Cooperative tracking control method and system for heavy-load trains based on coupling and buffer uncertainty

Abstract

The present application discloses a method and system for cooperative tracking control of heavy-loaded trains based on coupling and buffer uncertainty, and relates to the field of cooperative control and safe driving of heavy-loaded trains. The method comprises establishing a multi-particle dynamic model of heavy-loaded trains; establishing a system equation of heavy-loaded trains with an actuator fault model; establishing a system dynamic error model; converting the system dynamic error model into a system state space equation; obtaining an error transformation state space equation based on the error variable after filtering transformation; obtaining sufficient conditions for the stability of heavy-loaded trains based on the error transformation state space equation by using the cyclic small gain theorem and linear matrix inequality; constructing a distributed adaptive cooperative controller of heavy-loaded trains to ensure the safety of each heavy-loaded train, and realizing asymptotic tracking of the locomotive to its own desired speed and displacement curve based on the minimum safety distance, and consistent tracking of the truck to its own desired speed and displacement curve; the present application realizes cooperative tracking control of the speed and displacement of heavy-loaded trains.

Description

Technical Field

[0001] The present application relates to the field of cooperative control and safe driving of heavy-loaded trains, and in particular to a method and system for cooperative tracking control of heavy-loaded trains based on coupling and buffer uncertainty. Background Art

[0002] The heavy-haul railway system has become the main mode of transportation for mineral resources in countries around the world with its excellent transportation capacity, significant cost advantages and safety. With the growth of freight volume, communication-based train control systems (moving block and virtual coupling technology) are used to promote automatic train driving, thereby improving train operation efficiency. However, the above technology is mainly based on the coordinated control of multiple vehicles with a single particle, ignoring the characteristics of strong internal coupling and large longitudinal impulse of heavy-haul trains, which makes safety accidents very easy to occur.

[0003] A heavy-load train is composed of multiple locomotives and freight cars. The coupler-buffer system is an important component that connects the cars and plays a role in buffering and transmitting the longitudinal force of the train. The coupler-buffer system can be simplified as a spring and damping system. The magnitude of the internal force of the train is determined by the displacement error and the speed error. During the operation of a heavy-load train, the coupling force between adjacent cars is crucial to the safety and stability of the train. Due to the influence of factors such as long-term operation, high-load transportation and steep slopes of heavy-load trains, the coupler-buffer system and actuators inevitably experience wear and aging, resulting in coupler-buffer uncertainty. Therefore, it is of great practical value to study the problem of cooperative tracking control of heavy-load trains with coupler-buffer uncertainty.

[0004] At present, neural networks and fuzzy control have been used to study the influence of internal forces on heavy-load trains, but there are few studies on the uncertainty of coupling. Most of them only consider the stability of locomotives, and less consideration is given to the stability of freight cars. In addition, the operating conditions of heavy-load trains are complex, and they are affected by actuator failures, unknown air resistance, and external interference, making it difficult for the system to stabilize and obtain satisfactory performance.

[0005] Therefore, there is an urgent need to provide a distributed adaptive collaborative control strategy to achieve the asymptotic tracking of the locomotive's desired speed and displacement curve and the consistent tracking of the freight car's desired speed and displacement curve based on the minimum safety distance between heavy-loaded trains. This is very necessary for this field. Summary of the invention

[0006] The purpose of this application is to provide a method and system for coordinated tracking control of heavy-load trains based on coupling uncertainty, which can achieve coordinated tracking control of the speed and displacement of heavy-load trains.

[0007] To achieve the above objectives, this application provides the following solutions:

[0008] In a first aspect, the present application provides a heavy-load train collaborative tracking control method based on coupling-buffer uncertainty, the heavy-load train collaborative tracking control method based on coupling-buffer uncertainty comprising:

[0009] The coupling-buffer system is equivalent to a spring-damper system, and a multi-mass point dynamic model of the heavy-load train is established based on the coupling force between the carriages of the heavy-load train and the train internal force equation of the coupling-buffer uncertainty obtained from the spring-damper system.

[0010] Obtaining an actuator fault model, and establishing a heavy-load train system equation with the actuator fault model based on the actuator fault model and a multi-mass point dynamic model of the heavy-load train;

[0011] According to the heavy-load train system equation with actuator fault model and error variables, a system dynamic error model is established; and the system dynamic error model is converted into a system state space equation; the error variables include: displacement tracking error variables and speed tracking error variables;

[0012] According to the error variable after filtering transformation, the error transformation state space equation is obtained;

[0013] According to the error transformation state space equation, the cyclic small gain theorem and linear matrix inequality are used to obtain the sufficient conditions for the stability of heavy-load trains.

[0014] Based on the error transformation state space equation and the sufficient conditions for the stability of heavy-haul trains, a distributed adaptive cooperative controller for heavy-haul trains is constructed.

[0015] A distributed adaptive cooperative controller is used to control each heavy-load train to asymptotically track the locomotive's desired speed and locomotive displacement curve and consistently track the freight car's desired speed and freight car displacement curve based on the minimum safety distance between trains.

