High-speed train group control method based on tracking and communication distance constraints

Abstract

The present invention discloses a method for controlling a high-speed train group under tracking and communication distance constraints, and relates to the technical field of high-speed train safe operation methods. The method comprises the following steps: establishing a dynamic model of a high-speed train in an equilibrium state, and constructing an error system model of the high-speed train based on the dynamic model; designing an adaptive robust controller by considering the constraints of the train running distance and setting the constraints that the train system state must meet; and introducing an obstacle function into the Lyapunov function to address the problem of limited running distance of high-speed trains. The method can effectively ensure that high-speed trains can operate safely under the dual constraints of maximum communication distance and minimum safety distance, and can accurately track all trains.

Description

Technical Field

[0001] The present invention relates to the technical field of high-speed train safe operation methods, and in particular to a high-speed train group tracking control method under the constraints of a minimum tracking distance and a maximum communication distance based on an obstacle function. Background Art

[0002] In railway transportation, advanced train control systems and precise signaling technology are used to rationally control the running distances between multiple high-speed trains. This control not only ensures a minimum safe distance between trains to avoid accidents such as rear-end collisions, but also involves setting a maximum communication distance to ensure stable transmission of communication signals between trains. The minimum safe distance is calculated based on factors such as the train's braking performance and operating speed, ensuring sufficient buffer distance during emergency braking. The maximum communication distance, on the other hand, is determined by the communication system's coverage and signal strength. When the distance between trains exceeds this, communication quality will significantly degrade or even be interrupted.

[0003] As a core signaling system for improving railway line capacity and operational safety, the Moving Block System (MBS) makes train interaction a key issue in optimized control by setting train movement authorizations to the preceding train's location point in real time (with an additional safety margin). To further shorten train tracking intervals, virtual coupling (VC) technology has emerged, based on the relative braking distance principle of the Moving Block System and train-to-train communication. With the widespread adoption of intelligent driving technologies within the MBS and VC systems in the railway sector, high-density following operations of high-speed trains have become an increasingly important application scenario for high-speed railways. However, existing research has failed to fully consider the critical issue of inter-train communication distance constraints. In actual operation, when the distance between trains exceeds the maximum effective communication distance of the communication equipment, signal delays or loss can occur, affecting real-time interaction and coordinated control between trains.

[0004] Currently, several control strategies have been introduced to control the spacing between trains, including the use of artificial potential functions to ensure that the distance between trains is strictly limited to a safe range. However, this approach also has certain limitations in practice, particularly the fluctuations in the position of local minima and unwanted reciprocating vibrations. These not only affect the operational stability of the trains but can also lead to unstable communication signals between trains. Therefore, how to stably and effectively maintain the distance between trains within the safe range throughout the entire train operation and gradually promote it to approach the ideal nominal value remains a challenging problem that needs to be solved. Summary of the Invention

[0005] The technical problem to be solved by the present invention is how to provide a method that can effectively ensure that high-speed trains can operate safely under the dual constraints of maximum communication distance and minimum safety distance and can accurately track all trains.

[0006] To solve the above technical problems, the technical solution adopted by the present invention is: a high-speed train group control method based on tracking and communication distance constraints, comprising the following steps:

[0007] Establish a dynamic model of the high-speed train in equilibrium state, and based on this dynamic model, construct an error system model of the high-speed train;

[0008] Considering the constraints of train running distance and setting the constraints that the train system state must meet, an adaptive robust controller is designed;

[0009] The barrier function is introduced into the Lyapunov function to solve the problem of limited running distance of high-speed trains.

[0010] A further technical solution is that the design method of the adaptive robust controller includes the following steps:

[0011] Establish A single-mass dynamics model of a high-speed train is proposed, and the position and speed signals of each train are measurable;

[0012] Construct high-speed train position error variables, speed error variables and acceleration error variables;

[0013] Convert the defined error variables into train error state space equations;

[0014] Considering the dual constraints of the maximum communication distance and the minimum safety distance of the train, the constraints that the train system state must meet are set;

[0015] According to the designed train system and state constraints, an adaptive robust controller is designed so that the maximum communication distance and minimum safety distance of the train group meet the constraints, and as the running time goes by, the train spacing and tracking error converge to the equilibrium point.

