Virtual Train Tracking Control System and Method Based on Model Predictive Control

Abstract

This invention discloses a virtual train tracking control system and method based on model predictive control (MPC), relating to the field of rail transit signal control. Within the same train unit of this system: an information processing module, a dynamic equation construction module, a trajectory prediction module, a tracking control target calculation module, an optimal problem construction module, and a quadratic programming problem solving module are sequentially connected; the information processing module is connected to the tracking control target calculation module; and the quadratic programming problem solving module is connected to the trajectory prediction module. In two adjacent train units: the information interaction processing module of the latter train unit is connected to the trajectory prediction module of the former train unit. This invention employs predicted trajectories, achieving small-interval tracking between train units under the safety constraints imposed by the EBI speed in the tracking control target calculation module. This avoids introducing the EBI speed calculation function into the constrained optimal control problem in MPC, saving significant computational resources.

Description

Technical Field

[0001] This invention relates to the field of rail transit signal control technology, and in particular to a virtual train tracking control system and method based on model predictive control. Background Technology

[0002] To address the uneven spatial and temporal distribution of passenger flow in urban rail transit (hereinafter referred to as "urban rail"), virtual coupling (VC) technology has attracted widespread attention in the industry. This technology, based on vehicle-to-vehicle communication and active control, combines multiple train units that do not have physical coupling into a virtual train formation, while maintaining a very small tracking distance between adjacent train units. This virtual coupling method allows all train units to provide transportation services similar to physically coupled trains. Based on this flexible coupling method, the number of train units can be quickly and dynamically adjusted, thereby achieving real-time flexible matching between line capacity and passenger flow needs.

[0003] The challenge in implementing virtual train formation operation lies in controlling the trains to maintain the smallest possible tracking distance while meeting safety protection conditions. These safety protection conditions are typically set at an Emergency Braking Intervention (EBI) speed. Once a train exceeds the EBI speed, emergency braking is applied until the train comes to a complete stop to ensure operational safety. In reality, the EBI speed is usually related to multiple variables (e.g., the position, speed, and acceleration of the preceding and following trains) and exhibits high-order, nonlinear characteristics.

[0004] Existing control methods for virtual train formations mainly fall into two categories. One category is feedback control methods, such as negative feedback control and sliding mode control. These methods control train operation based on the error between the current actual tracking distance and the desired tracking distance. Due to a lack of understanding of the train's future operating trends, the control effect is usually delayed. The other category is optimal control methods, primarily model predictive control. These methods use maintaining the desired tracking distance over a future period as the control objective, establishing an optimal control problem and solving it to derive the corresponding control commands. This method can predict the train's future operating trends, but because solving the optimal control problem requires certain computational resources, it usually has certain requirements regarding the problem form; for example, a quadratic programming form of optimal control problem can be solved quickly.

[0005] Therefore, the following problems still need to be solved in realizing virtual grouping small-pitch tracking operation:

[0006] 1) Difficulty in maintaining a small tracking interval: Because EBI velocity calculation is extremely complex and cannot be represented analytically, it is difficult to derive an analytical expression for a tracking interval suitable for the EBI velocity. Furthermore, solving the optimal control problem through numerical iteration (which is a non-quadratic programming form due to the introduction of EBI velocity) to find a tracking interval suitable for the EBI velocity requires significant computational resources, making it difficult to meet the real-time requirements of engineering projects. Therefore, existing research typically employs simplified tracking intervals (e.g., fixed time intervals), inevitably increasing the tracking interval.

[0007] 2) The problem of the following train overspeeding and triggering emergency braking is prone to occur: In a virtual train formation, the following train needs to adjust its own control commands according to the status of the preceding train, so that adjacent train units can maintain a small distance for tracking. However, it usually takes one to two seconds from the output of the train control command to the complete response. If a feedback control method is used to control the virtual train formation, when the following train detects that the preceding train has entered the braking state and then applies the brakes, it will cause the two trains to brake asynchronously, which can easily lead to the problem of overspeeding and triggering emergency braking. Summary of the Invention

[0008] To address the aforementioned problems in the existing technology, this invention provides a virtual train formation tracking control system and method based on Model Predictive Control (MPC).

