A high-speed train cooperative control method based on a distributed sampling observer

Abstract

The application discloses a high-speed train cooperative control method based on a distributed sampling observer, and comprises the following steps: S1, force analysis is conducted on multiple trains running in the same direction, and a longitudinal dynamics model of the multiple trains is established; S2, an error state space model of a leading train and a following train is established; S3, a distributed sampling observer with sampling and delay output measurement is constructed; S4, a high-speed train distributed controller based on a communication network and the distributed sampling observer is constructed; and S5, an observer gain and a feedback controller gain capable of enabling the train to run safely and stably are determined. The application solves the problem of measurement delay of the train observer, and improves the flexibility and efficiency of a train communication system.

Description

Technical Field

[0001] This invention relates to the field of train driving technology, and in particular to a high-speed train cooperative control method based on a distributed sampling observer. Background Technology

[0002] In recent years, high-speed rail has developed rapidly, and urbanization and economic development have placed increasing demands on passenger transport systems. The ever-increasing demand for passenger volume has made the cooperative control of high-speed trains an important research topic, and many advanced research methods have been proposed to control the safe and reliable operation of multiple trains, such as multi-agent theory.

[0003] Currently widely adopted sampling mechanisms can avoid continuous state monitoring and transmission to reduce communication overhead. They utilize sampling channels and zero-order hold circuits to enter the network medium, with signals changing only at the sampling moment. However, during actual train operation, train state information is not always available, and the sampling process can be unstable due to variations in the sampling period. Therefore, the introduction of an observer is crucial, but a significant problem with distributed observers is the lack of observability. Furthermore, measurement delays are prevalent during operation; factors such as delays caused by physical distance in the communication process and bandwidth limitations mean that train state information can only be transmitted to the observer through a speed-limited network. Summary of the Invention

[0004] To address the measurement delay issue inherent in high-speed trains equipped with observers and to ensure the safe and reliable operation of multiple high-speed trains tracking predefined trajectories, this invention proposes a high-speed train cooperative control method based on distributed sampling observers, thus resolving the aforementioned problems.

[0005] This application discloses a high-speed train cooperative control method based on a distributed sampling observer, including the following steps:

[0006] S1. Perform force analysis on multiple trains running in the same direction according to the train's direction of travel, and establish a longitudinal dynamic model for the multiple trains.

[0007] S2. Establish error state space models for the leading train and the following train based on the displacement and speed errors between the two trains.

[0008] S3. Construct a distributed sampling observer with sampling and delayed output measurements;

[0009] S4. Construct a high-speed train distributed controller based on a communication network and a distributed sampling observer, allowing the train to be driven by unknown control inputs;

[0010] S5. Determine the observer gain and feedback controller gain that enable the train to run safely and smoothly.

[0011] Preferably, the longitudinal dynamics model of the multiple trains is as follows:

[0012]

[0013] Where t is the train running time, i represents the i-th train, i = 1, 2, ..., n, n is the total number of train carriages, p i (t) represents the actual displacement of the i-th train, v i (t) represents the actual speed of the i-th train, m i Let F represent the mass of the i-th train. i (t) represents the actual traction / braking force of the i-th train, ω i (t) represents interference from the external environment, and c0, c1, and c2 are the Davis coefficients for each train, where c0, c1, and c2 are all positive numbers. This represents the actual acceleration of the i-th train.

[0014] Preferably, to ensure a safe distance between adjacent trains and avoid collisions, the displacement and speed of each train are subject to the following limitations:

[0015]

[0016] Where, d max v is the maximum permissible displacement error of the train. max Let represent the maximum permissible tracking speed of the train, il represent the distance between the i-th train and the lead train, l represent the expected distance between two adjacent trains, p0(t) represent the displacement reference curve of the lead train, and v0(t) represent the speed reference curve of the lead train.

