains, and heavy-haul trains. Among various modes of transport, sea freight is the most economical in terms of cost, but its connection points are limited to ports. Road transport is more expensive, costing 2 to 3 times that of rail, while air freight is the most expensive. In terms of efficiency, although rail is not as fast as air freight, its efficiency for transporting large tonnage is significantly higher than that of road and sea transport.

[0003] In the process of train control, maximizing driving safety, comfort, and railway utilization is a current hot topic in academia. Solving this problem requires achieving precise train cooperative control. Compared to car models, although the operating environment of trains is relatively stable and simple, and model building is relatively simple, the design of their control systems still faces many challenges, including: First, for non-electrically controlled heavy-haul trains, the control inputs have input delays, and acceleration and braking signals cannot be immediately transmitted to the train's control system; second, trains are affected by external environmental factors such as running resistance during operation, and traditional control methods such as PID (Proportional-Integral-Differential) cannot achieve precise control in conjunction with the environment, but can only correct the speed based on the deviation after the train deviates due to changes in resistance; third, offline optimization using modern methods such as artificial intelligence is needed to improve train operating efficiency and energy utilization. However, firstly, the offline optimization-based speed curve and online follow-up control mode lacks flexibility and struggles to handle unexpected situations. Secondly, different types of trains require different multi-objective optimization schemes, with personalized optimizations targeting aspects such as energy saving, stability, and efficiency. For example, heavy-haul trains and freight trains face coupler force issues, limiting train acceleration, while urban rail transit such as subways require good acceleration and braking performance while ensuring transport efficiency. In conclusion, achieving stable, safe, and efficient train control is a challenging task.

[0004] Currently, PID control remains the most widely used control method in train operation. For example, the control scheme used in subway operation employs PID control to guide trains to follow a pre-set speed-time curve. The reasons for adopting PID control include: firstly, its simplicity and reliability; although parameter tuning requires some skill, its engineering applications are intuitive and convenient; secondly, the design of a PID controller does not require precise train model information or specific road environment information, thus reducing the time spent on establishing a precise model in the overall design. However, because PID control is a single-objective control method that is almost entirely independent of the model, when dealing with complex coupled multi-objective optimization problems, the nonlinearity and strong coupling characteristics of the system will cause the controller performance to rapidly decline near the linearization equilibrium point; furthermore, PID control can only control the current state of the train system itself and cannot incorporate specific road information and train control input delays for predictive control, resulting in very limited room for improvement in the control method itself. In practical applications of train operation, it is necessary to coordinate road information and vehicle information ahead to avoid energy and efficiency losses caused by large accelerations and decelerations. Summary of the Invention

[0005] In view of this, the present invention provides a virtual coupling strategy and model predictive control method for train operation, which realizes precise control of the train in response to changes in the train operation environment, and solves the problem of train control input delay.

[0006] This invention provides a virtual coupling strategy and model predictive control method for train operation, comprising the following steps:

[0007] Step 1: Augment the state variables using the control variables from the previous moment to obtain the discrete spatial dynamics model of the train, as shown in equation (1):

[0008]

[0009] Wherein, parameters A, B, C, and H are respectively represented as:

[0010]

[0011] The train's state variables are represented by b1 and b2, which are coefficients in the linearized resistance force f = b1v + b2. K represents the steady-state gain, T represents the transition time of the inertial element, m represents the total mass of the train, γ represents the train's slewing mass parameter, and η represents the train's rotational mass parameter. (k) T represents the system output that can be observed by instruments. s This represents the discrete time step of the system, which is also the control step. Indicates control input in incremental form;

[0012] Step 2: Using virtual coupling, determine the train control objective, i.e., calculate the minimum distance between the front and rear trains; introduce control delay, and determine the train control state equation based on the control objective as shown in equation (2):

[0013]

[0014] Among them, Ξ k This represents the set of all state variables in the prediction time domain;

[0015] Based on the determined train control state equations, the cost function required for MPC control is determined as shown in equation (3):

[0016]

[0017] Among them, Ψ=CM, Θ=CW, Λ=CΓ-Y ref|k Q and R are both weighting coefficients;

[0018] Step 3: Initialize the train control state and load the operating environment data; during train operation, when the operating conditions change, the train updates its own running trajectory. At the same time, at each control moment, it is determined whether there is a train ahead within the set range. If not, the hard wall mode is executed; otherwise, the coupling process with the train ahead is executed to follow the running trajectory of the train ahead. Based on the determined train state constraints, the control delay is offset by a quadratic programming solver, and the train control state equation obtained in Step 2 is solved to obtain the control sequence. The control sequence is used to control the train; when the distance between the two trains enters the buffer, buffer docking is performed; the process ends when the train arrives at the station and stops.

[0019] Furthermore, the set range in step 3 is the safe distance range between two trains, and the value of the set range is determined by the coupling process and vehicle performance.