[0016] Optionally, the coupling-buffer system is equivalent to a spring-damper system, and a multi-mass point dynamic model of the heavy-load train is established according to the coupling force between carriages of the heavy-load train and the coupling-buffer uncertainty obtained according to the spring-damper system, specifically including:

[0017] Using the formula Determine the train internal force equations ;

[0018] Using the formula

[0019]

[0020] Establish a multi-mass point dynamic model of heavy-load train;

[0021] in, It is i Heavy haul train j The quality of the carriage, and Represents the i Heavy-load train j The displacement and speed of the carriages, is the sum of the carriage length and the coupler length, Indicates whether there is a power unit. , indicating a locomotive, When it means a truck, It is i Heavy-load train j The output signal of the carriage; the output signal is traction or braking force, , is the elastic coupling coefficient and uncertainty, , is the damping coupling coefficient and uncertainty, Indicates i Heavy-load train j The additional resistance on the carriage is represents the external disturbance to the jth carriage of the i-th heavy-load train, , , is the Davis coefficient, Represents mechanical resistance, represents air resistance, N is the total number of heavy-load trains, n is the total number of carriages, For the i Heavy haul train j The net force on the carriage is For the i Heavy-load train j The speed of the carriage, For the i Heavy-load train j The acceleration of the carriage.

[0022] Optionally, the acquiring of the actuator fault model and establishing a heavy-load train system equation with the actuator fault model according to the actuator fault model and a multi-particle dynamic model of the heavy-load train specifically includes:

[0023] Using the formula Determine actuator failure model;

[0024] Using the formula Determine the system equations for a heavy-haul train with an actuator failure model;

[0025] in, represents the output signal of the jth actuator failure mode of the i-th heavy-load train, is the efficiency factor of the jth actuator failure mode of the i-th heavy-load train, represents the input signal of the jth actuator of the i-th heavy-load train, Indicates the jth actuator offset fault of the i-th heavy-load train, For composite interference, , , , is the Davis coefficient, Represents mechanical resistance, Represents air resistance, parameter ,parameter ,parameter .

[0026] Optionally, a system dynamic error model is established based on the heavy-load train system equation with the actuator failure model and the error variables, specifically including:

[0027] Using the formula Determine the displacement tracking error variable; where, is the displacement tracking error variable, is the displacement of the jth carriage of the i-th heavy-load train, is the expected displacement, is the displacement of the rear carriage of the i-1th heavy-load train, is the expected safety distance between heavy-load trains, parameter ,parameter ;

[0028] Using the formula Determine the velocity tracking error variable; where, is the speed tracking error variable, is the speed of the jth carriage of the i-th heavy-load train, is the expected displacement, is the speed of the tail car of the i-1th heavy-load train;

[0029] Using the formula Establish the system dynamic error model.

[0030] Optionally, the system dynamic error model is converted into a system state space equation, specifically including:

[0031] Using the formula Determine the system state space equations;

[0032] in, and is the system state matrix, is the system output matrix, is the composite interference matrix, is the hook uncertainty matrix, is the reference velocity matrix.

[0033] Optionally, obtaining the error transformation state space equation according to the error variable after filtering transformation specifically includes:

[0034] Using the formula Determine the error variable after filtering transformation;

[0035] Using the formula Determine the error transformation state space equation;

[0036] in, is the transformation coefficient, and the error variable after filtering transformation is used for locomotive. , indicating that the truck does not need to be transformed, is the displacement tracking error variable after filtering transformation, is the velocity tracking error variable after filtering transformation, parameter , and Represent the locomotive set and the freight car set respectively, and the parameters ,parameter ,parameter ,parameter ,parameter ,parameter ,parameter ,parameter ,variable , and Represent the locomotive set and the freight car set respectively, and the parameters ,parameter ,parameter ,parameter ,parameter ,parameter ,parameter ,parameter , To find the derivative of the locomotive variable after filtering transformation, Derivative of the truck variable after filtering transformation, is a zero matrix with one row and eight columns. is the hook uncertainty coefficient matrix, parameter ,parameter ,parameter ,parameter , is the reference acceleration, is the acceleration of the nth car of the i-1th train.

[0037] Optionally, the sufficient conditions for the stability of the heavy-load train are obtained by using the cyclic small gain theorem and the linear matrix inequality according to the error transformation state space equation, which specifically include:

[0038] Using the formula <0 is a sufficient condition for determining the stability of heavy-load trains;

[0039] Among them, the parameters ,parameter ,parameter , a positive definite symmetric matrix , the superscript T indicates transposition, the parameter , , is the symmetric part of the corresponding position in the symmetric matrix, is the square of the upper bound of the uncertainty coefficient, For a parameter greater than 0, is the interconnection positive coefficient, parameter , is a diagonal matrix, is the intrinsic parameter of the hook buffer uncertainty coefficient matrix, is a positive definite symmetric matrix The inverse, For the matrix The inverse, is the system robust positive coefficient, parameter .