[0017] Preferably, step S2 includes the following steps:

[0018] S21. Construct dynamic models of the lead train and follower trains;

[0019] Assume a following train:

[0020]

[0021] Among them, u i (t) is the control input for the i-th train following the current train, f i (t) represents the interference experienced by the i-th train following it;

[0022] The displacement reference curve of the lead train is p0(t), and its first derivative is... Since a velocity reference curve exists, u0(t) is defined as the acceleration of the lead train. Therefore:

[0023]

[0024] definition:

[0025] x i (t)=[p i (t)+il,v i (t)] T ;

[0026] x0(t) = [p0(t), v0(t)] T ;

[0027] Where, x i (t) is the state vector of the i-th following train, x0(t) is the state vector of the leading train, and f0(t) is the disturbance received by the leading train;

[0028] S22. Construct error state-space models for the leading train and the following train;

[0029] First, the state-space model of the following train with observation delay is obtained as follows:

[0030]

[0031] in, B = [0 1] T D = I, where I is the identity matrix, and C i For the output matrix, y i (t) represents the delayed output measurement values ​​acquired at different times. Indicates the delay time. The positive constant of the maximum delay. This is the upper limit of the maximum sampling time, and

[0032] The state-space model of the leader train with observation delay is as follows:

[0033]

[0034] Since each sampled output measurement is only performed at time t k It is available and there is a measurement delay, corresponding to time t. k -τ(t k The sampled output measurement is used; therefore, the sampled and delayed output is expressed as: And the delayed system output satisfies This represents the k-th sampling time of the i-th train following the i-th column.

[0035] Let δ i (t)=x iGiven x(t) - x0(t), the error state-space model for the leading train and the following train is obtained as follows:

[0036]

[0037] Where, δ i (t) is the error state vector between the i-th following train and the leading train.

[0038] Preferably, step S3 includes the following steps:

[0039] S31. Assume a multi-agent directed graph consisting of n high-speed trains is strongly connected, and the augmented matrix (A,C) is observable, but (A,C) i If the output measurement is not necessarily observable, then a distributed observer with sampling and delayed output measurement is:

[0040]

[0041] in, Let a be the estimated vector of the train error state. ij Let γ be the (i,j)th element of the adjacency matrix A of a multi-agent system consisting of n trains, and let L be the coupling gain. i and M i Let η be the gain matrix. i (t) is the internal state variable determined by the above equation, η i (t) in time interval Upper continuous;

[0042] S32. Establish the following error estimation state equation, assuming the estimated error state... Combining the relationships in S1 and S31, we have:

[0043]

[0044] It is noted that The state equation for estimating the error can then be rewritten as:

[0045]

[0046] Among them, matrix Let I be a multi-agent Laplacian matrix consisting of n high-speed trains. n This represents an n-dimensional identity matrix.

[0047] S33. For unobservable matrices or matrix pairs (A, C) that cannot be fully observed. i Orthogonal transformations are performed to achieve observability of matrix pairs.

[0048] Define an orthogonal matrix Z i , Matrix A and C i Through a feasible state-space transformation Z i Perform the transformation:

[0049]

[0050] Among them, A io and C io A is an observable submatrix after orthogonal decomposition. iu A is an unobservable partial submatrix. iu This is the uncertain part of the submatrix.

[0051] Preferably, the high-speed train distributed controller in S4 is specifically designed as a different controller for each following train, and the control input for the i-th following train is:

[0052]

[0053] Where K is the controller gain coefficient, λ i Let λ represent the communication status between the i-th following train and the leading train. If the i-th train can communicate with the leading train, then λ... i =1, otherwise λ i =0.

[0054] Preferably, step S5 includes the following steps:

[0055] S51. The conditions and constraints for setting parameters are as follows:

[0056] A. For all trains, calculate n independent orthogonal matrices Z. i (i = 1, ..., n), such that all (A io C io It is observable;

[0057] B. Calculating the matrix eigenvectors Thus, we can obtain A set of row vectors h = h1, h2, ..., h n ;

[0058] C. Let Z = diag(Z1,…,Z n Within the initial range, a binary search is used to find a positive number ε such that... in I2 is a two-dimensional identity matrix, I 2n Given a 2n-dimensional identity matrix, if an ε satisfying the condition is not found within the initial range, the search range is expanded.