[0020] Furthermore, in step 3, before solving the train control state equation obtained in step 2 using a quadratic programming solver based on the determined train state constraints, the train driving state is changed by adjusting the weight coefficient Q.

[0021] Furthermore, the virtual coupling strategy and model predictive control method also include the following train state constraints: system acceleration change constraint, system acceleration constraint, system speed constraint, and train displacement constraint.

[0022] Beneficial effects:

[0023] 1. This invention utilizes the predictive and multi-objective optimization characteristics of model predictive control to combine train control with road information, enabling more precise and stable train speed control. The proposed method for calculating the minimum distance between trains can effectively improve the reliability and flexibility of train following and shorten the train-to-train distance to within 100m, effectively improving the utilization efficiency of the railway. At the same time, it solves the input delay problem of train control and can more accurately control the train state when two trains are coupled and close together.

[0024] 2. This invention proposes a buffering scheme when the following train is close to the following point, which realizes the smooth coupling of the train and strengthens the speed constraint conditions to achieve better control effect.

[0025] 3. This invention achieves a unified control strategy by using the real-time adjustment of weight coefficients in the model predictive control model, without switching control schemes during virtual coupling, which can effectively reduce the complexity of control. Attached Figure Description

[0026] Figure 1 This is a schematic diagram of the control flow formed by using a virtual coupling strategy and model predictive control method for train operation provided by the present invention.

[0027] Figure 2 This diagram illustrates train information exchange under the control of a virtual coupling strategy and model predictive control method for train operation provided by the present invention.

[0028] Figure 3 A schematic diagram of the train operating environment constructed for an example.

[0029] Figure 4 The gradient curve for train operation is set for the example.

[0030] Figure 5 The speed limit curve for train operation is set for the example.

[0031] Figure 6 The train speed diagram is shown as the result of a single-train operation experiment in the embodiment.

[0032] Figure 7 This is a train acceleration diagram based on the results of a single-train operation experiment in the embodiment.

[0033] Figure 8 The image shows the train speed diagram based on the results of the dual-train operation experiment in the embodiment.

[0034] Figure 9 The image shows the train acceleration diagram based on the results of the dual-train operation experiment in the example.

[0035] Figure 10 The train time-shift diagram shows the results of the dual-train operation experiment in the embodiment.

[0036] Figure 11 This is a diagram showing the train displacement difference from the results of a dual-train operation experiment in the embodiment.

[0037] Figure 12 This is an enlarged view of the train speed results from the dual-train operation experiment in the embodiment.

[0038] Figure 13 The train time-shift diagram shows the train operation experiment results of the three trains in the example.

[0039] Figure 14 The train speed diagram shows the results of the three train operation experiments in the embodiment.

[0040] Figure 15 The image shows the train acceleration diagrams based on the experimental results of the three trains in the example.

[0041] Figure 16 This is a diagram showing the train displacement difference based on the experimental results of the three trains in the example.

[0042] Figure 17 The diagram shows the solver's solution status for the three train operation experiments in the embodiment.

[0043] Figure 18 The image shows the train speed diagram during the train coupling period, based on the experimental results of the three trains in the example.

[0044] Figure 19 The image shows the acceleration during the train coupling period, based on the experimental results of the three trains in the example.

[0045] Figure 20 The train time-shift diagram shows the experimental results of the three trains operating under MPC control in the embodiment.

[0046] Figure 21 The train speed diagram shows the experimental results of the three trains operating under MPC control in the embodiment.

[0047] Figure 22 The image shows the train acceleration diagrams based on the experimental results of the three trains operating under MPC control in the example.

[0048] Figure 23 The train time-shift diagram shows the experimental results of the three trains operating under PID control in the embodiment.

[0049] Figure 24 The image shows the train speed diagrams based on the experimental results of the three trains operating under PID control in the embodiment.

[0050] Figure 25 The image shows the train acceleration diagrams based on the experimental results of the three trains operating under PID control in the example.

[0051] Figure 26This is a schematic diagram of the emergency braking scenario of the three trains in the embodiment.

[0052] Figure 27 The train speed diagram shows the experimental results of the three trains operating under an emergency braking scenario in the embodiment.

[0053] Figure 28 The image shows the train acceleration diagrams based on the experimental results of the three trains operating under an emergency braking scenario in the example.

[0054] Figure 29 The train time-shift diagram shows the experimental results of the three trains operating under an emergency braking scenario in the embodiment.

[0055] Figure 30 This is a diagram showing the train displacement difference of the three trains in the example experiment under an emergency braking scenario. Detailed Implementation

[0056] The following examples illustrate the invention in detail.

[0057] Based on the analysis of the problems existing in the current train control methods, it is essential to propose a virtual coupling strategy and model predictive control method for train operation with input delay.

[0058] Virtual coupling transforms the physical links between trains into virtual links without physical contact through precise control. It eliminates control obstacles caused by differences in train types through modeling and calculation, enabling different train models to be used as a common model for coordinated formation. Virtual coupling is a further improvement on moving block signaling, allowing trains to be separated by relative braking distance rather than absolute braking distance. Moving block signaling refers to trains being separated by absolute braking distance, i.e., the relative displacement required for the following train to brake to zero speed; relative braking distance refers to the relative displacement required for the following train to brake to the same speed as the preceding train.

