Train operation control method under random disturbance

Abstract

The present application relates to a kind of train operation control methods under random interference, comprising: in the case where train is subjected to random interference, construct train time-varying multi-particle dynamics model;Based on the given ideal position relative displacement and actual relative position displacement, calculate position relative displacement error, and based on the given target speed curve and car speed, calculate speed tracking error, and based on position relative displacement error and speed tracking error, establish error state equation, based on error state equation design time-varying state feedback controller capable of meeting constraint condition, and convert constraint condition into time-varying differential matrix inequality;Solve time-varying state feedback controller that meets time-varying differential matrix inequality condition, and based on the time-varying state feedback controller after solving, control the operation of train, so that train can effectively be realized in the case where random interference is subjected to to meet the stability requirement while also having good transient performance, and ensure that cost reaches minimum.

Description

Technical Field

[0001] This invention relates to the field of high-speed train operation control technology, and in particular to a train operation control method under random disturbances. Background Technology

[0002] As a crucial component of building a high-quality, comprehensive, and three-dimensional transportation network, high-speed rail has experienced rapid development. With its advantages of safety, reliability, comfort, punctuality, and cost-effectiveness, high-speed rail has become one of the most popular modes of transportation. To ensure the safe and efficient operation of high-speed trains, automatic train control systems are used to control train operation, and automatic train control methods have received widespread attention.

[0003] Furthermore, in actual high-speed train operation, the system is inevitably subject to unknown external disturbances and internal fluctuations, such as grid voltage fluctuations, random measurement signals, sudden mechanical failures, and severe weather. Under the influence of random disturbances, the train cannot track the target speed curve, which may lead to safety risks and energy waste. Therefore, further research should be conducted on high-speed train systems with internal random fluctuations and external disturbances to improve speed tracking control performance.

[0004] However, these disturbances are often unknown and cannot be described by a deterministic function. Therefore, stochastic process theory is used to study unknown stochastic disturbances. Furthermore, most studies on train speed tracking control do not consider the system's transient performance. Overshoot and slow response caused by various disturbances and uncertainties will affect the safe and reliable operation of the train. Therefore, finite-time control is used to study transient performance. In addition, the goal of train control is not only to meet stability requirements but also to have good transient performance and minimize costs. Therefore, it is necessary to combine cost-optimal control methods. Summary of the Invention

[0005] (a) Technical problems to be solved

[0006] In view of the above-mentioned shortcomings and deficiencies of the prior art, the present invention provides a train operation control method under random disturbances, which not only meets the stability requirements, but also has good transient performance (overshoot and slow response), and can also ensure that the cost is minimized.

[0007] (II) Technical Solution

[0008] To achieve the above objectives, the main technical solutions adopted by the present invention include:

[0009] In a first aspect, embodiments of the present invention provide a train operation control method under random disturbances, comprising: constructing a time-varying multi-mass dynamics model of the train considering random disturbances; wherein the time-varying multi-mass dynamics model of the train includes the actual relative position offset between the i-th car and the (i+1)-th car of the train, and the car speed of the i-th car, where i is a positive integer; calculating the relative position offset error between the i-th car and the (i+1)-th car based on the given ideal relative position offset and the actual relative position offset, and calculating the speed tracking error of the i-th car based on the given target speed curve and car speed, and establishing an error state equation based on the relative position offset error and the speed tracking error; designing a time-varying state feedback controller that can satisfy the constraint conditions based on the error state equation, and converting the constraint conditions into time-varying differential matrix inequalities; wherein the constraint conditions include transient performance constraint conditions and cost minimization constraint conditions; solving for the time-varying state feedback controller that satisfies the time-varying differential matrix inequality conditions, and controlling the operation of the train based on the time-varying state feedback controller that satisfies the time-varying differential matrix inequality conditions.