[0059] D. Use binary search within the initial range to find a positive number γ such that all trains satisfy:

[0060]

[0061] in, To be with A iu An identity matrix of the same dimension, μ is a positive number used to limit the convergence speed. If an ε that satisfies the condition is not found in the initial range, the search range is expanded, such as to (0,10).

[0062] S52, Calculate the observer gain L i M i and controller gain coefficient K;

[0063] Constructing the Lyapunov-Krasovskii functional V(t) of the train system:

[0064]

[0065] Among them, P i Q i All are positive definite symmetric matrices;

[0066] Taking the first derivative of V(t) over time and rearranging it using Schur complement lemma, we get... The necessary condition can be transformed into a set of linear matrix inequalities;

[0067] After solving using the feasp function from the LMI toolbox in MATLAB, we obtain L io And K, and guarantee A io -L io C io The eigenvalues ​​converge to the region The observer gain is then obtained by solving the problem.

[0068] The beneficial effects of this invention are:

[0069] (1) This invention takes into account the unobservable state information and the observation delay of the train-mounted observer, and uses a more practical observer model to solve the measurement delay.

[0070] (2) The sampling communication proposed in this invention allows for continuous estimation between sampling points, thereby eliminating the need for frequent communication and allowing for longer sampling intervals without sacrificing accuracy, thus improving the flexibility and efficiency of the train communication system.

[0071] (3) The present invention employs a controller based on a communication network and a distributed observer, which allows the lead train to be driven by unknown control inputs. Attached Figure Description

[0072] Figure 1 This is a flowchart of the high-speed train cooperative control method based on a distributed sampling observer according to an embodiment of the present invention;

[0073] Figure 2 This is a diagram showing the force distribution of each train in an embodiment of the present invention;

[0074] Figure 3 This is a diagram showing the displacement curves of each train under the conditions of maximum sampling period and measurement delay according to an embodiment of the present invention.

[0075] Figure 4 This is a speed curve diagram of each train under the conditions of maximum sampling period and measurement delay according to an embodiment of the present invention. Detailed Implementation

[0076] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided with reference to the accompanying drawings and embodiments.

[0077] This application discloses a high-speed train cooperative control method based on a distributed sampling observer, the process of which is as follows: Figure 1 As shown, it includes the following steps:

[0078] S1. Based on the train's direction of travel, perform a force analysis on multiple trains traveling in the same direction. High-speed trains in operation will be subject to traction force, braking force, mechanical resistance, air resistance, and external disturbances, such as... Figure 2 As shown, when multiple high-speed trains are running on the same line, the Radio Block Center (RBC) can collect real-time information such as train speed and location through the Global System for Rail Mobile Communication (GSM-R) and transmit the information to the onboard equipment of adjacent trains. Therefore, there is long-distance two-way wireless communication between the train and the ground. In the figure, p o Let d represent the real-time displacement of train i, and d represent the distance between adjacent trains. The longitudinal dynamics model of multiple trains is established as follows:

[0079]

[0080] Where t is the train running time, i represents the i-th train, i = 1, 2, ..., n, n is the total number of train carriages, p i (t) represents the actual displacement of the i-th train, v i (t) represents the actual speed of the i-th train, m i Let F represent the mass of the i-th train. i (t) represents the actual traction / braking force of the i-th train, ω i (t) represents interference from the external environment, and c0, c1, and c2 are the Davis coefficients for each train, where c0, c1, and c2 are all positive numbers. This represents the actual acceleration of the i-th train.

[0081] To ensure a safe distance between adjacent trains and avoid collisions, the displacement and speed of each train are subject to the following limitations:

[0082]

[0083] Where, d max v is the maximum permissible displacement error of the train. max Let represent the maximum permissible tracking speed of the train, il represent the distance between the i-th train and the lead train, l represent the expected distance between two adjacent trains, p0(t) represent the displacement reference curve of the lead train, and v0(t) represent the speed reference curve of the lead train.

[0084] S2. Establish the error state space model of the leading train and the following train based on the displacement error and speed error between the two trains.