[0059] Model Predictive Control (MPC), also known as Receding Horizon Control (RHC), has been gradually applied in industrial fields since 1980. MPC is a control method that combines open-loop optimization and closed-loop correction. Its basic idea consists of three parts: open-loop model prediction, rolling optimization, and closed-loop feedback correction. MPC control requires establishing a model of the controlled object. The MPC controller performs predictive optimization in the predictive time domain based on the established state-space model, applies the calculated control scheme to the actual model, and provides feedback on the model's control effect to the controller. This process is repeated at each time step, resulting in rolling dynamic optimization in the time domain. Compared to PID control, MPC control has several advantages in train control: First, real-world systems have various constraints. For example, train operation must consider the physical upper limits of traction and braking acceleration, the maximum speed during operation, and the maximum rate of change of acceleration. These constraints are easy to implement in model predictive controllers but difficult to add to PID control. Second, model predictive control can achieve environmental perception within the prediction time domain and react in advance. Unlike optimal control, which considers an infinite time domain, model predictive control may not produce the optimal action across the entire time domain, but it achieves better control performance than PID control. For example, in the scenario where a train encounters an uphill slope, if the train is to pass the slope quickly and smoothly, acceleration control needs to begin before and during the entry into the slope. Since the PID controller can only perceive the current situation of the train and not the environment, it can only adjust acceleration to maintain the vehicle's speed when the train reaches the slope and its speed decreases. This control method will cause speed fluctuations in the train.

[0060] Typically, due to the large mass of trains and long control cycles (usually on the order of several minutes), the delay in control input is only a few seconds, making it easily negligible during modeling. However, in a virtual coupling scenario, considering the close proximity of two high-speed trains, even a small speed control error can cause a displacement deviation of tens of meters. Therefore, more precise control is required. Ignoring the delay in control input in this case would cause fluctuations in the distance between the two trains or even steady-state error, leading to safety hazards and affecting the reliability of the entire control algorithm. Therefore, this invention introduces a delay in control input during train dynamics modeling.

[0061] Train input delay is typically described using a first-order inertial-hysteresis loop. The forces acting on the train are considered to be traction and friction. Traction is divided into driving force and braking force, while friction is divided into basic resistance and additional resistance. Both basic and additional resistance are nonlinear and can be transformed into linear components using linearization methods. On the other hand, train modeling analysis mainly includes single-mass models and multi-mass models. Single-mass models ignore the coupling between carriages within a train, while multi-mass models can better analyze the force conditions of the train under complex traction and braking conditions. For example, when analyzing data from the CR400F EMU train, since the CR400F is an electric train, the driving and electric braking performance of all carriages is good. In this case, the entire train can be modeled as a single-mass model with length.

[0062] This invention provides a virtual coupling strategy and model predictive control method for train operation. The basic idea is to solve the input delay problem by using model predictive control, optimize the stability and comfort of control by combining model predictive control with road and train information ahead, improve virtual coupling by combining model predictive controller to achieve unified control throughout the entire process, and optimize the control effect by setting minimum safe distance, buffer zone and strengthening speed limit.

[0063] This invention provides a virtual coupling strategy and model predictive control method for train operation, specifically including the following steps:

[0064] Step 1: Augment the state variables using the control variables from the previous moment to obtain the discrete spatial dynamics model of the train, as shown in equation (7):

[0065]

[0066] Wherein, parameters A, B, C, and H are respectively represented as:

[0067]

[0068] This represents the status parameters of the train. The control input is expressed in incremental form; b1 and b2 represent the coefficients in the linearized resistance f = b1v + b2; K represents the steady-state gain; T represents the transition time of the inertial element; m represents the total mass of the train; γ represents the train's slewing mass parameter; and η represents the linearized control input. (k) T represents the system output that can be observed by instruments. s T represents the system s This indicates that the sampling period of the discrete model is also the control period of the controller. Represents the state variable, u (k) =[a c(k)[] represents the input control quantity. For ease of writing, the constant parameter that still exists after discretization due to the train control delay is denoted as...