[0009] To achieve the above objectives, the present invention provides the following solution:

[0010] A virtual train tracking control system based on model predictive control, wherein each train unit in the virtual train includes: an information processing module, a dynamic equation construction module, a trajectory prediction module, a tracking control target calculation module, an optimal problem construction module, and a quadratic programming problem solving module;

[0011] Within the same train unit: the information processing module is connected to both the dynamic equation construction module and the tracking control target calculation module; the dynamic equation construction module is connected to the trajectory prediction module; the trajectory prediction module is connected to the tracking control target calculation module; the tracking control target calculation module is connected to the optimal problem construction module; the optimal problem construction module is connected to the quadratic programming problem solving module; and the quadratic programming problem solving module is connected to the trajectory prediction module.

[0012] In two adjacent train units: the information interaction processing module of the latter train unit is connected to the trajectory prediction module of the former train unit;

[0013] The information processing module of the current train unit is used to acquire the control target; the control target includes the target control command and the running trajectory; when the current train unit is the lead train unit, the running trajectory is the target running curve; when the current train unit is not the lead train unit, the running trajectory is the predicted running trajectory updated by the running trajectory prediction module in the previous train unit.

[0014] The dynamic equation construction module in each train unit is used to construct dynamic equations; the trajectory prediction module in each train unit is used to generate a predicted trajectory based on the dynamic equations; the tracking control target calculation module in each train unit is used to construct an optimal control problem based on the control target, the dynamic equations, and the real-time state of each train unit; the quadratic programming problem solving module is used to solve the optimal control problem to obtain the optimal control command; the trajectory prediction module is used to update the predicted trajectory based on the optimal control command, and to determine the target position and velocity sequence of each train unit based on the updated predicted trajectory; the optimal control problem is a problem with a quadratic programming form.

[0015] Optionally, the dynamic equation is:

[0016] x i，k+1 =Ax i，k +Bu i，k +C;

[0017] In the formula, x i，k Let u be the state of the i-th train unit at time k. i，k For the control command of the i-th train unit at time k, x i，k+1 Let A represent the state of the i-th train unit at time k+1, where A is the first matrix, B is the second matrix, and C is the third matrix. T is the inertial element coefficient, g i τ represents the external applied force, and τ is the sampling interval time.

[0018] Optionally, the predicted trajectory is:

[0019]

[0020] In the formula, X i，k For the predicted running trajectory of the i-th train unit at time k, U i，k Let I be the predictive control command sequence for the i-th train unit at time k, and let I be a unit vector. and All are matrices. T is the transpose, and N is the prediction time domain length.

[0021] Optionally, the trajectory prediction module determines the target position and speed sequence of each train unit based on the updated predicted trajectory, specifically as follows:

[0022] The trajectory prediction module defines a corresponding state extraction matrix Z. s With Z v This is used to extract the target position and velocity values ​​from the predicted sequence;

[0023] The target location is: S i，k =Z s X i，k The speed value is: V i，k =Z v X i，k ;

[0024] In the formula, S i，k Let V be the target position of the i-th train unit at time k. i，k Let Z be the speed of the i-th train unit at time k, and the state extraction matrix be Z. s With X v for:

[0025]

[0026]

[0027] Optionally, the optimal control problem is:

[0028] in,

[0029] In the formula, (·) represents the relationship between function J′ and U. i，k Unrelated constant terms, H represents the terms in the optimization function that are related to U. i，k The matrix coefficients related to the quadratic terms, U i，k transpose, x represents i，k The transpose of G x Indicates with U i，k The first term and The relevant matrix coefficients, G c Indicates with U i，k The coefficients of the linear term-related matrix, G s Indicates with U i，k The first term and Related matrix coefficients, Indicates the sequence of target positions for tracking and control. G represents the target sequence for tracking and controlling velocity. v Indicates with U i，k The first term and Related matrix coefficients.

[0030] Optionally, the optimal sequence of control commands is:

[0031]

[0032] In the formula, This is the sequence of optimal control commands.

[0033] Optionally, the updated predicted trajectory is:

[0034]

[0035] Optionally, it also includes:

[0036] The storage module is used to store the updated predicted trajectory.

[0037] Optionally, the target running curve is generated by an external system or retrieved based on the storage module.