[0010] In one possible embodiment, the expression for the time-varying multi-mass dynamics model of the train is:

[0011]

[0012] in, express The derivative; This represents the actual relative position offset between the i-th and (i+1)-th carriages; t represents time. This represents the speed of the i-th carriage; The speed of the (i+1)th carriage is indicated; n represents the total number of carriages in the train. This indicates the mass of the first carriage of the train; This indicates the speed of the first carriage. The derivative; This represents the actual control input for the first carriage at time t; This represents the interaction force between the first carriage and the second carriage of the train; This represents the first fundamental drag coefficient; This represents the second fundamental drag coefficient; The mass of the i-th carriage; This represents the third basic drag coefficient; express The derivative; This represents the actual control input of the i-th carriage at time t; This represents the interaction force between the (i-1)th and the ith carriage of the train; This represents the interaction force between the i-th car and the (i+1)-th car; This represents the mass of the nth carriage of the train; The speed of the nth carriage The derivative; The actual control input of the nth carriage at time t; This represents the interaction force between the (n-1)th and the nth carriage.

[0013] In one possible embodiment, the relative positional offset error between the i-th car and the (i+1)-th car is calculated using the following formula:

[0014]

[0015] in, This represents the relative offset error between the i-th and i+1-th carriages. This indicates the actual relative positional offset between the i-th carriage and the (i+1)-th carriage of the train. This indicates the relative offset of a given ideal position.

[0016] In one possible embodiment, the speed tracking error of the i-th carriage is calculated using the following formula:

[0017]

[0018] in, This represents the speed tracking error of the i-th carriage; This represents the given target velocity curve.

[0019] In one possible embodiment, the error state equation includes an error state sub-equation for representing the effect of continuous random disturbances during velocity tracking and an error state sub-equation for representing the effect of discrete random disturbances.

[0020] In one possible embodiment, the expression for the time-varying state feedback controller is:

[0021] ;

[0022] in, This indicates time-varying state feedback control; Represents the unknown time-varying control gain matrix; Indicates the state.

[0023] In one possible embodiment, the expression for the transient performance constraint is:

[0024] ;

[0025] in, Representing the error state equation transpose; Represents the first given upper bound matrix of the squared error; E represents the mean operation symbol; Representing state transpose; Let represent the second given upper bound matrix of the squared error.

[0026] In one possible embodiment, the expression for the cost minimization constraint is:

[0027] ;

[0028] in, The function represents the cost function; T represents the upper bound of time t; x represents the cost function. ’ (t) represents transpose; U represents the weight matrix of the first cost function; ’ (t) represents transpose; This represents the weight matrix of the second cost function; This represents the upper bound of a given cost function.

[0029] In one possible embodiment, the time-varying differential matrix inequality includes unknown matrix function variables and Poisson intensity; solving for a time-varying state feedback controller that satisfies the time-varying differential matrix inequality conditions includes: performing piecewise linearization on the unknown matrix function variables to obtain a time-series piecewise linear function; and in a given cost function... Value and In the case of a certain value, by changing the Poisson strength in the time-varying differential matrix inequality, the piecewise linear function of the time series is solved iteratively to obtain a time-varying state feedback controller that satisfies the conditions of the time-varying differential matrix inequality.

[0030] Secondly, embodiments of this application provide a storage medium storing a computer program, which, when executed by a processor, performs the method described in the first aspect or any optional implementation thereof.

[0031] Thirdly, embodiments of this application provide an electronic device, including: a processor, a memory, and a bus. The memory stores machine-readable instructions executable by the processor. When the electronic device is running, the processor communicates with the memory via the bus. When the machine-readable instructions are executed by the processor, they perform the method described in the first aspect or any optional implementation of the first aspect.

[0032] Fourthly, this application provides a computer program product that, when run on a computer, causes the computer to perform the method in the first aspect or any possible implementation thereof.