[0069] The process of establishing a discrete spatial dynamics model of a train includes the following steps:

[0070] Step 1.1: Perform dynamic modeling of the train using existing methods. The equations describing the dynamic model are shown in equation (1):

[0071]

[0072] Where v(m / s) and s(m) represent the train's speed and distance traveled, respectively, and a c (t) represents the train's control acceleration as an input to the train, a r (t) represents the actual response acceleration of the train to the input, K represents the steady-state gain, T represents the transition time of the inertial element, n represents the pure time delay, m represents the total mass of the train, γ represents the train's slewing mass parameter, and a r ∈[a rmin ,a rmax ] represents the traction or braking response acceleration of the train, a rmin and a rmax Let represent the maximum braking acceleration and maximum traction acceleration of the train, respectively. The train's input-output transfer function is described using a first-order inertial element plus a hysteresis element, as shown in equation (2):

[0073]

[0074] The second equation in equation (1) is the result obtained by transforming equation (2) into the time domain. Since there are great differences in train operating environment, power unit configuration and traction and braking characteristics, these three parameters are often inconsistent. In this invention, the parameters of one train are used as a reference test, which can also be changed according to the actual situation. The model used is shown in equation (3):

[0075]

[0076] In equation (1), the third equation represents the force analysis of the train. The basic resistance in the resistance f is R = a1v 2 In the form of +a2v+a3, for example, if the resistance data of the CR400F EMU is selected, it is expressed as shown in equation (4):

[0077] R = 0.00052v 2 +0.0063V +4.5(kN) (4)

[0078] The basic resistance can be linearized in the optimization time domain, replacing the quadratic curve with the form of tangent (b1v+b2); at the same time, the additional resistance caused by the arc and slope of the track and the additional resistance caused by the curve are also nonlinear models. However, for the convenience of calculation, the instantaneous value is taken into b2 at each calculation step, and the force equation is finally obtained as shown in the third equation in equation (1).

[0079] Step 1.2: MPC control requires a discrete state-space model. By discretizing equation (1) using forward difference, we can obtain equation (5):

[0080]

[0081] Step 1.3: Rearranging equation (5) yields the state-space equation as shown in equation (6):

[0082]

[0083] Wherein, the parameters a, b, and h are respectively represented as:

[0084]

[0085] Step 1.4: Augment the state variables using the control input from the previous time step.

[0086] To avoid control steady-state error caused by input control, and because the prediction and control time domains are of different lengths when designing the MPC controller, the prediction part outside the control time domain is set to a constant value for the control input, i.e., the increment of the control input is zero. In this case, it is more convenient to use an incremental form of control input. Therefore, the state-space equations are modified as follows in this invention.

[0087] The state variable ξ is augmented using the control input from the previous time step. (k) Expressed as The state variable ξ at the next moment can then be derived. (k+1) As shown in equation (7):

[0088]

[0089] Wherein, parameters A, B, C, and H are respectively represented as:

[0090]

[0091] Through the above process, a discrete spatial dynamics model of the train was established.

[0092] Step 2: Using virtual coupling, determine the train control objective, i.e., calculate the minimum distance between the front and rear trains; introduce control delay, and determine the train control state equation based on the control objective; based on the determined train control state equation, determine the cost function required for MPC control.

[0093] Step 2.1: Using virtual coupling, determine the control target of the train and then calculate the minimum distance between the front and rear trains.

[0094] Based on the concept of virtual coupling, the control objectives of the trains are clearly defined. During the movement of two trains, the following train needs to follow the preceding train and achieve the same driving state. The displacement difference between the two trains needs to be minimized to match the minimum distance between the preceding and following trains, and the speed needs to be consistent with the preceding train. Therefore, the minimum distance between the preceding and following trains must first be calculated.

[0095] Suppose there are two trains, A and B, where A is the preceding train and B is the following train. Calculating the minimum distance between the two trains requires considering their current speeds, V. A and V B At the same time, the different braking accelerations A of the two vehicles must also be considered. A and A B Even if the speed of the following vehicle B is less than or equal to the speed of the preceding vehicle A, and the braking speed of the following vehicle B is also faster than that of the preceding vehicle A, it does not mean that the following vehicle B can get infinitely close to the preceding vehicle A. This is because there may be a certain time lag in the process of the braking information from the preceding vehicle A to the following vehicle B. During this time period, the preceding vehicle A has already started to brake while the following vehicle B is still accelerating. Therefore, there is still a risk of collision in this situation.

[0096] Let S b The minimum distance between the two vehicles (S-break) can be used to further optimize vehicle distances, especially for locomotives with slow braking and acceleration, allowing for a better balance between safety and efficiency. The general formula for calculating this distance involves calculating the braking time-displacement curves of both vehicles in the prediction time domain, integrating the speed difference over time during the period when vehicle B's speed is greater than vehicle A's, and then obtaining the minimum distance by which vehicle B approaches vehicle A. The minimum distance between the two vehicles, S-break, is the minimum distance between them. b The calculation method is shown in equation (8):

[0097]

[0098] Therefore, the displacement target following point s' of the following vehicle B is expressed as shown in equation (9):

[0099] s' = s A -Tlong-S b -S m (9)

[0100] Among them, s ALet Tlong be the displacement of the train's front end, Tlong be the train length, and S be the displacement of the train's front end. m For additional safety margin.

[0101] Step 2.2: Introduce control delay and determine the train control state equation.