[0040] Optionally, constructing a distributed adaptive cooperative controller for a heavy-haul train according to the error transformation state space equation and sufficient conditions for the stability of the heavy-haul train specifically includes:

[0041] Using the formula Building a distributed adaptive collaborative controller for heavy-haul trains;

[0042] in, To eliminate offset faults and compound disturbances, , To eliminate or , , To enhance the system robustness, , for The estimated value of , is the unknown adaptive coefficient, is the basis of the error-transformed variables, , , , and is a constant greater than zero, is any positive uniformly continuous bounded smooth function.

[0043] In a second aspect, the present application provides a heavy-load train cooperative tracking control system based on coupling and buffer uncertainty, and the heavy-load train cooperative tracking control system based on coupling and buffer uncertainty includes:

[0044] The multi-mass point dynamic model building module is used to equate the coupler-buffer system to a spring-damper system, and to build a multi-mass point dynamic model of a heavy-load train based on the coupling force between carriages of the heavy-load train and the train internal force equation of the coupler-buffer uncertainty obtained from the spring-damper system;

[0045] A heavy-load train system equation building module is used to obtain an actuator fault model and build a heavy-load train system equation with an actuator fault model based on the actuator fault model and a multi-mass point dynamic model of the heavy-load train;

[0046] The system state space equation establishment module is used to establish a system dynamic error model according to the heavy-load train system equation with the actuator fault model and the error variables; and convert the system dynamic error model into the system state space equation; the error variables include: displacement tracking error variables and speed tracking error variables;

[0047] An error transformation state space equation building module is used to obtain an error transformation state space equation according to the error variable after filtering transformation;

[0048] A sufficient condition determination module is used to obtain sufficient conditions for the stability of heavy-load trains based on the error transformation state space equation, using the cyclic small gain theorem and linear matrix inequality;

[0049] A distributed adaptive cooperative controller building module is used to build a distributed adaptive cooperative controller for heavy-haul trains based on error transformation state space equations and sufficient conditions for heavy-haul train stability;

[0050] The cooperative control module is used to control each heavy-load train to perform asymptotic tracking of the locomotive desired speed and locomotive displacement curve and consistent tracking of the freight car desired speed and freight car displacement curve based on the minimum safety distance between trains by using a distributed adaptive cooperative controller.

[0051] According to the specific embodiments provided in this application, this application has the following technical effects:

[0052] The present application provides a method and system for cooperative tracking control of heavy-loaded trains based on coupling and buffer uncertainty. First, the coupling force between carriages of heavy-loaded trains and the coupling and buffer uncertainty are considered, and a multi-particle dynamic model of heavy-loaded trains with unknown air resistance, additional resistance and external interference is established; then, the actuator fault model is combined to obtain the system equation of heavy-loaded trains with the actuator fault model; according to the system tracking control target, the error variable is introduced to obtain the system dynamic error model, and it is converted into the system state space equation; inspired by the sliding surface and filter transformation, the error transformation state space equation is obtained; the cyclic small gain theorem and linear matrix inequality are introduced to solve the coupling and buffer uncertainty and the stability of the freight car, and a low-complexity distributed adaptive cooperative control protocol for heavy-loaded trains is designed to ensure the safety of each heavy-loaded train, and based on the minimum safety distance, the locomotive realizes the asymptotic tracking of its own expected speed and displacement curve, and the freight car realizes the consistent tracking of its own expected speed and displacement curve. The present application adopts a distributed adaptive cooperative controller to adaptively adjust the control parameters in real time to cope with the dynamic changes of the system, so as to realize the cooperative tracking control of the speed and displacement of the heavy-loaded train. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0054] Figure 1 This is a flow chart of a heavy-load train cooperative tracking control method based on coupling and buffer uncertainty in one embodiment of the present application;

[0055] Figure 2 A train internal force structure block diagram in a heavy-load train cooperative tracking control method based on coupling and buffer uncertainty provided in an embodiment of the present application;

[0056] Figure 3 A schematic diagram of a multi-particle model of a heavy-load train in a heavy-load train cooperative tracking control method based on coupling and buffer uncertainty provided in an embodiment of the present application;

[0057] Figure 4 A partial parameter diagram of an experimental line in a heavy-load train cooperative tracking control method based on coupling and buffer uncertainty provided in an embodiment of the present application;

[0058] Figure 5 A speed and displacement curve diagram of an experimental line in a heavy-load train cooperative tracking control method based on coupling and buffer uncertainty provided in an embodiment of the present application;

[0059] Figure 6A multi-vehicle tracking displacement curve diagram in a heavy-load train cooperative tracking control method based on coupling buffer uncertainty provided in an embodiment of the present application;

[0060] Figure 7 A multi-vehicle tracking speed curve diagram in a heavy-load train cooperative tracking control method based on coupling buffer uncertainty provided in an embodiment of the present application;