[0033] (III) Beneficial Effects

[0034] The beneficial effects of this invention are:

[0035] This application provides a train operation control method under random disturbances. By considering the random disturbances affecting the train, a time-varying multi-mass dynamics model of the train is constructed. This model includes the actual relative position offset between the i-th and (i+1)-th carriages of the train, and the speed of the i-th carriage. Then, based on the given ideal and actual relative position offsets, the relative position offset error between the i-th and (i+1)-th carriages is calculated. Furthermore, based on a given target speed curve and carriage speed, the speed tracking error of the i-th carriage is calculated. Finally, the relative position offset error and speed tracking error are combined. Error is identified by establishing an error state equation. Subsequently, a time-varying state feedback controller that satisfies the constraints is designed based on this equation. The constraints are then transformed into time-varying differential matrix inequalities, including transient performance constraints and cost minimization constraints. Finally, the time-varying state feedback controller satisfying the time-varying differential matrix inequalities is solved. Based on this controller, train operation is controlled, effectively ensuring that the train meets stability requirements under random disturbances while maintaining good transient performance (overshoot and slow response) and minimizing cost.

[0036] To make the above-mentioned objectives, features and advantages to be achieved by the embodiments of this application more apparent and understandable, preferred embodiments are described below in detail with reference to the accompanying drawings. Attached Figure Description

[0037] To more clearly illustrate the technical solutions of the embodiments of this application, the accompanying drawings used in the embodiments of this application will be briefly introduced below. It should be understood that the following drawings only show some embodiments of this application and should not be regarded as a limitation of the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0038] Figure 1 A flowchart of a train operation control method under random disturbances provided in an embodiment of this application is shown;

[0039] Figure 2This document illustrates a flowchart of a time-varying state feedback controller that solves for time-varying differential matrix inequalities, according to an embodiment of this application.

[0040] Figure 3 A schematic diagram of a control input for each power car provided in an embodiment of this application is shown;

[0041] Figure 4 This diagram illustrates the acceleration of each power car in a train according to an embodiment of this application.

[0042] Figure 5 A schematic diagram of the speed-time curves of each carriage provided in an embodiment of this application is shown;

[0043] Figure 6 A schematic diagram of an error time curve provided in an embodiment of this application is shown;

[0044] Figure 7 A schematic diagram illustrating an error comparison provided in an embodiment of this application is shown;

[0045] Figure 8 This illustration shows a schematic diagram of a comparison of the mean of the squared errors provided in an embodiment of this application. Detailed Implementation

[0046] To better explain and facilitate understanding of the present invention, the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0047] Currently, existing technologies have at least three problems: most existing studies on train speed tracking control do not consider the transient performance of the system, and overshoot and slow response caused by various disturbances and uncertainties will affect the safe and reliable operation of the train; the random disturbances experienced by high-speed trains are often unknown and cannot be described by a deterministic function; train control has high requirements, and the control objectives must meet stability, speed, accuracy and energy efficiency.

[0048] Based on this, embodiments of this application provide a train operation control method under random disturbances. By considering the random disturbances experienced by the train, a time-varying multi-mass dynamics model of the train is constructed. This model includes the actual relative position offset between the i-th and (i+1)-th carriages of the train, and the speed of the i-th carriage. Then, based on the given ideal and actual relative position offsets, the relative position offset error between the i-th and (i+1)-th carriages is calculated. Furthermore, based on the given target speed curve and carriage speed, the speed tracking error of the i-th carriage is calculated. Finally, based on the relative position offset error and speed... Error tracking is performed to establish an error state equation. Then, a time-varying state feedback controller that satisfies the constraints is designed based on this equation. The constraints are then transformed into time-varying differential matrix inequalities, including transient performance constraints and cost minimization constraints. Finally, the time-varying state feedback controller satisfying the time-varying differential matrix inequalities is solved. Based on this controller, train operation is controlled, effectively ensuring that the train meets stability requirements under random disturbances while maintaining good transient performance (overshoot and slow response) and minimizing cost.

[0049] To better understand the above technical solutions, exemplary embodiments of the present invention will be described in more detail below with reference to the accompanying drawings. Although exemplary embodiments of the present invention are shown in the drawings, it should be understood that the present invention can be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that the present invention can be understood more clearly and thoroughly, and that the scope of the present invention can be fully conveyed to those skilled in the art.