[0102] Set the prediction step size for MPC rolling optimization to N. p The control step size is N. c The derivation starts from time k, so the prediction domain is [k, k+T]. s ·N p Given the current state of the train [S] k V k A k And in the prediction time domain at time k, it is necessary to follow the reference curve Y. ref|k Solve for the control sequence ΔU k Take the first step Δu (k+1) As a control input, the above process is repeated at time k+1 for iterative optimization.

[0103] For ease of description, the following definitions are provided:

[0104]

[0105] Among them, Ξ k U represents the set of all state variables in the prediction time domain. k Y represents the set of all control accelerations within the control domain. ref|k E represents the set of all reference quantities in the prediction time domain. k This represents the set of all prediction errors in the prediction time domain. The predicted data for the vehicle ahead is Therefore, the error can be expressed as e (k) =y (k) -y ref(k) Then E = YY ref The cost function can be expressed as shown in equation (10):

[0106]

[0107] Among them, the last item e T (k+N|k) Fe (k+N|k) This indicates the terminal error.

[0108] To facilitate the derivation, let ξ (k|k) =ξ k After multi-step derivation of the state equations, the following results were obtained:

[0109]

[0110] Regarding the latency issue, this invention provides the following analysis. The analysis of the above process... The state of the train can be seen from the time and the time before it, which is determined by Δu. (k) The previous control input decision, if based on ξ (k+1) If the initial sequence is directly used for prediction optimization, then prediction will be performed again. To Δu (k) The input is fixed, but this results in a loss of prediction efficiency. However, if we take Δu from the solution sequence... (k+1) Using this directly as the control input for the next moment may lead to inaccurate judgments, because the previous... The reprogramming of control at specific times cannot be reapplied to the system, and such control errors will increase with the delay. It increases as increases. Further observation of the system of equations reveals... Subsequent control sequences are all determined by Δu at the next time step. (k+1) This is determined by the control inputs thereafter. Therefore, based on the above analysis, the method proposed in this invention is to determine... and from After Predictive optimization control will begin.

[0111] The above analysis and derivation process is expressed as follows:

[0112]

[0113] From the above derivation process, it can be seen that, Since it has been determined by the control input at time k and before, it can be considered a known variable. The following formulas, when rearranged and written in matrix form, are represented as follows:

[0114]

[0115] Replacing the matrix expansion with M, W, and Γ respectively yields the expression shown in equation (11):

[0116] Ξ k =Mξ k +WU k +Γ (11).

[0117] Step 2.3: Based on the determined train control state equations, determine the cost function required for MPC control.

[0118] Further derivation of the objective function (10), by expanding and simplifying the summation form, yields equation (12):

[0119]

[0120] Simplifying equation (12) yields equation (13):

[0121]

[0122] Then E k After unfolding, you will get:

[0123]

[0124] Substituting equation (11) into equation (14) yields:

[0125]

[0126] Among them, Ψ=CM, Θ=CW, Λ=CΓ-Y ref|k .

[0127] After rearranging equation (15), we get the information about U. k The quadratic, linear, and constant terms are in the form of equation (16):

[0128]

[0129] This yields the cost function required for MPC control.

[0130] Step 3: During train operation, the control state is first initialized, and operating environment data is loaded. After initialization, when the train updates its own trajectory periodically, when a following train requests an update, or when the route changes, the predictor updates the train's trajectory for future trains that may be coupled with it. Simultaneously, at each control moment, the train must determine its own state. If there are no trains within a specified range ahead, it operates in the conventional hard-wall mode. If there are trains within a certain range ahead that can be caught and share the subsequent route, the train coupling process begins, and it follows the trajectory of the preceding train. Based on the determined train state constraints, a quadratic programming solver is used to solve the train control state equations obtained in Step 2 to obtain the control sequence required for train control. The control sequence is used to control the train. After completing the above control, it is determined whether the train has reached its destination and stopped. If it has, it exits the system until the next startup. The control process is as follows: Figure 1 As shown.

[0131] The train control state equations obtained in step 2 are solved using a quadratic programming solver based on the determined train state constraints.

[0132] As a characteristic of MPC control, modifying the weight coefficients Q, F, and R in the cost function before the controller solves for the optimal input allows for convenient stepless switching of control states. For example, when trains are far apart, the coefficients in the controller of the train behind can be set as follows:

[0133]

[0134] This means that the control primarily focuses on the displacement of the train behind to quickly catch up with the target train, without placing excessive demands on the train's speed and acceleration. However, as the train gradually approaches the train in front, the weighting function... (x represents the distance difference between the two vehicles, and y represents the corresponding coefficient; this is for illustrative purposes only, and an appropriate function should be selected based on the specific situation.) The train's speed and acceleration coefficients are inversely proportional to the train's displacement difference, thus continuously increasing, while the displacement coefficient's weight decreases, eventually stabilizing at:

[0135]

[0136] This enables seamless switching of train control states. The coefficients in Q above are normalized references; in actual control operations, the coefficients in Q should be denormalized based on the data corresponding to those coefficients.