[0061] Figure 8 An adaptive parameter diagram in a heavy-load train cooperative tracking control method based on coupling and buffer uncertainty provided in an embodiment of the present application;

[0062] Fig. 9 A multi-vehicle tracking displacement error curve diagram in a heavy-load train cooperative tracking control method based on coupling buffer uncertainty provided in an embodiment of the present application;

[0063] Fig.10 A multi-vehicle tracking speed error curve diagram in a heavy-load train cooperative tracking control method based on coupling buffer uncertainty provided in an embodiment of the present application;

[0064] Fig.11 A first train coupler force curve diagram in a heavy-load train cooperative tracking control method based on coupler buffer uncertainty provided in an embodiment of the present application;

[0065] Fig.12 A graph of actual control input in a heavy-load train cooperative tracking control method based on coupling and buffer uncertainty provided in an embodiment of the present application;

[0066] Fig.13 A graph of displacement error of multiple vehicles tracking based on a neural network for a comparison algorithm provided in one embodiment of the present application;

[0067] Fig.14 A multi-vehicle tracking speed error curve diagram based on a neural network for a comparison algorithm provided in an embodiment of the present application;

[0068] Fig.15 A first train coupler force curve diagram based on a neural network for a comparison algorithm provided in an embodiment of the present application;

[0069] Fig.16 The comparison algorithm provided in one embodiment of the present application is based on an actual control input curve diagram of a neural network. DETAILED DESCRIPTION

[0070] The following will be combined with the drawings in the embodiments of the present application to clearly and completely describe the technical solutions in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of this application.

[0071] In order to make the above-mentioned objects, features and advantages of the present application more obvious and easy to understand, the present application is further described in detail below with reference to the accompanying drawings and specific implementation methods.

[0072] In an exemplary embodiment, Figure 1 As shown, a heavy-load train cooperative tracking control method based on coupling and buffer uncertainty is provided, and the method includes the following S101 to S107. Among them:

[0073] S101, the coupling and damping system is equivalent to a spring-damper system, and a multi-mass point dynamic model of the heavy-load train is established according to the coupling force between the heavy-load train carriages and the train internal force equation of the coupling and damping uncertainty obtained from the spring-damper system; the obtained multi-mass point dynamic model takes into account the unknown air resistance, additional resistance and external interference;

[0074] First, select a car in a heavy-load train and Figure 2 , the hook-buffer system is approximated to obtain a spring-damper system, considering its uncertainty, Figure 2 middle To reduce the original length of the hook, is the elastic deformation length of the hook, using the formula Determine the train internal force equations ;

[0075] Subsequently, through Figure 3 The force analysis of

[0076] Establish a multi-mass point dynamic model of heavy-load train;

[0077] in, It is i Heavy haul train j The quality of the carriage, and Represents the i Heavy-load train j The displacement and speed of the carriages, is the sum of the carriage length and the coupler length, Indicates whether there is a power unit. , indicating a locomotive, When it means a truck, It isi Heavy-load train j The output signal of the carriage is traction or braking force. , is the elastic coupling coefficient and uncertainty, , is the damping coupling coefficient and uncertainty, Indicates i Heavy-load train j The additional resistance on the carriage is represents the external disturbance to the jth carriage of the i-th heavy-load train, , , is the Davis coefficient, Represents mechanical resistance, represents air resistance, N is the total number of heavy-load trains, n is the total number of carriages, For the i Heavy haul train j The net force on the carriage is For the i Heavy-load train j The speed of the carriage, For the i Heavy-load train j The acceleration of the carriage. , is the Davis coefficient, It represents the mechanical resistance per unit mass, N is the total number of heavy-load trains, and n is the total number of carriages.

[0078] S102, obtaining an actuator fault model, and establishing a heavy-load train system equation with the actuator fault model according to the actuator fault model and a multi-mass point dynamic model of the heavy-load train;

[0079] S102 specifically includes:

[0080] Using the formula Determine actuator failure model;

[0081] Using the formula Determine the system equations for a heavy-haul train with an actuator failure model;

[0082] in, represents the output signal of the jth actuator failure mode of the i-th heavy-load train, is the efficiency factor of the jth actuator failure mode of the i-th heavy-load train, represents the input signal of the jth actuator of the i-th heavy-load train, Indicates the jth actuator offset fault of the i-th heavy-load train. hour, , indicating that the actuator has not failed or has partially failed; when hour, or , which respectively represent that the actuator has an interruption fault and an offset fault. For composite interference, , , , is the Davis coefficient, Represents mechanical resistance, Represents air resistance, parameter ,parameter ,parameter .

