High-speed train cooperative control method based on distributed sampling observer

Abstract

The invention discloses a high-speed train cooperative control method based on a distributed sampling observer, and the method comprises the following steps: S1, carrying out the stress analysis of a plurality of trains running in the same direction, and building a longitudinal dynamic model of the plurality of trains; s2, establishing an error state space model of the leading train and the following train; s3, constructing a distributed sampling observer with sampling and delay output measurement; s4, constructing a high-speed train distributed controller based on the communication network and the distributed sampling observer; and S5, determining an observer gain and a feedback controller gain which can enable the train to operate safely and stably. According to the method, the problem of measurement delay of the train observer is solved, and the flexibility and efficiency of a train communication system are improved.

Description

Technical Field

[0001] The present 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 Art

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

[0003] The currently widely used sampling mechanism can avoid continuous state monitoring and transmission to reduce communication occupancy. It uses sampling channels and zero-order holders to enter the network medium, and the signal only changes at the sampling moment. However, in the actual operation of the train, the train state information is not always available, and the sampling process will also be unstable due to changes in the sampling period. Therefore, the introduction of the observer is crucial, but an important problem of the distributed observer is the unobservability problem. In addition, measurement delays are also common in operation. For example, the delay caused by the physical distance of the communication process and the influence of bandwidth limitations will make the train state information only transmitted to the observer through the speed-limited network. Summary of the invention

[0004] In order to solve the problem of measurement delay of observers carried by high-speed trains and ensure the safe and reliable operation of multiple high-speed trains and track predefined trajectories, the present invention proposes a high-speed train collaborative control method based on distributed sampling observers to solve the above problems.

[0005] The present application discloses a high-speed train coordinated control method based on a distributed sampling observer, comprising the following steps:

[0006] S1. According to the running direction of the trains, the force analysis is performed on multiple trains running in the same direction, and the longitudinal dynamic model of the multiple trains is established;

[0007] S2, establishing the error state space model of the leading train and the following train according to the displacement error and speed error between the front and rear trains;

[0008] S3, build a distributed sampling observer with sampling and delayed output measurement;

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

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

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

[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 represents the mass of the i-th train, F i (t) represents the actual traction / braking force of the i-th train, ω i (t) represents the interference from the external environment, c0, c1 and c2 are the Davis coefficients of each train, c0, c1 and c2 are all positive numbers, represents the actual acceleration of the i-th train.

[0014] Preferably, in order to ensure a safe distance between two adjacent trains and avoid collision, the displacement and speed of each train are subject to the following restrictions:

[0015]

[0016] Among them, d max is the maximum allowable displacement error of the train, v max is the maximum permissible tracking speed of the train, il represents the distance between the ith train and the leading train, l is the expected distance between two adjacent trains, p0(t) represents the displacement reference curve of the leading train, and v0(t) represents the speed reference curve of the leading train.

[0017] Preferably, S2 comprises the following steps:

[0018] S21. Construct the dynamic model of the leading train and the following train;

[0019] Assume following train:

[0020]

[0021] Among them, u i (t) is the control input of the i-th following train, f i (t) is the interference received by the i-th following train;

[0022] The displacement reference curve of the leading train is p0(t), and its first-order derivative That is, the speed reference curve exists, and u0(t) is defined as the acceleration of the leading train. Then:

[0023]

[0024] definition:

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

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

[0027] Among them, x i (t) is the state vector of the ith 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, constructing error state space models of the leading train and the following train;

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

[0030]

[0031] in, B=[0 1] T , D=I, I is the unit matrix, C i is the output matrix, y i (t) represents the delayed output measurement value obtained at different times, Indicates the delay time. is a positive constant of the maximum delay, is the upper limit of the maximum sampling time, and

[0032] The state space model of the leader train with output measurements with observation delay is:

[0033]

[0034] Since each sampled output measurement is only performed at time t k Available and there is a measurement delay, corresponding to time t k -τ(t k ), so the sampled and delayed output is expressed as: And the delayed system output satisfies represents the kth sampling time of the i-th following train.

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

[0036]

[0037] Among them, δ i (t) is the error state vector between the ith following train and the leading train.

[0038] Preferably, S3 comprises the following steps:

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

[0040]

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

[0042] S32, establish the following error estimation state equation, assuming that the estimated error state Combining the relations in S1 and S31, we have:

[0043]

[0044] Notice that Then the estimated error state equation can be rewritten as:

[0045]

[0046] Among them, the matrix is the multi-agent Laplacian matrix composed of n high-speed trains, I n Represents the n-dimensional identity matrix.

[0047] S33、For unobservable matrices or matrix pairs that cannot be fully observed (A, C i ) to perform orthogonal transformation to achieve observability of matrix pairs.