[0038] A virtual train tracking control method based on model predictive control is applied to the aforementioned virtual train tracking control system based on model predictive control; the method includes:

[0039] Construct the dynamic equations of a virtual train formation;

[0040] A predicted trajectory is generated based on the aforementioned dynamic equations;

[0041] The optimal control problem is constructed based on the control objective, the dynamic equations, and the real-time state of each train unit.

[0042] Solving the optimal control problem yields the optimal control command;

[0043] Update the predicted trajectory based on the optimal control command;

[0044] The target position and speed sequence of each train unit in the virtual train formation are determined based on the updated predicted trajectory.

[0045] According to specific embodiments provided by the present invention, the present invention discloses the following technical effects:

[0046] The virtual train tracking control system based on model predictive control provided by this invention uses the predicted trajectory of train units to achieve small-interval tracking of train units under the safety constraints brought by EBI speed in the tracking control target calculation module. This avoids introducing the EBI speed calculation function into the constrained optimal control problem in MPC, saving a lot of computing resources and meeting the real-time requirements of engineering algorithms. Attached Figure Description

[0047] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0048] Figure 1 This is an architecture diagram of the virtual train tracking control system based on model predictive control provided by the present invention.

[0049] Figure 2 This is a schematic diagram of the organization of a virtual train formation provided by the present invention;

[0050] Figure 3 A flowchart of the virtual train tracking control method based on model predictive control provided by the present invention;

[0051] Figure 4 This is a diagram illustrating the virtual train tracking control process under the model predictive control-based virtual train tracking control method provided in this invention.

[0052] Figure 5 This is a diagram illustrating the tracking control process of a virtual train formation under feedback control.

[0053] Figure 6 This is a diagram illustrating the tracking and control process for virtual train formations using a fixed time interval. Detailed Implementation

[0054] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0055] The purpose of this invention is to provide a virtual train tracking control system and method based on model predictive control, which can ensure that small-interval tracking of train units is achieved while meeting safety protection conditions. It can also avoid introducing the EBI speed calculation function into the solution of the constrained optimal control problem, thus saving computing resources and having good real-time performance.

[0056] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0057] This invention provides a virtual train tracking control system based on model predictive control. This system establishes virtual train tracking control as a constrained optimal control problem with a quadratic programming form. The control objective is set based on the predicted information of all train units and the EBI speed calculation function. To achieve this objective, a virtual train is configured to consist of multiple train units, as shown below. Figure 2 As shown, the first train at the front is called the lead train unit, and the rest are called follower train units. Among adjacent train units, the one at the front is called the lead car, and the one at the back is called the follower car.

[0058] Based on this, such as Figure 1 As shown, the virtual train tracking control system based on model predictive control provided by this invention consists of an information interaction processing module, a train dynamics equation construction module, a trajectory prediction module, a tracking control target calculation module, an optimal control problem construction module, and a quadratic programming problem solving module, all located on each train unit. Within the same train unit: the information processing module is connected to both the dynamics equation construction module and the tracking control target calculation module. The dynamics equation construction module is connected to the trajectory prediction module. The trajectory prediction module is connected to the tracking control target calculation module. The tracking control target calculation module is connected to the optimal control problem construction module. The optimal control problem construction module is connected to the quadratic programming problem solving module. The quadratic programming problem solving module is connected to the trajectory prediction module. In two adjacent train units: the information interaction processing module of the latter train unit is connected to the trajectory prediction module of the former train unit.

[0059] The functions of each module in the system are as follows:

[0060] The information interaction processing module is responsible for handling information interaction between the current train unit and external systems (e.g., the curve planning module) and other train units. For example, the information interaction processing module on the lead train unit receives control objectives (e.g., recommended driving curves or target speeds) from the external curve planning module and sends the predicted trajectory to other train units. The information interaction processing module on the following train unit receives the predicted trajectory from the train ahead of it and sends its own predicted trajectory to the train following it.

[0061] The dynamic equation construction module constructs the dynamic equations of each train unit in the virtual train formation based on the train's traction / braking characteristics, track gradient and curvature, and basic resistance.