[0083] S103, in order to achieve the control target, a system dynamic error model is established according to the heavy-load train system equation with the actuator fault model and the error variables; and the system dynamic error model is converted into a system state space equation; the error variables include: a displacement tracking error variable and a speed tracking error variable;

[0084] S103 specifically includes:

[0085] Using the formula Determine the displacement tracking error variable; where, is the displacement tracking error variable, is the displacement of the jth carriage of the i-th heavy-load train, is the expected displacement, is the displacement of the rear carriage of the i-1th heavy-load train, is the expected safety distance between heavy-load trains, parameter ,parameter ;

[0086] Using the formula Determine the velocity tracking error variable; where, is the speed tracking error variable, is the speed of the jth carriage of the i-th heavy-load train, is the expected displacement, is the speed of the tail car of the i-1th heavy-load train;

[0087] Using the formula Establish the system dynamic error model.

[0088] For the system dynamic error model, in order to achieve the control target, the following assumptions need to be met:

[0089] 1) The expected displacement and velocity trajectory norms of the system are bounded;

[0090] 2) Time-varying offset fault is norm-bounded;

[0091] Furthermore, using the formula Determine the system state space equations;

[0092] in, and is the system state matrix, is the system output matrix, is the composite interference matrix, is the hook uncertainty matrix, is the reference velocity matrix.

[0093] in:

[0094] ;

[0095] ;

[0096] ;

[0097] ;

[0098] ;

[0099] ;

[0100] ;

[0101] S104, inspired by the sliding surface and filtering transformation, the error variable is subjected to filtering transformation, and the error transformation state space equation is obtained according to the error variable after filtering transformation;

[0102] S104 specifically includes:

[0103] Using the formula Determine the error variable after filtering transformation;

[0104] Using the formula Determine the error transformation state space equation;

[0105] in, is the transformation coefficient, and the error variable after filtering transformation is used for locomotive. , indicating that the truck does not need to be transformed, is the displacement tracking error variable after filtering transformation, is the velocity tracking error variable after filtering transformation, parameter , and Represent the locomotive set and the freight car set respectively, and the parameters ,parameter ,parameter ,parameter ,parameter ,parameter ,parameter ,parameter , To find the derivative of the locomotive variable after filtering transformation, Derivative of the truck variable after filtering transformation, is a zero matrix with one row and eight columns. is the hook uncertainty coefficient matrix, parameter ,parameter ,parameter ,parameter , is the reference acceleration, is the acceleration of the nth car of the i-1th train.

[0106] S105, in order to ensure the stability of each heavy-load train locomotive and freight car, according to the error transformation state space equation, the cyclic small gain theorem and linear matrix inequality are used to obtain the sufficient conditions for the stability of the heavy-load train;

[0107] S105 specifically includes:

[0108] Using the formula <0 is a sufficient condition for determining the stability of heavy-load trains;

[0109] Among them, the parameters ,parameter ,parameter , a positive definite symmetric matrix , the superscript T indicates transposition, the parameter , , is the symmetric part of the corresponding position in the symmetric matrix, is the square of the upper bound of the uncertainty coefficient, For a parameter greater than 0, is the interconnection positive coefficient, parameter , is a diagonal matrix, is the intrinsic parameter of the hook buffer uncertainty coefficient matrix, is a positive definite symmetric matrix The inverse, For the matrix The inverse, is the system robust positive coefficient, parameter .

[0110] S106, constructing a distributed adaptive cooperative controller of the heavy-haul train according to the error transformation state space equation and the sufficient condition for the stability of the heavy-haul train;

[0111] Using the formula Building a distributed adaptive collaborative controller for heavy-haul trains;

[0112] in, To eliminate offset faults and compound disturbances, , To eliminate or , , To enhance the system robustness, , for The estimated value of , is the unknown adaptive coefficient, is the basis of the error-transformed variables, , , , and is a constant greater than zero, is any positive uniformly continuous bounded smooth function.

[0113] S107, using a distributed adaptive collaborative controller to control each heavy-load train to perform asymptotic tracking of the locomotive desired speed and locomotive displacement curve and consistent tracking of the freight car desired speed and freight car displacement curve based on the minimum safety distance between trains.

[0114] The following is a simulation example to verify the performance of the distributed adaptive cooperative tracking controller proposed in this application. Consider the cooperative tracking control of three heavy-load trains, each of which consists of a locomotive and 51 freight cars. Figure 4 As shown in the figure, the experimental line speed and displacement curves are as follows Figure 5 The parameters of the heavy-haul train are shown in Table 1.

[0115] Table 1

[0116]

[0117] The actuator efficiency in this experiment , offset fault , the external interference is:

[0118] ;

[0119] Pick , , , , , , , , , , , , , , the expected minimum safety interval , the initial position of the three heavy-load trains is 0 m , -800 m , -1600 m .