[0048] Define the orthogonal matrix Z i , Matrices A and C i Through a feasible state space transformation Z i To transform:

[0049]

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

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

[0052]

[0053] Where K is the controller gain coefficient, λ i represents the communication between the ith train and the leading train. If the ith train can communicate with the leading train, then i =1, otherwise λ i =0.

[0054] Preferably, S5 comprises the following steps:

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

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

[0057] B. Calculation Matrix The eigenvector of So as to obtain A set of row vectors h=h1,h2,…,h n ;

[0058] C. Let Z = diag(Z1,…,Z n ), use binary search in the initial range to find a positive number ε such that in I2 is the two-dimensional identity matrix, I 2n is a 2n-dimensional identity matrix. If no ε that meets the conditions is found in the initial range, the search range is expanded;

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

[0060]

[0061] in, For A iu The unit matrix of the same dimension, μ is a positive number, which is used to limit the convergence speed. If the ε that meets the conditions is not found in the initial range, the search range is expanded, such as to (0,10).

[0062] S52, calculate observer gain L i 、M i and controller gain factor K;

[0063] Construct 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-order derivative of V(t) along time, we can use Schur's complement lemma to get The necessary conditions for are transformed into a set of linear matrix inequalities;

[0067] After solving using the LMI toolbox function feasp in MATLAB, we get L io and K, and ensure A io -L io C io The eigenvalues ​​of converge to the region And solve for the observer gain

[0068] Beneficial effects of the present invention:

[0069] (1) The present invention takes into account the problem of partial unobservability of state information and 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 the present invention allows continuous estimation between sampling points, thereby eliminating the need for frequent communication, allowing longer sampling intervals to be used without sacrificing accuracy, and improving the flexibility and efficiency of the train communication system.

[0071] (3) The present invention adopts a class of controllers based on communication networks and distributed observers, allowing the lead train to be driven by unknown control inputs. BRIEF DESCRIPTION OF THE DRAWINGS

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

[0073] Figure 2 A diagram showing the distribution of forces acting on each train according to an embodiment of the present invention;

[0074] Figure 3 It is a displacement curve diagram of each train under the condition of maximum sampling period and measurement delay in an embodiment of the present invention;

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

[0076] In order to make the objectives, technical solutions and advantages of the present application more clearly understood, the present application is further described in detail below with reference to the accompanying drawings and examples.

[0077] The present application embodiment discloses a high-speed train coordinated control method based on a distributed sampling observer, and the process is as follows: Figure 1 As shown, the following steps are included:

[0078] S1. According to the running direction of the train, the force analysis of multiple trains running in the same direction is carried out. During the running process, the high-speed train will be subject to traction, braking force, mechanical resistance, air resistance and external disturbance, such as Figure 2 When multiple high-speed trains run on the same line, the radio block center (RBC) can collect train speed, position and other information in real time through the global railway mobile communication system (GSM-R), and transmit the information to the on-board equipment of adjacent trains, so there is long-distance two-way wireless communication between the train and the ground. o represents the real-time displacement of train i, and d represents the distance between adjacent trains. The longitudinal dynamic 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 represents the mass of the i-th train, F i (t) represents the actual traction / braking force of the i-th train, ω i (t) represents the interference from the external environment, c0, c1 and c2 are the Davis coefficients of each train, c0, c1 and c2 are all positive numbers, 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 restrictions:

[0082]

[0083] Among them, d max is the maximum allowable displacement error of the train, v max is the maximum permissible tracking speed of the train, il represents the distance between the ith train and the leading train, l is the expected distance between two adjacent trains, p0(t) represents the displacement reference curve of the leading train, and v0(t) represents the speed reference curve of the leading 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 front and rear trains.

[0085] S21. Construct the dynamic model of the leading train and the following train;

[0086] Assume following train:

[0087]

[0088] Among them, u i (t) is the control input of the i-th following train, f i (t) is the interference received by the i-th following train.

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

[0090] Then 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] Among them, x i (t) is the state vector of the ith 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, constructing error state space models of the leading train and the following train;

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

[0100]

[0101] in, B=[0 1] T , D=I, I is the unit matrix, C i is the output matrix, y i (t) represents the delayed output measurement value obtained at different times, Indicates the delay time. is a positive constant of the maximum delay, is the upper limit of the maximum sampling time, and

[0102] The state space model of the leader train with output measurements with observation delay is:

[0103]

[0104] Since each sampled output measurement is only performed at time t k Available and there is a measurement delay, corresponding to time t k -τ(t k ), so the sampled and delayed output is expressed as: And the delayed system output satisfies represents the kth sampling time of the i-th following train.

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

[0106]

[0107] Among them, δ i (t) is the error state vector between the ith following train and the leading train.