[0050] Please see Figure 1 , Figure 1 A flowchart illustrating a train operation control method under random disturbances provided in an embodiment of this application is shown. It should be understood that this train operation control method can be executed by a train operation control device, and the specific device of the train operation control device can be configured according to actual needs; this embodiment is not limited thereto. For example, the train operation control device can be a computer or a server, etc. Specifically, the train operation control method includes:

[0051] Step S110: Considering the random disturbances experienced by the train, a time-varying multi-mass dynamics model of the train is constructed. This model includes the actual relative positional offset between the i-th and (i+1)-th carriages of the train, and the velocity of the i-th carriage, where i is a positive integer.

[0052] Specifically, considering the random disturbances experienced by the train, the forces acting on the train during operation and the interaction forces between the carriages are uncertain. Therefore, a time-varying multi-mass dynamics model of the train is constructed.

[0053] It should be understood that the specific expression of the time-varying multi-mass dynamics model of the train can be set according to actual needs, and the embodiments of this application are not limited thereto.

[0054] Alternatively, considering a train with n carriages running on the track, the following time-varying multi-mass dynamics model of the train is established:

[0055]

[0056] in, express The derivative; This represents the actual relative position offset between the i-th and (i+1)-th carriages; t represents time. This represents the speed of the i-th carriage; The speed of the (i+1)th carriage is indicated; n represents the total number of carriages in the train. This indicates the mass of the first carriage of the train; This indicates the speed of the first carriage. The derivative; This represents the actual control input for the first carriage at time t; This represents the interaction force between the first carriage and the second carriage of the train; This represents the first fundamental drag coefficient; This represents the second fundamental drag coefficient; The mass of the i-th carriage; This represents the third basic drag coefficient; express The derivative; This represents the actual control input of the i-th carriage at time t; This represents the interaction force between the (i-1)th and the ith carriage of the train; This represents the interaction force between the i-th car and the (i+1)-th car; This represents the mass of the nth carriage of the train; The speed of the nth carriage The derivative; The actual control input of the nth carriage at time t; This represents the interaction force between the (n-1)th and the nth carriage.

[0057] It should also be understood that , , and The process of obtaining the result can be set according to actual needs, and the embodiments of this application are not limited thereto.

[0058] Optionally, The expression is:

[0059] ;

[0060] in, This represents the stiffness coefficient.

[0061] Correspondingly, , and The expression is similar; please refer to the above for details. The expression will not be described in detail here.

[0062] Step S120: Based on the given ideal position relative offset and actual position offset, calculate the position relative offset error of the i-th car and the (i+1)-th car, and based on the given target speed curve and car speed, calculate the speed tracking error of the i-th car, and establish the error state equation based on the position relative offset error and speed tracking error.

[0063] Specifically, considering random disturbances, based on the actual relative position offset between the i-th and i+1-th carriages in the time-varying multi-mass dynamics model of the train, the carriage velocity of the i-th carriage, and the given ideal position and target velocity curves, the relative position offset error between the i-th and i+1-th carriages and the velocity tracking error of the i-th carriage are calculated, and their expressions are as follows:

[0064]

[0065] ;

[0066]

[0067] ;

[0068] in, This represents the relative offset error between the i-th and i+1-th carriages. This indicates the actual relative positional offset between the i-th carriage and the (i+1)-th carriage of the train. This represents the relative offset of a given ideal position; This represents the speed tracking error of the i-th carriage; This represents the given target velocity curve.

[0069] And, in the following text, the Wiener process It can be viewed as continuous random fluctuations, such as randomly transmitted signals. And, the Poisson process. It is a discrete stochastic process that can be used to simulate discrete random disturbances such as sudden voltage jumps in circuits and sensors during train operation. It can be viewed as a Wiener process The differential, and It is a Poisson process The derivative of . According to stochastic process theory, , , The value is Poisson's strength. The relative position offset error is considered. and speed tracking error Represented as a matrix vector, i.e., the state Therefore, the error state equation is:

[0070] ;

[0071] in, Representing state The differential; Represent the existing error calculation equation; Used to represent the effect of continuous random disturbances during velocity tracking; Used to represent the effect of discrete random disturbances.

[0072] And, the initial value of the error state equation. .

[0073] And, the expression for U(t) is:

[0074] ;

[0075] in, ,and This indicates that the train has an ideal relative position offset. and target velocity curve The required control input; T indicates the transpose operation.