[0120] Figure 6 It is the displacement curve of multiple vehicles tracking based on distributed adaptive cooperative control. Figure 7 It is the multi-vehicle tracking speed curve based on distributed adaptive cooperative control. Figure 8 is an adaptive parameter map based on distributed adaptive cooperative control; Fig. 9 is the displacement error curve of multi-vehicle tracking based on distributed adaptive cooperative control, Fig.10 is the multi-vehicle tracking speed error curve based on distributed adaptive cooperative control, Fig.11 This is the first train coupler force curve based on distributed adaptive cooperative control. Figure 8-Figure 9 It can be seen that the displacement and speed errors of the locomotive converge to 0 asymptotically, and the displacement and speed errors of the freight car are consistent and stable. The displacement tracking error range is [-0.047, 0.066] m, and the speed error range is [-0.033, 0.019] m / s. Fig.11 It can be seen that the maximum hook pull force and hook pressure force range is .from Fig.12 It can be seen that the actual maximum and minimum input values ​​are and ,The proposed algorithm takes into account the hook and buffer uncertainty, external ,interference, and actuator failure, and the experiments verify the ,effectiveness of the algorithm.

[0121] In order to further highlight the advantages of this algorithm, it is compared with the literature "L. Chen, H. Yang, F. Jin, and Y. Ren, "Distributed global composite learning cooperative control of virtually coupled heavy haul train formations," IEEE Transactions on Intelligent Transportation Systems, 2024." Figure 13-14 It can be seen that the displacement tracking and velocity tracking error ranges of the algorithm are [-55.09, 0] respectively. m and [-0.2011, 0.213] m / s , the tracking performance is inferior to the proposed algorithm. Figure 15-16 It can be seen that the train internal force and control input range are and , which is basically similar to the result of this application.

[0122] The scheme proposed in this application first considers the coupling force between the carriages of the heavy-loaded train and the uncertainty of the coupling and buffer, and establishes a multi-particle dynamic model of the heavy-loaded train with unknown air resistance, additional resistance and external interference; then combines the actuator fault model to obtain the system equation of the heavy-loaded train with actuator faults; according to the system tracking control target, the error variable is introduced to obtain the system dynamic error model and transform it into the system state space equation; inspired by the sliding surface and filter transformation, the error transformation state space equation is obtained; the cyclic small gain theorem and linear matrix inequality are introduced to solve the uncertainty of the coupling and buffer and the stability of the freight car, and a low-complexity distributed adaptive cooperative control protocol for heavy-loaded trains is designed to ensure the safety of each heavy-loaded train, and based on the minimum safety distance, the locomotive can achieve asymptotic tracking of its own expected speed and displacement curve, and the freight car can achieve consistent tracking of its own expected speed and displacement curve. The scheme of this application realizes the cooperative tracking control of the speed and displacement of the heavy-loaded train by designing a low-complexity distributed adaptive cooperative controller, adaptively adjusting the control parameters in real time to cope with the dynamic changes of the system.

[0123] Based on the same inventive concept, the embodiment of the present application also provides a heavy-load train collaborative tracking control system based on coupling buffer uncertainty for implementing the above-mentioned heavy-load train collaborative tracking control method based on coupling buffer uncertainty. The implementation scheme for solving the problem provided by the system is similar to the implementation scheme recorded in the above-mentioned method, so the specific limitations in one or more embodiments of the heavy-load train collaborative tracking control system based on coupling buffer uncertainty provided below can be referred to the limitations of the heavy-load train collaborative tracking control method based on coupling buffer uncertainty in the above text, and will not be repeated here.

[0124] In an exemplary embodiment, a heavy-load train cooperative tracking control system based on coupling and buffer uncertainty is provided, comprising:

[0125] The multi-mass point dynamic model building module is used to equate the coupler-buffer system to a spring-damper system, and to build a multi-mass point dynamic model of a heavy-load train based on the coupling force between carriages of the heavy-load train and the train internal force equation of the coupler-buffer uncertainty obtained from the spring-damper system;

[0126] A heavy-load train system equation building module is used to obtain an actuator fault model and build a heavy-load train system equation with an actuator fault model based on the actuator fault model and a multi-mass point dynamic model of the heavy-load train;

[0127] The system state space equation establishment module is used to establish a system dynamic error model according to the heavy-load train system equation with the actuator fault model and the error variables; and convert the system dynamic error model into the system state space equation; the error variables include: displacement tracking error variables and speed tracking error variables;

[0128] An error transformation state space equation building module is used to obtain an error transformation state space equation according to the error variable after filtering transformation;

[0129] A sufficient condition determination module is used to obtain sufficient conditions for the stability of heavy-load trains based on the error transformation state space equation, using the cyclic small gain theorem and linear matrix inequality;

[0130] A distributed adaptive cooperative controller building module is used to build a distributed adaptive cooperative controller for heavy-haul trains based on error transformation state space equations and sufficient conditions for heavy-haul train stability;

[0131] The cooperative control module is used to control each heavy-load train to perform asymptotic tracking of the locomotive desired speed and locomotive displacement curve and consistent tracking of the freight car desired speed and freight car displacement curve based on the minimum safety distance between trains by using a distributed adaptive cooperative controller.

[0132] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, stored data, displayed data, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties, and the collection, use and processing of relevant data must comply with relevant regulations.