[0062] The trajectory prediction module performs matrix operations based on the train dynamics equations to form a function. Its inputs are the train unit's current position, speed, control acceleration state, and a sequence of control commands for a future period. The output is the train's trajectory for that future period, including position, speed, and control acceleration. Here, control acceleration represents the acceleration value caused by the train's traction / braking forces.

[0063] The tracking and control target calculation module calculates the sequence of control targets for this train unit, including target position and speed, based on the predicted operating trajectories of this train unit and other train units.

[0064] The optimal control problem construction module establishes the virtual train tracking control problem as an optimal control problem with a quadratic programming form based on the control objective, train dynamics equations, and real-time train status.

[0065] The quadratic programming problem solving module is responsible for solving the optimal control problem with quadratic programming form, obtaining the optimal control command sequence for a future period of time (where the first value is used as the control command at the current moment), and then outputting the optimal control command sequence to the trajectory prediction module to update the predicted trajectory.

[0066] Furthermore, this invention also provides a virtual train formation tracking control method based on model predictive control, such as... Figure 3 As shown, the method includes:

[0067] Step 1: Establish the third-order train dynamics equations based on the track gradient, curvature (i.e., curvature), and train traction / braking characteristics. Specifically:

[0068] Step 1.1: Calculate the external resistance experienced by the train based on the track gradient, curvature, etc. at the train's location.

[0069] Step 1.2: Based on the train's traction / braking characteristics and external resistance, establish the train's third-order dynamic equations to describe the changing state of the train system. The selected system state variables include train position, speed, and control acceleration.

[0070] Step 2: Establish the train trajectory prediction function, specifically:

[0071] A train trajectory prediction function is established based on matrix operations performed on the train dynamics equations. The inputs of this function are the train's current position, speed, control acceleration status, and the sequence of control commands for a future period. The output is the train's trajectory for a future period, including its position, speed, and control acceleration.

[0072] Step 3: Based on the predicted trajectories of this train unit and other train units, calculate the target position and velocity sequence in the predicted time domain. Specifically:

[0073] Step 3.1: Based on the predicted running trajectories of other train units received and the predicted running trajectory generated by the optimal control command sequence of the previous moment of this train unit, calculate the target speed sequence for all moments in the prediction time domain except the last moment.

[0074] Step 3.2: Set the target velocity at the last moment in the prediction time domain to be equal to the target velocity at the second-to-last moment.

[0075] Step 3.3: Calculate the target position sequence in the predicted time domain using the target speed sequence and the train's current actual position.

[0076] Step 4: Based on the final control objective of the virtual train formation, establish an optimal control problem with a quadratic programming form, specifically:

[0077] Step 4.1: Calculate the weight coefficient matrix required to establish the objective function in the optimal control problem.

[0078] Step 4.2: Calculate the matrix required to establish the constraints in the optimal control problem.

[0079] Step 4.3: Combine the virtual train formation tracking and control objective to establish an optimal control problem in the form of quadratic programming.

[0080] Step 5: Solve the optimal control problem to obtain the optimal control command sequence.

[0081] Step 6: Obtain the predicted trajectory of the train based on the optimal control command sequence. That is, input the optimal control command sequence and the train's current real-time status into the train trajectory prediction function, and output the predicted train trajectory.

[0082] Based on this, the system and method provided by the present invention have the following advantages compared with the prior art:

[0083] 1) It can ensure that the virtual train formation maintains the smallest possible tracking distance while meeting safety protection conditions.

[0084] 2) Saves computational resources: This invention uses the predicted trajectory of the train unit and processes the safety constraints brought by the EBI speed in the tracking control target calculation module. This avoids introducing the EBI speed calculation function into the constrained optimal control problem in MPC, saving a lot of computational resources and meeting the real-time requirements of engineering algorithms.

[0085] The following is an example Figure 1The specific implementation process of the above-mentioned solution provided by the present invention will be described using a virtual train consisting of two train units (train unit 1 and train unit 2) as an example.

[0086] (1) Modeling the train dynamics. Based on Newton's equations of motion, the system state equations for the train's position, velocity, and control acceleration can be written as follows:

[0087]

[0088] In the formula, s i v i f i These represent the position, speed, and control acceleration of train unit i (i = 1, 2 represent the front and rear trains, respectively), and and Then they are the derivatives of their respective variables, g i This represents the external additional force consisting of track gradient, curvature, and basic resistance, u. i This represents a control command, whose physical meaning is the desired output control acceleration value, and T is the inertial element coefficient.