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

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

[0110]

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

[0112] S32, establish the following error estimation state equation, assuming that the estimated error state Combining the relations in S1 and S31, we have:

[0113]

[0114] Notice that set up Then the estimated error state equation can be rewritten as:

[0115]

[0116] Among them, the matrix is the multi-agent Laplacian matrix composed of n high-speed trains, I n Represents the n-dimensional identity matrix.

[0117] S33、For unobservable matrices or matrix pairs that cannot be fully observed (A, C i ) to perform orthogonal transformation to achieve observability of matrix pairs.

[0118] Define the orthogonal matrix Z i , Matrices A and C i Through a feasible state space transformation Z i To transform:

[0119]

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

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

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

[0123]

[0124] Where K is the controller gain coefficient, λ i represents the communication between the ith train and the leading train. If the ith train can communicate with the leading train, then i =1, otherwise λ i =0.

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

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

[0127] B. Calculation Matrix The eigenvector of So as to obtain A set of row vectors h=h1,h2,…,h n .

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

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

[0130]

[0131] in, For A iu The unit matrix of the same dimension, μ is a positive number, which is used to limit the convergence speed. If the ε that meets the conditions is not found in the initial range, the search range is expanded, such as to (0,10).

[0132] S52, calculate observer gain L i 、M i and controller gain factor K;

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

[0134]

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

[0136] Taking the first-order derivative of V(t) along time, we can use Schur's complement lemma to get The necessary conditions are transformed into a set of linear matrix inequalities. After solving using the LMI toolbox function feasp in MATLAB, we get L io and K, and ensure A io -L io C io The eigenvalues ​​of converge to the region And solve for the observer gain

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

[0138] like Figure 2 The diagram shows the running trains and force distribution of the embodiment. As shown in the figure, there are 4 trains running in the same direction on a line, of which train 0 is the leading train and trains 1-3 are following trains. Among them, only train 1 can obtain the information of the leading train, train 1 can communicate with train 2 in two directions, and train 2 can communicate with train 3 in two directions. In the simulation experiment, the Davis coefficients are set as: c0 = 1.176e-2N / kg, c1 = 7.7616e-4Ns / mkg, c2 = 1.6e-5Ns 2 / m 2 kg; mass of each train m i =8e5kg,i=1,2,3; the maximum distance between trains is set to d max= 300m, the maximum speed difference between each following train and the leading train is set to v max =20m / s. The reference trajectory of the leading train is obtained by fitting the values ​​of the Japanese Shinkansen HST.

[0139] Based on the above parameters, a MATLAB simulation experiment was carried out and the controller gain K = [-0.0961, -1.2886] and the observer gain L were obtained by 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. Figure 3 The displacement state curve of the high-speed train under the above conditions is shown. Figure 4 The speed state curve of the high-speed train under the above conditions is shown. It can be seen that the response time is not only short but also the overshoot is not large, that is, the asymptotic stability of the high-speed train system is achieved in the presence of observation delay and sampling period. Through simulation, it can be seen that the embodiment of the present application effectively reduces the negative impact of observation delay, and can quickly enable the high-speed train system to track the reference trajectory and show excellent dynamic performance. The effectiveness and superiority of the high-speed train collaborative control method based on distributed sampling observer proposed in this application are proved.

[0145] The above shows and describes the basic principles, main features and advantages of the present invention. It should be understood by those skilled in the art that the present invention is not limited to the above embodiments. The above embodiments and descriptions are only for explaining the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, which fall within the scope of the present invention. The scope of protection of the present invention is defined by the attached claims and their equivalents.

Claims

1. A high-speed train cooperative control method based on distributed sampling observer, characterized in that: The following steps are involved: S1. According to the running direction of the trains, the force analysis is performed on multiple trains running in the same direction, and the longitudinal dynamic model of the multiple trains is established; S2, establishing the error state space model of the leading train and the following train according to the displacement error and speed error between the front and rear trains; S3, build a distributed sampling observer with sampling and delayed output measurement; S4. Construct a high-speed train distributed controller based on a communication network and a distributed sampling observer, allowing the leading train to be driven by unknown control inputs; S5. Determine the observer gain and feedback controller gain that can enable the train to run safely and smoothly.

2. The high-speed train cooperative control method based on distributed sampling observer according to claim 1 is characterized in that: The longitudinal dynamic model of the multiple trains is: 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 represents the mass of the i-th train, F i (t) represents the actual traction / braking force of the i-th train, ω i (t) represents the interference from the external environment, c0, c1 and c2 are the Davis coefficients of each train, c0, c1 and c2 are all positive numbers, represents the actual acceleration of the i-th train.