[0133] Those skilled in the art can understand that all or part of the processes in the above-mentioned embodiment methods can be completed by instructing the relevant hardware through a computer program, and the computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above-mentioned methods. Among them, any reference to the memory, database or other medium used in the embodiments provided in this application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetoresistive random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM may be in various forms, such as Static Random Access Memory (SRAM) or Dynamic Random Access Memory (DRAM).

[0134] The database involved in each embodiment provided in this application may include at least one of a relational database and a non-relational database. The non-relational database may include a distributed database based on blockchain, etc., but is not limited thereto. The processor involved in each embodiment provided in this application may be a general-purpose processor, a central processing unit, a graphics processor, a digital signal processor, a programmable logic device, a data processing logic device based on quantum computing, etc., but is not limited thereto.

[0135] In this application, all actions to obtain signals, information or data are carried out in compliance with the relevant data protection laws and policies of the country where they are located and with the authorization given by the owner of the corresponding device.

[0136] The technical features of the above embodiments may be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0137] This article uses specific examples to illustrate the principles and implementation methods of this application. The description of the above embodiments is only used to help understand the method and core ideas of this application. At the same time, for those skilled in the art, according to the ideas of this application, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as limiting this application.

Claims

1. A heavy-load train cooperative tracking control method based on coupling uncertainty, characterized in that: The heavy-load train cooperative tracking control method based on coupling and buffer uncertainty includes: The coupling-buffer system is equivalent to a spring-damper system, and a multi-mass point dynamic model of the heavy-load train is established based on the coupling force between the carriages of the heavy-load train and the train internal force equation of the coupling-buffer uncertainty obtained from the spring-damper system. Obtaining an actuator fault model, and establishing a heavy-load train system equation with the actuator fault model based on the actuator fault model and a multi-mass point dynamic model of the heavy-load train; According to the heavy-load train system equation with actuator fault model and error variables, a system dynamic error model is established; and the system dynamic error model is converted into a system state space equation; the error variables include: displacement tracking error variables and speed tracking error variables; According to the error variable after filtering transformation, the error transformation state space equation is obtained; According to the error transformation state space equation, the cyclic small gain theorem and linear matrix inequality are used to obtain the sufficient conditions for the stability of heavy-load trains. Based on the error transformation state space equation and the sufficient conditions for the stability of heavy-haul trains, a distributed adaptive cooperative controller for heavy-haul trains is constructed. A distributed adaptive cooperative controller is used to control each heavy-load train to asymptotically track the locomotive's desired speed and locomotive displacement curve and to consistently track the freight car's desired speed and freight car displacement curve based on the minimum safe distance between trains. The coupling-damping system is equivalent to a spring-damping system, and a multi-mass point dynamic model of a heavy-load train is established according to the coupling force between carriages of the heavy-load train and the coupling-damping uncertainty obtained according to the spring-damping system, which specifically includes: Using the formula Determine the train internal force equations ; Using the formula Establish a multi-mass point dynamic model of heavy-load train; in, It is i Heavy haul train j The quality of the carriage, and They represent the i Heavy-load train j The displacement and speed of the carriages, is the sum of the carriage length and the coupler length, Indicates whether there is a power unit. , indicating a locomotive, When it means a truck, It is i Heavy-load train j The output signal of the carriage is traction or braking force. , is the elastic coupling coefficient and uncertainty, , is the damping coupling coefficient and uncertainty, Indicates i Heavy-load train j The additional resistance on the carriage is represents the external disturbance to the jth carriage of the i-th heavy-load train, , , is the Davis coefficient, Represents mechanical resistance, represents air resistance, N is the total number of heavy-load trains, n is the total number of carriages, For the i Heavy haul train j The net force on the carriage is For the i Heavy-load train j The speed of the carriage, For the i Heavy-load train j The acceleration of the carriage.

2. The heavy-load train cooperative tracking control method based on coupling and buffer uncertainty according to claim 1 is characterized in that: The method of obtaining the actuator fault model and establishing a heavy-duty train system equation with the actuator fault model according to the actuator fault model and the multi-mass point dynamic model of the heavy-duty train specifically includes: Using the formula Determine actuator failure model; Using the formula Determine the system equations for a heavy-haul train with an actuator failure model; in, represents the output signal of the jth actuator failure mode of the i-th heavy-load train, is the efficiency factor of the jth actuator failure mode of the i-th heavy-load train, represents the input signal of the jth actuator of the i-th heavy-load train, Indicates the jth actuator offset fault of the i-th heavy-load train, For composite interference, , , , is the Davis coefficient, Represents mechanical resistance, Represents air resistance, parameter ,parameter ,parameter .

3. The heavy-load train cooperative tracking control method based on coupling and buffer uncertainty according to claim 2 is characterized in that: According to the heavy-duty train system equations and error variables with actuator failure model, the system dynamic error model is established, including: Using the formula Determine the displacement tracking error variable; where, is the displacement tracking error variable, is the displacement of the jth carriage of the i-th heavy-load train, is the expected displacement, is the displacement of the rear carriage of the i-1th heavy-load train, is the expected safety distance between heavy-load trains, parameter ,parameter ; Using the formula Determine the velocity tracking error variable; where, is the speed tracking error variable, is the speed of the jth carriage of the i-th heavy-load train, is the expected displacement, is the speed of the tail car of the i-1th heavy-load train; Using the formula Establish the system dynamic error model.