[0089] The above dynamic equations can be converted into matrix form as follows:

[0090]

[0091] In the formula, x i =[s i v i f i ] T The superscript T indicates transpose. Represents state x i The derivative of matrix A c B c With C c Write them separately as:

[0092]

[0093] Since train position and speed information in practice is usually sampled in a time-discrete manner, the final discrete dynamics equation for the train can be derived as follows:

[0094] x i，k+1 =Ax i，k +Bu i，k +C.

[0095] In the formula, the subscript k represents the discrete sampling time. τ represents the sampling interval time. The three matrices A, B and C are matrices required to construct the system state-space equations, denoted as the first matrix, the second matrix and the third matrix.

[0096] (2) Establish a train trajectory prediction function. The input to this function is the current train state x. i，k With control command sequence U i，k The output is the predicted trajectory X. i，k This function is implemented by calculating the following equation.

[0097]

[0098] The predicted trajectory is defined as follows: x i，j|k The variable s represents the state at time k+j predicted from time k. i，j|k v i，j|k f i，j|k These represent the predicted position, velocity, and control acceleration, respectively, with N representing the prediction time domain length. The corresponding predictive control command sequence is defined as: U i，k =[u i，0|k u i，1|k , ..., u i，N-1|k ] T ,for u i，j|k Let represent the control input at time k+j predicted at time k, and I represent a unit vector with appropriate dimensions. These are all matrices required for prediction, and are structured as follows:

[0099]

[0100]

[0101]

[0102] Additionally, a corresponding state extraction matrix Z can be defined. s With Z v The following equations are implemented to extract the position and velocity values ​​from the predicted sequence:

[0103] S i，k =Z s X i，k .

[0104] V i，k =Z v X i，k .

[0105] Among them, S i，k =[s i，1|k si，2|k , ..., s i，N|k ] T V i，k =[v i，1|k v i，2|k , ..., v i，N|k ] T State extraction matrix Z s With Z v It can be defined as:

[0106]

[0107]

[0108] (3) Calculate the target sequence for tracking control of the virtual train formation. The target sequence for tracking control position is defined as follows: The target position at time k+j, calculated at time k, and the target sequence for tracking and control velocity are defined as follows: This represents the target velocity at time k+j calculated at time k. The specific calculation method is as follows:

[0109] If this train is the lead train (i=1), then the target position and speed are assumed to be calculated based on the pre-planned recommended driving curve.

[0110] If this train is a following train (i=2), then the maximum operating speed calculation function needs to be used in the calculation of the train tracking control target sequence. When the train tracks with the maximum operating speed as the target, considering the control error that occurs under actual control, the train can always maintain a speed below the EBI speed. In existing train control methods, a very common way to calculate the maximum operating speed is to subtract a control margin value from the EBI speed. The maximum operating speed function used in this embodiment can be defined based on this idea, expressed as: The input variables include the states of the vehicles in front and behind, represented by x1 and x2 respectively.

[0111] Furthermore, the position and target speed of the train tracking and control target sequence at each moment are calculated as follows:

[0112] Initialize j = 0, as well as

[0113] judge Is it true? If it is true, then... If not, then

[0114] If j < N, j = j + 1, return to step (2). Otherwise, Proceed to step (4).

[0115]

[0116] By utilizing the predicted future trajectories of each other's train units, the calculated control target sequence can identify the decreasing trend of EBI speed in advance, thus preventing the following train from triggering emergency braking due to speeding.

[0117] (4) Based on the previously calculated control objective sequence, establish the optimal control problem for virtual train formation tracking control. This problem mainly consists of two parts: the optimization objective function and the constraints.

[0118] The train control objective is to minimize the difference between the predicted train trajectory's position and speed in the predicted time domain and the target position and speed sequence. Therefore, the optimization objective function can be designed as follows:

[0119]

[0120] Where, q s q v q u These are the weighted penalty coefficients for position, velocity, and control commands, respectively. The optimization function J above is transformed into a sequence of control commands U. i，k The relevant standard quadratic form is:

[0121]

[0122] Where (·) represents the relationship between function J and U i，k The correlation matrices for the uncorrelated constant terms are defined as follows:

[0123]

[0124]

[0125]

[0126]

[0127]

[0128] Q s =diag(q) s ,0,0,q s ,0,0,...,q s ,0,0).