[0076] as well as, The expression is:

[0077] ;

[0078] ;

[0079] ;

[0080] ;

[0081] ;

[0082] in, for Zero-dimensional matrix.

[0083] as well as, The expression is:

[0084] ;

[0085] ;

[0086] ;

[0087] in, for Zero-dimensional matrix; for 3D identity matrix.

[0088] Step S130: Design a time-varying state feedback controller that satisfies the constraints based on the error state equation, and transform the constraints into time-varying differential matrix inequalities. The constraints include transient performance constraints and cost minimization constraints.

[0089] In other words, the design of the time-varying state feedback controller for the i-th power car in the train speed tracking error system aims to ensure that the state equation of the closed-loop error system has a stable and bounded solution, satisfying stability requirements while exhibiting good transient performance (overshoot and slow response), and minimizing cost. After converting the requirements of stability, transient performance, and cost minimization into formula constraints, the finite-time stochastic optimal control inequality constraints for the train speed tracking error are obtained through formula derivation. These constraints, which involve time-varying matrix variables and their derivatives, are presented in the form of time-varying differential matrix inequalities.

[0090] Specifically, a time-varying state feedback controller is designed to achieve cost-effective control of trains within a finite time frame:

[0091] ;

[0092] in, This indicates a time-varying state feedback controller; Represents the unknown time-varying control gain matrix; Indicates the state.

[0093] Furthermore, the time-varying state feedback controller has corresponding constraints, including transient performance constraints and cost minimization constraints, thereby enabling finite-time cost-optimal control of the train.

[0094] The expression for this transient performance constraint is as follows:

[0095] ;

[0096] In the formula, Representing the error state equation transpose; Represents the first given upper bound matrix of the squared error; E represents the mean operation symbol; Representing state transpose; Let represent the second given upper bound matrix of the squared error;

[0097] And the expression for this cost-minimum constraint is:

[0098] ;

[0099] In the formula, The function represents the cost function; T represents the upper bound of the time period t under study; x ’ (t) represents transpose; U represents the weight matrix of the first cost function; ’ (t) represents transpose; This represents the weight matrix of the second cost function; This represents the upper bound of a given cost function.

[0100] In addition, considering the actuator saturation limit, the controller of the error system... , yes The One element, It is a given constant.

[0101] as well as, The optimal control constraints in the form of time-varying differential matrix inequalities (i.e., time-varying differential matrix inequalities, which can also be called constraint formulas, etc.) are obtained as follows:

[0102] Objective function: ;

[0103] Finite-time cost-optimal control constraints (transient performance constraints and cost-minimum constraints):

[0104] ;

[0105] ;

[0106] ;

[0107] ;

[0108] Controller constraints:

[0109] ;

[0110] in,

[0111] ;

[0112] ;

[0113] It should be noted here that... Representing matrix functions transpose, Representing matrix functions transpose, Representing matrix functions transpose, Representing vectors transpose, Represents unknown matrix function variables, The derivative of the matrix function, and the gain of the time-varying controller. ,Y(t) -1 This represents finding the inverse of Y(t). Given a positive real number, Representing matrix functions The value at time zero.

[0114] Step S140: Solve for the time-varying state feedback controller that satisfies the time-varying differential matrix inequality condition, and control the train operation based on the time-varying state feedback controller that satisfies the time-varying differential matrix inequality condition.

[0115] Specifically, since time-varying matrix variables are not easy to solve, the matrix function can be piecewise linearized first, assuming... It is a matrix function, which is obtained by piecewise linearization:

[0116]

[0117] in, All are unknown time-invariant matrix variables. The piecewise time length for piecewise linearization Divide the total time by The quotient value, which represents the number of time segments.

[0118] Therefore, the unknown matrix function variables in the time-varying differential matrix inequalities can be determined using the method described above. Piecewise linearization is performed to obtain a piecewise linear function for the time series. Subsequently, in the cost function... and Given all factors, the Poisson intensity in the time-varying differential matrix inequality can be changed. By iteratively solving the piecewise linear function, a time-varying state feedback controller satisfying the time-varying differential matrix inequality condition can be obtained, thus yielding the upper bound of the cost function. and time-varying state feedback controller Furthermore, this can be further achieved through step S120. and control input The relational expression obtained Perform calculations to obtain Then you can The motion control of the train is then carried out by substituting the data into a time-varying multi-mass dynamics model.