[0137] Because trains themselves are subject to physical constraints, this invention imposes restrictions on the feasible region based on the optimal control solution obtained by the MPC controller in order to optimize the control performance predicted by the model. Based on this consideration, this invention identifies multiple types of train state constraints, including system acceleration change constraints, system acceleration constraints, system speed constraints, and train displacement constraints.

[0138] (1) Constraints on system acceleration change: The change in acceleration at any solution time during train operation should not exceed the limit value. Only by satisfying this condition can the acceleration avoid jumps and instability, thus improving the robustness of the control. Specifically, the change in control acceleration at any time needs to satisfy the system acceleration change constraint, which is shown in equation (17):

[0139] ΔU min ≤U k ≤ΔU max (17)

[0140] Among them, U k ΔU represents a column vector consisting of the optimized sequence of acceleration changes solved by MPC. min ΔU max They represent U respectively k The minimum and maximum values ​​in a column vector.

[0141] (2) System acceleration constraint. In practice, the acceleration and braking performance of a train are limited by its own performance. If the control result obtained in the control calculation causes the acceleration to exceed the range that the train's own performance can support, it may lead to repeated acceleration and deceleration or failure to brake in time, which may cause a collision between two trains. At the same time, the coupling force between the train cars will also limit the train's acceleration. Excessive coupling force between the train cars may pose a hidden danger to the train's operation. Only by maintaining the train's acceleration within a reasonable range can the problem of excessive coupling force between the cars be solved. Based on the above analysis, this invention proposes a system acceleration constraint, which is shown in equation (18):

[0142] U min ≤U≤U max (18)

[0143] Where, U = U0 + LU k U0 is the acceleration at the current moment, and L is a lower triangular matrix represented as follows:

[0144]

[0145] Arrange equation (18) to obtain:

[0146] (3) System speed constraints. The maximum speed of the train is subject to certain limitations. Due to speed limits and the vehicle's own performance, the speed limit of the vehicle should be dynamically changed. V in equation (20) max It can be set as a dynamic column vector to achieve dynamic changes in speed limits.

[0147] V≤V max (20)

[0148] The equation V = V0 + LT s U = V0 + LT s (U0+LU k Substituting into equation (20) and rearranging, we obtain the information about U. k Inequality constraints:

[0149] L 2 U k ≤(V max -V0) / T s -LU0 (21)

[0150] In order to achieve better control in practical applications, this invention proposes the following constraints to strengthen the speed constraints, as shown in equation (22):

[0151] L 2 U k ≤(V max-V0)-LU0 (22).

[0152] (4) Train displacement constraint refers to the fact that the position of the train cannot exceed the safe range behind the position of the preceding car, as shown in equation (23):

[0153] S≤S max (twenty three)

[0154] Let S = S0 + LT s V = S0 + LT s (V0+LT s (U0+LU k Substituting into equation (22), we obtain equation (24):

[0155] L 3 U k ≤(S max -S0) / T s 2 -LV0 / T s -L 2 U0 (24).

[0156] Using the above train displacement constraints, during train operation, when the train gets too close to the ideal control position, the feasible solution domain may become narrow or non-existent. However, in practice, a buffer S is provided. m Therefore, trains have a certain tolerance for safe positions. To avoid this situation, this invention proposes an indirect speed limit: assuming the preceding train moves at a constant speed, if the following train's speed is lower than the preceding train's speed, it is not calculated; otherwise, the maximum speed at which the following train decelerates to the rear of the preceding train without colliding is calculated, as shown in equation (25):

[0157]

[0158] in, For the speed of the train behind, s is the speed of the train ahead, and s is the displacement of the front of the train behind. f Let the displacement of the preceding vehicle be the position displacement. Simplify it to obtain equation (26):

[0159]

[0160] Therefore, the speed constraint of the train is obtained based on the train displacement limit. That is, the train speed needs to meet the condition shown in equation (26) in order to ensure that the train displacement limit is met, thus realizing the limitation of the train's safe position by using speed.

[0161] To further optimize train control, this invention proposes a buffer zone when a following train approaches a preceding train, combining the concepts of virtual coupling and model predictive control.

[0162] In classic virtual coupling schemes, the ideal following point when the following vehicle approaches the preceding vehicle is only one point. However, in practical applications, a smooth coupling between the two vehicles is desired during docking, making control to follow to the ideal following point unnecessary. To reduce unnecessary control overhead, this invention sets a buffer when the following vehicle B approaches the ideal following point of the preceding vehicle A. This buffer represents a safe distance range between the following vehicle B and the preceding vehicle A, and the value of this distance is determined based on coupling requirements and vehicle performance. If the distance between the following vehicle B and the preceding vehicle A is within this buffer, i.e., the two vehicles are within the safe distance range corresponding to the buffer, the displacement difference of the train is considered to meet the requirements. At this time, if the speed difference between the following vehicle and the preceding vehicle is less than a threshold and within the buffer range, the two vehicles are determined to enter a coupling state, i.e., the following vehicle and the preceding vehicle can be regarded as a whole. In this case, the same control strategy is used to uniformly control the train group, and speed following is achieved through the weight of Q in the MPC controller. If the distance between the following vehicle B and the preceding vehicle A is outside this buffer, the control of the following vehicle adopts the method of following the position of the preceding vehicle.