[0129] Q v =diag(0, q)v ,0,0,q v ,0,...,0,q v ,0).

[0130] Q u =diag(q) u q u , ..., q u ).

[0131] Where H represents the relationship between the optimization function and the decision variable U i，k The matrix coefficients related to the quadratic terms, G x This indicates that the optimization function relates to the decision variable U. i，k Linear terms and known terms The relevant matrix coefficients, G c This indicates that the optimization function relates to the decision variable U. i，k The coefficients of the linear term-related matrix, G s This indicates that the optimization function relates to the decision variable U. i，k Linear terms and known terms The relevant matrix coefficients, G v This indicates that the optimization function relates to the decision variable U. i，k Linear terms and known terms The relevant matrix coefficients, Q s Q v And Q u These represent the optimization weighting coefficients for tracking errors of position and velocity targets, and the size of the control input, respectively. `diag()` represents a diagonal matrix composed of its input parameters, for example...

[0132]

[0133] Where a, b, and c are scalars.

[0134] The above design enables the following equation to hold:

[0135]

[0136] The constraints involved in the optimal control problem include the maximum value constraint of train control commands and the impulse rate constraint, which can be expressed as follows:

[0137]

[0138]

[0139] Where u i，-1|k =u i，0|k-1 The two constraints above can be written in matrix form FU. i，k≤W, the required matrices F and W can be easily constructed based on the above constraints.

[0140] Finally, in step (4), the virtual train formation tracking and control problem is established as follows:

[0141] Satisfying constraint FU i，k If W ≤ W, the problem has the standard form of a quadratic programming problem.

[0142] (5) Using algorithms for solving quadratic programming problems (such as the interior-point method) to solve the virtual train formation tracking control problem can yield the corresponding optimal control command sequence, which is...

[0143] (6) The optimal control command sequence Substituting these values ​​into the train trajectory prediction function, we can obtain the predicted train trajectory over a future period of time, as follows:

[0144] The trajectory is cached locally for use in calculating the control target sequence of this vehicle in the next cycle. Simultaneously, the trajectory is sent to the following vehicle for its own use in calculating the control target sequence.

[0145] Figure 4 The paper presents the virtual train tracking control process using the system and method of this invention. It can be seen that a stable margin is maintained between the speed of the following train and the EBI speed. This margin can be adjusted according to the actual control effect; the smaller the margin, the smaller the tracking distance between the preceding and following trains. Figure 4 The results show that the maximum tracking distance between the two vehicles was 37.1 meters.

[0146] Figure 5 The paper presents the tracking control process of a virtual train formation controlled by a feedback control method, where the control objective is to track the maximum operating speed at the current moment. Because the following train failed to apply brakes in time to maintain the same braking trend as the preceding train, it triggered emergency braking at 61 seconds due to speeding.

[0147] Figure 6 The paper presents the tracking and control process for virtual train formations using a fixed time interval, where the fixed time interval is designed to be 2.5V. 2,k +5 (meters). It can be seen that the maximum tracking distance between stations is 53.9 meters. However, when using this tracking distance target, the following vehicle's actual speed during braking is already very close to the EBI speed. This also means that further reducing the fixed time interval will trigger emergency braking.

[0148] The above experimental results demonstrate some of the benefits of this invention, including:

[0149] 1) Control the train to meet safety protection conditions and avoid triggering emergency braking.

[0150] 2) Reduce the tracking distance between virtual train units based on safety protection conditions.

[0151] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.