[0119] It should also be noted here that in the cost function and If none of these are given, it can also be done by changing the cost function. and Poisson intensity in time-varying differential matrix inequalities The piecewise linear function of the time series is solved iteratively to obtain different parameters (i.e., , and The optimal solution under ().

[0120] To facilitate understanding of the process of finding the optimal solution, specific examples are described below.

[0121] Specifically, such as Figure 2 As shown, let as well as (Where I is the identity matrix, and q and r are unknowns if Q and R are not given.) The approximate range of the unknown parameters is given as follows: , and And also set , The calculation step size of r is , and And increase based on step size , The values ​​of r and t are obtained, and the time-varying matrix variables are piecewise linearized. The differential matrix inequalities (DLMIs, i.e., the four formulas related to the finite-time cost-preserving optimal control constraint) are solved iteratively to obtain all solutions that satisfy the constraints.

[0122] It should also be noted that, given Q and R, q and r become known quantities, so only the Poisson intensity needs to be considered. Adjustments will be made.

[0123] In summary, by using the above technical solutions, the embodiments of this application can effectively ensure that the train meets the stability requirements under random disturbances while also having good transient performance (overshoot and slow response) and minimizes costs.

[0124] To facilitate understanding of the embodiments of this application, specific embodiments are described below.

[0125] Specifically, a simulation experiment was conducted based on the parameters of the CRH380A train, which consists of six power cars. The specific parameters are as follows:

[0126] The masses of each carriage are as follows: , , , , , ;

[0127] The drag coefficients are as follows: , , ;

[0128] as well as, ;

[0129] Pick ; ; ;

[0130] .

[0131] Also, consider a temporary speed limit scenario, with the speed limit sections shown in Table 1 below.

[0132] Table 1

[0133]

[0134] By using the optimal control method for high-speed train operation under random disturbances, the control input, speed tracking error, acceleration, and speed of each power car can be found in [reference]. Figure 3-8 .

[0135] Therefore, compared with existing PID control and cost-saving optimal control, this application has smaller overshoot and faster response speed. Thus, this method can effectively improve the transient performance of the system by solving the minimum value problem with constraints.

[0136] It should be understood that the above-described train operation control method under random disturbances is merely exemplary, and those skilled in the art can make various modifications based on the above method, and the modified solutions also fall within the protection scope of this application.

[0137] This application provides a storage medium storing a computer program, which is executed by a processor to perform the methods described in the embodiments.

[0138] This application also provides a computer program product that, when run on a computer, causes the computer to perform the method described in the method embodiment.

[0139] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0140] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, as well as combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions.

[0141] It should be noted that any reference numerals placed between parentheses in the claims should not be construed as limiting the claims. The word "comprising" does not exclude the presence of components or steps not listed in the claims. The word "a" or "an" preceding a component does not exclude the presence of a plurality of such components. The invention can be implemented by means of hardware comprising several different components and by means of a suitably programmed computer. In claims that enumerate several means, several of these means may be embodied by the same hardware. The use of the terms first, second, third, etc., is merely for convenience of expression and does not indicate any order. These terms can be understood as part of the component names.

[0142] Furthermore, it should be noted that in the description of this specification, the terms "one embodiment," "some embodiments," "embodiment," "example," "specific example," or "some examples," etc., refer to specific features, structures, materials, or characteristics described in connection with that embodiment or example, which are included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Furthermore, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.

[0143] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the claims should be interpreted to include both the preferred embodiments and all changes and modifications falling within the scope of the invention.

[0144] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, then this invention should also include these modifications and variations.