[0163] To verify the effectiveness of the virtual coupling strategy and model predictive control method for train operation provided by this invention, targeted track simulation experiments and comparative experiments with PID controllers were conducted. The information exchange process of the train under virtual coupling control during the experiments was as follows: Figure 2 As shown.

[0164] The experimental scenario is designed based on the Daqin Railway, assuming three vehicles A, B, and C need to transport goods along partially overlapping routes. Figure 3 As shown. Both trains A and B depart from Datong Station. Train A departs first, and train B follows train A under safe conditions. During the train's journey, the train passes through speed bumps and uphill / downhill sections. After passing Hudong Station, train C joins the convoy under safe conditions, forming a convoy of three trains: A, B, and C. Upon arriving at Chawu Station, train B, which is in the middle of the convoy, leaves the convoy and heads towards Beijing and Tianjin. The remaining two trains, A and C, continue in convoy on the same route to Qinhuangdao.

[0165] During the above process, speed limit zones and gradient conditions were set on the road section: speed was reduced at 1.2km to safely pass the station, and then the standard operating speed was restored at 1.4km. The gradient curve is as follows: Figure 4 As shown; based on the actual gradient data of a certain section of high-speed railway along the entire route, the speed limit curve is as follows. Figure 5 As shown.

[0166] (1) Single-train simulation

[0167] After the initial acceleration phase, the train smoothly travels a certain distance. At a certain point after 400 seconds, it encounters a bottleneck and decelerates at full speed to smoothly reach the speed limit of 15 m / s. The deceleration process is smooth and without fluctuations, adhering to the principle of maximum efficiency. At a certain point after 500 seconds, the train accelerates at full speed and smoothly returns to its original speed of 30 m / s, passing through the deceleration section. Following this, there are uphill and downhill sections. It can be seen that the train's traction increases on the uphill sections, and the train decelerates on the downhill sections, while the train's speed remains almost unchanged, demonstrating good control. The train's speed changes during the process are as follows: Figure 6 As shown, the train's acceleration changes as follows: Figure 7 As shown.

[0168] (2) Dual-train simulation

[0169] As can be seen, after the two trains entered the coupling state at around 400 seconds, their speed and acceleration were almost synchronized during the acceleration and deceleration process. Afterwards, the two trains successively passed through uphill and downhill tests, with the uphill and downhill processes being gentle and smooth. Then, before approaching Chawu Station, train B first decelerated to create distance from train A, and then accelerated to maintain its normal operating speed. The process was smooth, gentle, and continuous, with the train's speed changes as follows: Figure 8 As shown, the train's acceleration changes as follows Figure 9 As shown, the distance difference between the two vehicles remained stable at the set target value during acceleration / deceleration and during uphill / downhill driving. The train's displacement changed over time as follows: Figure 10 As shown, the train's displacement difference changes with time as follows: Figure 11 As shown.

[0170] from Figure 8 and Figure 9 As can be seen, the speeds of cars A and B fluctuate when going over the slope. (Magnified image follows) Figure 12 As shown, the speed fluctuations are within a very small range. This is because the train operating environment is nonlinear while the prediction model is linear. However, the extremely small range of changes will not cause safety issues and meets the requirements.

[0171] (3) Three-train simulation

[0172] The three trains are coupled together, decelerating during coupling and accelerating after coupling, traversing uphill and downhill sections. The train's displacement changes over time as follows: Figure 13 As shown; during the decoupling process, smooth operation without vehicle collisions was observed; the control curve was observed to be smooth without fluctuations, and the speed change was stable, as shown. Figure 14 and Figure 15 As shown.

[0173] The displacement differences between the first two and last two trains, and the solver results for the last two trains, show that the displacement differences are gradual with no collisions. A solver result greater than 0 indicates that no optimal solution was found within the given number of iterations; this is a suboptimal solution, a phenomenon that occurs during uphill and downhill driving. Figure 16 and Figure 17 As shown.

[0174] During the docking process between the third train and the first two trains, the speed of the preceding train is observed in the enlarged graph as it traverses an uphill or downhill section. It can be seen that due to the coupling operation on the uphill and downhill sections, the acceleration control curve of train C exhibits some fluctuations before the uphill section. This is because it needs to both decelerate to keep up with the speed of the preceding train and maintain the distance to catch up during the uphill phase, resulting in small fluctuations as a trade-off. It can be seen that after 740 seconds, train C catches up with the speed and displacement of train B and then operates normally. During the coupling period, the speed of train C remains relatively stable and does not exceed the speed limit, eventually smoothly reaching the speed value of train B. Figure 18 and Figure 19 As shown.