[0152] This document uses specific examples to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of the present invention. Furthermore, those skilled in the art will recognize that, based on the ideas of the present invention, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A virtual train formation tracking control system based on model predictive control, characterized in that, Each train unit in the virtual train formation includes: an information processing module, a dynamic equation construction module, a trajectory prediction module, a tracking and control target calculation module, an optimal problem construction module, and a quadratic programming problem solving module; Within the same train unit: the information processing module is connected to both the dynamic equation construction module and the tracking control target calculation module; the dynamic equation construction module is connected to the trajectory prediction module; the trajectory prediction module is connected to the tracking control target calculation module; the tracking control target calculation module is connected to the optimal problem construction module; the optimal problem construction module is connected to the quadratic programming problem solving module; and the quadratic programming problem solving module is connected to the trajectory prediction module. In two adjacent train units: the information processing module of the latter train unit is connected to the trajectory prediction module in the former train unit; The information processing module of the current train unit is used to acquire the control target; the control target includes the target control command and the running trajectory; when the current train unit is the lead train unit, the running trajectory is the target running curve; when the current train unit is not the lead train unit, the running trajectory is the predicted running trajectory updated by the running trajectory prediction module in the previous train unit. Each train unit's dynamic equation construction module is used to construct dynamic equations; each train unit's trajectory prediction module is used to generate a predicted trajectory based on the dynamic equations; each train unit's tracking control target calculation module is used to construct an optimal control problem based on the control target, the dynamic equations, and the real-time state of each train unit; the quadratic programming problem solving module is used to solve the optimal control problem to obtain the optimal control command; the trajectory prediction module is used to update the predicted trajectory based on the optimal control command, and to determine the target position and velocity sequence of each train unit based on the updated predicted trajectory; the optimal control problem is a problem with a quadratic programming form. The trajectory prediction module determines the target position and speed sequence of each train unit based on the updated predicted trajectory, specifically as follows: The trajectory prediction module defines a corresponding state extraction matrix. and This is used to extract the target position and velocity values ​​from the predicted sequence; The target location is: The speed value is: ; In the formula, For the first i Each train unit k The target location at any given time For the first i Each train unit k The speed of time For the first i Each train unit k Predicted trajectory at any given moment N To predict the time-domain length state, extract the matrix. and for: 。 2. The virtual train tracking control system based on model predictive control according to claim 1, characterized in that, The dynamic equation is: ； In the formula, For the first i Each train unit k The state at any given moment, For the first i Each train unit k Time control commands, For the first i The state of each train unit at time k+1 A For the first matrix, B For the second matrix, C Let be the third matrix, where, , , , , , , The coefficient of inertial element, For external additional force, This is the sampling interval.

3. The virtual train tracking control system based on model predictive control according to claim 2, characterized in that, The predicted trajectory is as follows: ； In the formula, For the first i Each train unit k The sequence of predictive control commands at each time step. I It is a unit vector. , and All are matrices. , , , This is a transpose.

4. The virtual train tracking control system based on model predictive control according to claim 3, characterized in that, The optimal control problem is: ; in, ; In the formula, Representation function Zhongyu Unrelated constant terms In the optimization function, the terms "and" are used to represent the terms "and". The matrix coefficients related to the quadratic terms, express transpose, express transpose, Indicates and The first term and Related matrix coefficients, Indicates and The coefficients of the matrix related to the first-order terms, Indicates and The first term and Related matrix coefficients, Indicates the sequence of target positions for tracking and control. This indicates the target sequence for tracking and controlling speed. Indicates and The first term and Related matrix coefficients.

5. The virtual train tracking control system based on model predictive control according to claim 4, characterized in that, The optimal control command sequence is as follows: ； In the formula, This is the sequence of optimal control commands.

6. The virtual train tracking control system based on model predictive control according to claim 5, characterized in that, The updated predicted trajectory is as follows: 。 7. The virtual train tracking control system based on model predictive control according to claim 1, characterized in that, Also includes: The storage module is used to store the updated predicted trajectory.

8. The virtual train tracking control system based on model predictive control according to claim 7, characterized in that, The target operating curve is generated by an external system or retrieved based on the storage module.

9. A virtual train formation tracking control method based on model predictive control, characterized in that, The method is applied to the virtual train tracking control system based on model predictive control as described in any one of claims 1-8; the method includes: Construct the dynamic equations of a virtual train formation; A predicted trajectory is generated based on the aforementioned dynamic equations; The optimal control problem is constructed based on the control objective, the dynamic equations, and the real-time state of each train unit. Solving the optimal control problem yields the optimal control command; Update the predicted trajectory based on the optimal control command; The target position and speed sequence of each train unit in the virtual train formation are determined based on the updated predicted trajectory.

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