3. The high-speed train cooperative control method based on distributed sampling observer according to claim 2 is characterized in that: To ensure a safe distance between adjacent trains and avoid collisions, the displacement and speed of each train are subject to the following restrictions: Among them, d max is the maximum allowable displacement error of the train, v max is the maximum permissible tracking speed of the train, il represents the distance between the ith train and the leading train, l is the expected distance between two adjacent trains, p0(t) represents the displacement reference curve of the leading train, and v0(t) represents the speed reference curve of the leading train.

4. The high-speed train cooperative control method based on distributed sampling observer according to claim 3 is characterized in that: The S2 comprises the following steps: S21. Construct the dynamic model of the leading train and the following train; The dynamic model of the leader train is: The dynamic model of the following train is: definition: x i (t)=[p i (t)+il,v i (t)] T ; x0(t)=[p0(t),v0(t)] T ; Among them, x i (t) is the state vector of the i-th following train, u i (t) is the control input of the i-th following train, f i (t) is the disturbance received by the ith following train, x0(t) is the state vector of the leading train, f0(t) is the disturbance received by the leading train, and u0(t) is the acceleration of the leading train; S22, constructing error state space models of the leading train and the following train; The state space model of the following train with output measurements with observation delay is: in, B=[0 1] T , D=I, I is the unit matrix, C i is the output matrix, y i (t) represents the delayed output measurement value obtained at different times, Indicates the delay time. is a positive constant of the maximum delay, is the upper limit of the maximum sampling time, and represents the kth sampling moment of the i-th following train; The state space model of the leader train with output measurements with observation delay is: Let δ i (t) = x o (t)-x0(t), the error state space model of the leading train and the following train is obtained as: Among them, δ i (t) is the error state vector between the ith following train and the leading train.

5. The high-speed train cooperative control method based on distributed sampling observer according to claim 4 is characterized in that: The S3 comprises the following steps: S31. Assume that the multi-agent directed graph consisting of n high-speed trains is strongly connected, and the augmented matrix (A, C) is considerable, but (A, C o ) is not necessarily observable, then the distributed observer with sampling and delayed output measurement is: in, is the estimated vector of the train error state, a oj is the (i, j)th item of the adjacency matrix A of the multi-agent consisting of n trains, γ is the coupling gain, L o and M o is the gain matrix, η o (t) is the internal state variable determined by the above formula, η i (t) in time interval On continuous; S32. Establish the following error estimation state equation: in, is the multi-agent Laplacian matrix composed of n high-speed trains, I n represents the n-dimensional identity matrix; S33, for the matrix pair (A,C o ) performs orthogonal transformation to achieve observability of matrix pairs; Define the orthogonal matrix Z o , Matrices A and C o Through a feasible state space transformation Z o To transform: C o T o =[C oo 0]; Among them, A oo and C io is the observable part submatrix after orthogonal decomposition, A iu is the unobservable part submatrix, A iu is the uncertain partial submatrix.

6. The high-speed train cooperative control method based on distributed sampling observer according to claim 5 is characterized in that: The high-speed train distributed controller in S4 specifically designs a different controller for each following train, and the control input of the i-th following train is: Where K is the controller gain coefficient, λ i represents the communication between the ith train and the leading train. If the ith train can communicate with the leading train, then i =1, otherwise λ i =0.

7. The high-speed train cooperative control method based on distributed sampling observer according to claim 6 is characterized in that: The S5 The following steps are involved: S51. The conditional constraints for setting parameters are as follows: A. For all trains, calculate n independent orthogonal matrices Z i (i=1,…,n), so that all (A io ,C io ) is observable; B. Calculation Matrix The eigenvector of So as to obtain A set of row vectors h=h1,h2,…,h n ; C. Let Z = diag(Z1,…,Z n ), use binary search in the initial range to find a positive number ε such that in I2 is the two-dimensional identity matrix, I 2n is a 2n-dimensional identity matrix. If no ε that meets the conditions is found in the initial range, the search range is expanded; D. Use binary search in the initial range to find a positive number γ so that all trains satisfy: in, For A iu The unit matrix of the same dimension, μ is a positive number, which is used to limit the convergence speed. If the ε that meets the conditions is not found in the initial range, the search range is expanded, such as to (0,10); S52, calculate observer gain L i 、M i and controller gain factor K; Construct the Lyapunov-Krasovskii functional V(t) of the train system: Among them, P i , Q i All are positive definite symmetric matrices; Taking the first-order derivative of V(t) along time, we can use Schur's complement lemma to get The necessary conditions for are transformed into a set of linear matrix inequalities; After solving using the LMI toolbox function feasp in MATLAB, we get L io and K, and ensure A io -L io C io The eigenvalues ​​of converge to the region And solve for the observer gain

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