[0175] (4) Comparison with PID control

[0176] The parameters for PI control are determined by the critical proportional method. For PID control parameter selection, the trial-and-error method is highly practical, especially for systems with irregular control response curves or frequent disturbances. However, parameter trial-and-error requires extensive debugging experience and may involve significant time spent repeatedly adjusting several parameters. Therefore, the critical proportional method, which is easier to debug and has better tuning results, is chosen for debugging. Considering that the ultimate goal of train control is to control the relative position of the train, and the PID method can only perform single-objective optimization, its multi-objective optimization method is more complex, the lead car selects train speed as the control objective, and the following cars select the displacement difference of the train as the control objective for PID control.

[0177] PID control exhibits significant jitter in acceleration and velocity during coupling. This is because the only feedback parameter for PID control is distance; however, the feedback distance difference does not show noticeable jitter. Figure 23 , Figure 24 and Figure 25 As shown in the figure; secondly, PID control has a significant lag control problem, as shown in the figure. Figure 20 , Figure 21 and Figure 22 and Figure 23 , Figure 24 and Figure 25The comparison shows that at 200s, train B under MPC control had completed coupling and following train A, but train B under PID control was still chasing. PID control also had problems during speed change, with the distance difference between the two trains increasing significantly during acceleration because the following train did not have information that the preceding train was about to accelerate, so it could not make a more complete control.

[0178] (5) Emergency braking situation

[0179] like Figure 26 As shown, unexpected situations are inevitable during train operation. In such cases, the coupled train formation needs to be able to complete an emergency stop. Scenario: The first two trains couple as planned, decelerate, the three trains merge, and the three trains cross a slope; assuming an accident occurs near Chawu Station, the three trains need to make an emergency stop before the station.

[0180] like Figure 27 , Figure 28 , Figure 29 and Figure 30 As shown, it can be observed that the three trains travel normally in the first half of the course. After passing the gradient, approximately 950 seconds later, they receive a signal to brake urgently. The acceleration of all three trains reaches the minimum braking value almost simultaneously. From the train displacement difference results, it can be observed that the train displacement difference remains almost constant during the braking process, maintaining around 50m. The three trains can be considered as one train undergoing the braking process, indicating good control performance.

[0181] In summary, the above are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A virtual coupling strategy and model predictive control method for train operation, characterized in that, Includes the following steps: Step 1: Augment the state variables using the control variables from the previous moment to obtain the discrete spatial dynamics model of the train, as shown in equation (1): Wherein, parameters A, B, C, and H are respectively represented as: The train's state variables are represented by b1 and b2, which are coefficients in the linearized resistance force f = b1v + b2. K represents the steady-state gain, T represents the transition time of the inertial element, m represents the total mass of the train, γ represents the train's slewing mass parameter, and η represents the train's rotational mass parameter. (k) T represents the system output that can be observed by instruments. s This represents the discrete time step of the system, which is also the control step. Indicates control input in incremental form; Step 2: Using virtual coupling, determine the train control objective, i.e., calculate the minimum distance between the front and rear trains; introduce control delay, and determine the train control state equation based on the control objective as shown in equation (2): Among them, Ξ k This represents the set of all state variables in the prediction time domain; Based on the determined train control state equations, the cost function required for MPC control is determined as shown in equation (3): J=U T k (I T QΘ+R)U k +2(Px k +L) T QTHU k +(Px k +L) T Q(Πξ k +L) (3) Among them, Ψ=CM, Θ=CW, Λ=CΓ-Y ref|k Q and R are both weighting coefficients; N p For the prediction step size optimized for MPC rolling, N c Control step size optimized for MPC rolling, U k Y is the set of all control accelerations within the control domain. ref|k This represents the set of all reference values ​​in the prediction time domain; Step 3: Initialize the train control state and load the operating environment data; during train operation, when the operating conditions change, the train updates its own running trajectory. At the same time, at each control moment, it is determined whether there is a train ahead within the set range. If not, the hard wall mode is executed; otherwise, the coupling process with the train ahead is executed to follow the running trajectory of the train ahead. Based on the determined train state constraints, the control delay is offset by a quadratic programming solver, and the train control state equation obtained in Step 2 is solved to obtain the control sequence. The control sequence is used to control the train; when the distance between the two trains enters the buffer, buffer docking is performed; the process ends when the train arrives at the station and stops.

2. The virtual coupling strategy and model predictive control method according to claim 1, characterized in that, The set range in step 3 is the safe distance range between two trains, and the value of the set range is determined by the coupling process and vehicle performance.

3. The virtual coupling strategy and model predictive control method according to claim 1, characterized in that, In step 3, before solving the train control state equations obtained in step 2 using a quadratic programming solver based on the determined train state constraints, the train driving state is changed by adjusting the weight coefficient Q.

4. The virtual coupling strategy and model predictive control method according to claim 1, characterized in that, The virtual coupling strategy and model predictive control method also include the following train state constraints: system acceleration change constraints, system acceleration constraints, system speed constraints, and train displacement constraints.

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