[0085] S21. Construct dynamic models of the lead train and follower trains;

[0086] Assume a following train:

[0087]

[0088] Among them, u i (t) is the control input for the i-th train following the current train, f i (t) represents the interference experienced by the i-th following train.

[0089] The displacement reference curve of the lead train is p0(t), and its first derivative is... That is, a speed reference curve exists, and u0(t) is defined as the acceleration of the leading train.

[0090] The dynamic model of the leading train is:

[0091]

[0092] The dynamic model of the following train is:

[0093]

[0094] definition:

[0095] x i (t)=[p i (t)+il,v i (t)] T ;

[0096] x0(t) = [p0(t), v0(t)] T ;

[0097] Where, x i x0(t) is the state vector of the i-th following train, x0(t) is the state vector of the leading train, and f0(t) is the disturbance received by the leading train.

[0098] S22. Construct error state-space models for the leading train and the following train;

[0099] First, the state-space model of the following train with observation delay is obtained as follows:

[0100]

[0101] in, B = [0 1] T D = I, where I is the identity matrix, and C i For the output matrix, y i (t) represents the delayed output measurement values ​​acquired at different times. Indicates the delay time. The positive constant of the maximum delay. This is the upper limit of the maximum sampling time, and

[0102] The state-space model of the leader train with observation delay is as follows:

[0103]

[0104] Since each sampled output measurement is only performed at time t k It is available and there is a measurement delay, corresponding to time t. k -τ(t k The sampled output measurement is used; therefore, the sampled and delayed output is expressed as: And the delayed system output satisfies This represents the k-th sampling time of the i-th train following the i-th column.

[0105] Let δ i (t)=x i Given x(t) - x0(t), the error state-space model for the leading train and the following train is obtained as follows:

[0106]

[0107] Where, δ i (t) is the error state vector between the i-th following train and the leading train.

[0108] S3. Construct a distributed sampling observer with sampling and delayed output measurements.

[0109] S31. Assume a multi-agent directed graph consisting of n high-speed trains is strongly connected, and the augmented matrix (A,C) is observable, but (A,C) i If the output measurement is not necessarily observable, then a distributed observer with sampling and delayed output measurement is:

[0110]

[0111] in, Let a be the estimated vector of the train error state. ij Let γ be the (i,j)th element of the adjacency matrix A of a multi-agent system consisting of n trains, and let L be the coupling gain. i and M i Let η be the gain matrix. i (t) is the internal state variable determined by the above equation, η i (t) in time interval The upper continuous.

[0112] S32. Establish the following error estimation state equation, assuming the estimated error state... Combining the relationships in S1 and S31, we have:

[0113]

[0114] It is noted that set up The state equation for estimating the error can then be rewritten as:

[0115]

[0116] Among them, matrix Let I be a multi-agent Laplacian matrix consisting of n high-speed trains. n This represents an n-dimensional identity matrix.

[0117] S33. For unobservable matrices or matrix pairs (A, C) that cannot be fully observed. i Orthogonal transformations are performed to achieve observability of matrix pairs.

[0118] Define an orthogonal matrix Z i , Matrix A and C i Through a feasible state-space transformation Z i Perform the transformation:

[0119]

[0120] C i Ti =[C io 0];

[0121] Among them, A io and C io A is an observable submatrix after orthogonal decomposition. iu A is an unobservable partial submatrix. iu This is the uncertain part of the submatrix.

[0122] S4. Construct a high-speed train distributed controller based on a communication network and a distributed sampling observer, allowing the lead train to be driven by unknown control inputs. Specifically, design a different controller for each following train, where the control input for the i-th following train is:

[0123]

[0124] Where K is the controller gain coefficient, λ i Let λ represent the communication status between the i-th following train and the leading train. If the i-th train can communicate with the leading train, then λ... i =1, otherwise λ i =0.

[0125] S51. The conditions and constraints for setting parameters are as follows:

[0126] A. In S33, for all trains, calculate n independent orthogonal matrices Z. i (u=1,…,n), such that all (A io C io It is observable.

[0127] B. Calculating the matrix eigenvectors Thus, we can obtain A set of row vectors h = h1, h2, ..., h n .