4. The heavy-load train cooperative tracking control method based on coupling and buffer uncertainty according to claim 3 is characterized in that: The system dynamic error model is converted into a system state space equation, specifically including: Using the formula Determine the system state space equations; in, and is the system state matrix, is the system output matrix, is the composite interference matrix, is the hook uncertainty matrix, is the reference velocity matrix.

5. The heavy-load train cooperative tracking control method based on coupling and buffer uncertainty according to claim 4 is characterized in that: The error transformation state space equation is obtained according to the error variable after filtering transformation, which specifically includes: Using the formula Determine the error variable after filtering transformation; Using the formula Determine the error transformation state space equation; in, is the transformation coefficient, and the error variable after filtering transformation is used for locomotive. , indicating that the truck does not need to be transformed, is the displacement tracking error variable after filtering transformation, is the speed tracking error variable after filtering transformation, variable , and Represent the locomotive set and the freight car set respectively, and the parameters ,parameter ,parameter ,parameter ,parameter ,parameter ,parameter ,parameter , To find the derivative of the locomotive variable after filtering transformation, Derivative of the truck variable after filtering transformation, is a zero matrix with one row and eight columns. is the hook uncertainty coefficient matrix, parameter ,parameter ,parameter ,parameter , is the reference acceleration, is the acceleration of the nth car of the i-1th train.

6. The heavy-load train cooperative tracking control method based on coupling and buffer uncertainty according to claim 5 is characterized in that: According to the error transformation state space equation, the cyclic small gain theorem and the linear matrix inequality are used to obtain sufficient conditions for the stability of heavy-load trains, which specifically include: Using the formula <0 is a sufficient condition for determining the stability of heavy-load trains; Among them, the parameters ,parameter ,parameter , a positive definite symmetric matrix , the superscript T indicates transposition, the parameter , , is the symmetric part of the corresponding position in the symmetric matrix, is the square of the upper bound of the uncertainty coefficient, For a parameter greater than 0, is the interconnection positive coefficient, parameter , is a diagonal matrix, is the intrinsic parameter of the hook buffer uncertainty coefficient matrix, is a positive definite symmetric matrix The inverse, For the matrix The inverse, is the system robust positive coefficient, parameter .

7. The heavy-load train cooperative tracking control method based on coupling and buffer uncertainty according to claim 6 is characterized in that: The distributed adaptive cooperative controller of the heavy-haul train is constructed according to the error transformation state space equation and the sufficient condition for the stability of the heavy-haul train, which specifically includes: Using the formula Building a distributed adaptive collaborative controller for heavy-haul trains; in, To eliminate offset faults and compound disturbances, , To eliminate or , , To enhance the system robustness, , for The estimated value of , is the unknown adaptive coefficient, is the basis of the error-transformed variables, , , , and is a constant greater than zero, is any positive uniformly continuous bounded smooth function.

8. A heavy-load train cooperative tracking control system based on coupling and buffer uncertainty, used to implement the heavy-load train cooperative tracking control method based on coupling and buffer uncertainty according to any one of claims 1 to 7; characterized in that: The heavy-load train cooperative tracking control system based on coupling and buffer uncertainty includes: The multi-mass point dynamic model building module is used to equate the coupler-buffer system to a spring-damper system, and to build a multi-mass point dynamic model of a heavy-load train based on the coupling force between carriages of the heavy-load train and the train internal force equation of the coupler-buffer uncertainty obtained from the spring-damper system; A heavy-load train system equation building module is used to obtain an actuator fault model and build a heavy-load train system equation with an actuator fault model based on the actuator fault model and a multi-mass point dynamic model of the heavy-load train; The system state space equation establishment module is used to establish a system dynamic error model according to the heavy-load train system equation with the actuator fault model and the error variables; and convert the system dynamic error model into the system state space equation; the error variables include: displacement tracking error variables and speed tracking error variables; An error transformation state space equation building module is used to obtain an error transformation state space equation according to the error variable after filtering transformation; A sufficient condition determination module is used to obtain sufficient conditions for the stability of heavy-load trains based on the error transformation state space equation, using the cyclic small gain theorem and linear matrix inequality; A distributed adaptive cooperative controller building module is used to build a distributed adaptive cooperative controller for heavy-haul trains based on error transformation state space equations and sufficient conditions for heavy-haul train stability; The cooperative control module is used to control each heavy-load train to perform asymptotic tracking of the locomotive desired speed and locomotive displacement curve and consistent tracking of the freight car desired speed and freight car displacement curve based on the minimum safety distance between trains by using a distributed adaptive cooperative controller.

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