Claims

1. A train operation control method under random disturbance, characterized by, include: Considering the random disturbances experienced by the train, a time-varying multi-mass dynamics model of the train is constructed; wherein, the time-varying multi-mass dynamics model of the train includes the actual relative position offset between the i-th car and the (i+1)-th car of the train, the car velocity of the i-th car, and i is a positive integer; Based on the given ideal position relative offset and the actual position offset, calculate the position relative offset error between the i-th car and the (i+1)-th car, and based on the given target speed curve and the car speed, calculate the speed tracking error of the i-th car, and based on the position relative offset error and the speed tracking error, establish the error state equation. Based on the aforementioned error state equation, a time-varying state feedback controller that satisfies the constraints is designed, and the constraints are transformed into time-varying differential matrix inequalities; wherein, the constraints include transient performance constraints and cost minimization constraints. Solve for the time-varying state feedback controller that satisfies the time-varying differential matrix inequality condition, and control the operation of the train based on the time-varying state feedback controller that satisfies the time-varying differential matrix inequality condition.

2. The train operation control method according to claim 1, characterized by, The expression for the time-varying multi-mass dynamics model of the train is: ； in, express The derivative; This indicates the actual relative positional offset between the i-th car and the (i+1)-th car; t represents time. This represents the speed of the i-th carriage; This represents the speed of the (i+1)th carriage; n represents the total number of carriages in the train. This indicates the mass of the first carriage of the train; This indicates the speed of the first carriage. The derivative; This represents the actual control input of the first carriage at time t; This represents the interaction force between the first carriage and the second carriage of the train; This represents the first fundamental drag coefficient; This represents the second fundamental drag coefficient; The mass of the i-th carriage; This represents the third basic drag coefficient; Indicates the The derivative; This represents the actual control input of the i-th carriage at time t; This represents the interaction force between the (i-1)th car and the i-th car of the train; This represents the interaction force between the i-th car and the (i+1)-th car; This represents the mass of the nth carriage of the train; The speed of the nth carriage The derivative; The actual control input of the nth carriage at time t; This represents the interaction force between the (n-1)th car and the nth car.

3. The train operation control method according to claim 2, characterized in that, The relative positional offset error between the i-th car and the (i+1)-th car is calculated using the following formula: ； in, This represents the relative offset error between the i-th car and the (i+1)-th car; This indicates the actual relative position offset between the i-th carriage and the (i+1)-th carriage of the train; This indicates the relative offset of the given ideal position.

4. The train operation control method according to claim 2, characterized in that, The speed tracking error of the i-th carriage is calculated using the following formula: ； in, This represents the speed tracking error of the i-th carriage; This represents the given target velocity curve.

5. The train operation control method according to claim 1, characterized in that, The error state equation includes an error state sub-equation for representing the effect of continuous random disturbances during velocity tracking and an error state sub-equation for representing the effect of discrete random disturbances.

6. The train operation control method according to claim 5, characterized in that, The expression for the time-varying state feedback controller is: ； in, This indicates time-varying state feedback control; Represents the unknown time-varying control gain matrix; Indicates the state.

7. The train operation control method according to claim 6, characterized in that, The expression for the transient performance constraint is: ； in, The error state equation represents Transpose of; Represents the first given upper bound matrix of the squared error; E represents the mean operation symbol; Representing state Transpose of; Let represent the second given upper bound matrix of the squared error.

8. The train operation control method according to claim 7, characterized in that, The expression for the minimum cost constraint is: ； in, The function represents the cost function; T represents the upper bound of time t; x represents the cost function. ’ (t) represents the... Transpose of; U represents the weight matrix of the first cost function; ’ (t) represents the... Transpose of; This represents the weight matrix of the second cost function; This represents the upper bound of a given cost function.

9. The train operation control method according to claim 8, characterized in that, The time-varying differential matrix inequality includes unknown matrix function variables and Poisson intensity; the solution for the time-varying state feedback controller that satisfies the time-varying differential matrix inequality includes: The unknown matrix function variables are piecewise linearized to obtain a time-series piecewise linear function; In the given cost function Value and In the case of a certain value, the time-series piecewise linear function is iteratively solved by changing the Poisson intensity in the time-varying differential matrix inequality to obtain a time-varying state feedback controller that satisfies the conditions of the time-varying differential matrix inequality.

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