[0128] C. Let Z = diag(Z1,…,Z n In the initial range, such as the interval (0,1), a binary search is used to find a positive number ε such that... in I2 is a two-dimensional identity matrix, I 2n Given a 2n-dimensional identity matrix, if no ε satisfying the condition is found in the initial range, the search range is expanded, such as to (0,10).

[0129] D. Within the initial range, in the interval (0,1), use binary search to find a positive coupling gain γ such that all trains satisfy:

[0130]

[0131] in, To be with A iu An identity matrix of the same dimension, μ is a positive number used to limit the convergence speed. If an ε that satisfies the condition is not found in the initial range, the search range is expanded, such as to (0,10).

[0132] S52, Calculate the observer gain L i M i and controller gain coefficient K;

[0133] Constructing the Lyapunov-Krasovskii functional V(t) of the train system:

[0134]

[0135] Among them, P i Q i All are positive definite symmetric matrices.

[0136] Taking the first derivative of V(t) over time and rearranging it using Schur complement lemma, we get... The necessary condition is transformed into a set of linear matrix inequalities. Solving these inequalities using the feasp function from the LMI toolbox in MATLAB yields L. io And K, and guarantee A io -L io C io The eigenvalues ​​converge to the region The observer gain is then obtained by solving the problem.

[0137] In one specific embodiment, the effectiveness of the high-speed train cooperative control method based on a distributed sampling observer proposed in this application is verified through simulation experiments.

[0138] like Figure 2 The diagram shows the train operation and force distribution in an embodiment. As shown, four trains run in the same direction on a line, with train 0 being the lead train and trains 1-3 being follower trains. Only train 1 can obtain information about the lead train; train 1 can communicate bidirectionally with train 2, and train 2 can communicate bidirectionally with train 3. In the simulation experiment, the Davis coefficients were set as follows: c0 = 1.176e-2 N / kg, c1 = 7.7616e-4 Ns / mkg, c2 = 1.6e-5 Ns. 2 / m 2 kg; Mass of each train (m) i =8e5kg, i=1,2,3; the maximum spacing between trains is set to d. max=300m, the maximum speed difference between each following train and the lead train is set to v. max =20m / s. The reference trajectory of the lead train was obtained by fitting the values ​​of the Japanese Shinkansen HST.

[0139] Based on the above parameters, a MATLAB simulation experiment was conducted. The controller gain K = [-0.0961, -1.2886] and the observer gain L were obtained using the LMI toolbox solver. i M i as follows:

[0140] L1 = [0.3590, 0.0591] T ;

[0141] L2 = [0, 1.4052] T ;

[0142] L3 = [0.1611, 0] T ;

[0143]

[0144] The maximum sampling interval is set to 0.0168s, and the maximum measurement delay is set to 0.0196s. For example... Figure 3 The displacement state curves of the high-speed train under the above conditions are shown. Figure 4 The speed state curves of the high-speed train under the above conditions are shown. It can be seen that the response time is not only short but also the overshoot is small, indicating asymptotic stability of the high-speed train system even with observation delay and sampling period. Simulation results show that the embodiment of this application effectively reduces the negative impact of observation delay and can quickly enable the high-speed train system to track the reference trajectory and exhibit superior dynamic performance. This demonstrates the effectiveness and superiority of the high-speed train cooperative control method based on a distributed sampling observer proposed in this application.

[0145] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed. The scope of protection of this invention is defined by the appended claims and their equivalents.

Claims

1. A high-speed train cooperative control method based on a distributed sampling observer, characterized in that, The method comprises the following steps: S1, performing force analysis on multiple trains running in the same direction according to the train running direction, and establishing a longitudinal dynamics model of the multiple trains; S2, establishing an error state space model of a leading train and a following train according to displacement error and speed error between the two trains; S3, constructing a distributed sampling observer with sampling and delayed output measurement; S31, Assuming that by The directed graph of multiple agents composed of high-speed trains is strongly connected, and the augmented matrix... It is considerable, but If the measurement is not necessarily observable, then a distributed observer with sampling and delayed output measurements is: wherein is an estimation vector of the train error state, is is a neighboring matrix of the multi-agent consisting of trains is the th element of is a coupling gain, and is a gain matrix, is an internal state variable determined by the above equation, is continuous over a time interval . S32, establishing the following error estimation state equation: wherein , , , is Laplacian matrix of multi-agent of high-speed train composition, denotes dimension identity matrix; S33, performing orthogonal transformation to realize observability of the matrix pair performing orthogonal transformation to realize observability of the matrix pair; Definition of an orthogonal matrix , , matrix and by a feasible state space transformation : wherein and are the observable part submatrices of the orthogonal decomposition, are the unobservable part submatrices, are the indeterminate part submatrices; S4, constructing a high-speed train distributed controller based on a communication network and the distributed sampling observer, and allowing the leading train to be driven by unknown control input; The distributed controller of the high-speed train is specifically designed for each following train, and the first The control input of the following train is: wherein, is the acceleration of the leading train, is a controller gain coefficient, denotes the column following train and the leading train, if the train can communicate with the leading train, then , otherwise , is the state vector of the leading train; S5, determining observer gain and feedback controller gain capable of enabling the trains to run safely and stably; S51, setting the conditional constraints of the parameters as follows: A. For all trains, compute an independent orthogonal matrix such that all are observable; B, compute the matrix of eigenvectors , so that the set of row vectors satisfying ; C, let , find a positive number in the initial range using binary search , such that , where , , is a two-dimensional identity matrix, is dimensional identity matrix, if the initial range is not found to meet the conditions , expand the search range; D. Find a positive number in the initial range using binary search such that all trains satisfy: wherein, is a unit matrix of the same dimension as is a unit matrix of the same dimension as is a positive number to limit the convergence speed, if no is found in the initial range, the search range is enlarged, such as to (0, 10); S52, compute observer gain , and controller gain coefficient ; Lyapunov-krasovskii functional for constructing train systems : wherein , are positive definite symmetric matrices, is the error state vector of the following train with respect to the leading train. For the first order derivative, the necessary condition of is obtained by using the Schur complement lemma, which is transformed into a set of linear matrix inequalities. After solving by using the LMI toolbox function feasp in MATLAB, we get and , and ensure that the eigenvalues of the region converge to the region , .

2. The high-speed train cooperative control method based on a distributed sampling observer according to claim 1, characterized in that, The longitudinal dynamics model of the multiple trains is: wherein, is the train operation time, denotes the th train, , is the total number of train cars, denotes the th train, denotes the th train, denotes the th train, denotes the th train, denotes the disturbance from the external environment, , and are the Davis coefficients for each train, , and are all positive numbers, denotes the th train.

3. The distributed-sampling-observer-based high-speed train cooperative control method according to claim 2, characterized in that, In order to ensure that the safe distance between the adjacent two trains is maintained and collision is avoided, the displacement and speed of each train are limited as follows: wherein is the maximum allowed displacement error of the train, is the maximum allowed pursuit speed of the train, denotes the column denotes the distance between the train and the leading train, is the desired distance between two adjacent trains, denotes the displacement reference curve of the leading train, denotes the speed reference curve of the leading train.

4. The distributed-sampling-observer-based high-speed train cooperative control method according to claim 3, characterized in that, The S2 comprises the following steps: S21, constructing a dynamics model of the leading train and the following train; The dynamics model of the leading train is: The dynamics model of the following train is: Definition: wherein, is the state vector of the leader train, is the control input of the leader train, is the disturbance to the leader train, is the state vector of the leader train, is the acceleration of the leader train; S22, constructing an error state space model of the leading train and the following train; The state space model of the following train with the output measurement of the observation delay is: wherein , , , is an identity matrix, is an output matrix, denotes a delayed output measurement taken at a different time, denotes a delay time, is a positive number of maximum delay, is an upper bound of maximum sampling time, and , , , , denotes the column following train at the sampled time instant; The state space model of the leading train with the output measurement of the observation delay is: Let The error state space model of the leading train and the following train is obtained as wherein, is the Error state vector of following train with respect to leading train.

Images