[0016] A further technical solution is that the method for solving the problem of the maximum communication distance and the minimum safety distance being limited includes the following steps:

[0017] Redefine the closed-loop system and error system of high-speed trains;

[0018] Design a Lyapunov function, set the barrier function as the first term of the function, and when the state of the train error system containing the train spacing change is in an ellipsoidal domain, the Lyapunov function value is positive;

[0019] By derivatizing and scaling the Lyapunov function, it is proved that the error state of the train system converges to the ellipsoid domain, and the distance between trains is strictly limited to an appropriate range.

[0020] The beneficial effect of the above technical solution is that it can ensure the safe operation of high-speed trains under the dual constraints of maximum communication distance and minimum safety distance. Even if the distance between trains is initially too large or too small, the adaptive control method proposed in this invention will eventually converge to a near-equilibrium point over time.

[0021] For a given target speed, all trains can achieve precise tracking under the control method described in this application, converging to near zero in a relatively short period of time. Furthermore, the maximum speed tracking error is much smaller than the actual train tracking error allowable value, demonstrating a high tracking control progress. Under the control method, the speed tracking error fluctuates very little, ensuring, to a certain extent, the smoothness of the train during travel and possessing strong anti-interference capabilities. This control method strategy has high application value. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0023] Figure 1 This is the main flow chart of the tracking control method of the present invention;

[0024] Figure 2 This is a flow chart of the tracking control method of the present invention;

[0025] Figure 3 Graph showing the relationship between the minimum safety distance and the maximum communication distance between adjacent trains in an embodiment of the present invention;

[0026] Figure 4 This is a block diagram of the principle of adaptive robust control for high-speed trains according to an embodiment of the present invention;

[0027] Figure 5 This is a high-speed train expected speed tracking trajectory diagram in an embodiment of the present invention;

[0028] Figure 6 This is a diagram of the expected displacement tracking trajectory of a high-speed train in an embodiment of the present invention;

[0029] Figure 7 2. It is a curve diagram of spacing variation under the adaptive control strategy of high-speed train in an embodiment of the present invention;

[0030] Figure 8 2. A displacement tracking error curve diagram of a high-speed train under an adaptive control strategy according to an embodiment of the present invention;

[0031] Figure 9 2. A speed tracking error curve diagram of a high-speed train under an adaptive control strategy according to an embodiment of the present invention;

[0032] Figure 10 This is a system state trajectory diagram under the high-speed train adaptive control strategy in an embodiment of the present invention. DETAILED DESCRIPTION

[0033] The following is a clear and complete description of the technical solutions in the embodiments of the present invention, in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts are within the scope of protection of the present invention.

[0034] In the following description, many specific details are set forth to facilitate a full understanding of the present invention. However, the present invention may also be implemented in other ways different from those described herein. Those skilled in the art may make similar generalizations without violating the connotation of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below.

[0035] Overall, such as Figure 1 As shown, an embodiment of the present invention discloses a high-speed train group control method based on tracking and communication distance constraints, the method comprising the following steps:

[0036] Firstly, a dynamic model of the high-speed train in equilibrium state is established. Based on this dynamic model, an error system model of the high-speed train is further constructed.

[0037] Secondly, on this basis, the constraints of train running distance are considered, and the constraints that the train system state must meet are set to design an adaptive robust controller.

[0038] Finally, a barrier function is introduced into the Lyapunov function to ensure that the problem of limited running spacing of high-speed trains is effectively solved.

[0039] Further, such as Figure 2 As shown, the embodiment of the present invention discloses a high-speed train tracking control method under the dual constraints of maximum communication distance and minimum safety distance based on an obstacle function, and designs an adaptive robust controller. The steps of the adaptive robust controller are as follows:

[0040] S101: Establishment A single-mass dynamics model of a high-speed train is proposed and it is assumed that the position and velocity signals of each train can be measured;

[0041] S102: constructing position error variables, velocity error variables and acceleration error variables;

[0042] S103: converting the error variables defined above into train error state space equations;

[0043] S104: Considering the dual constraints of the maximum communication distance and the minimum safety distance of the train, set the constraints that the train system state must meet;

[0044] S105: Based on the designed train system and state constraints, an adaptive robust controller is designed so that the maximum communication distance and minimum safety distance of the train group meet the constraints, and as the running time goes by, the train spacing and tracking error converge to the equilibrium point.

[0045] The single-point equation of a high-speed train is as follows:

[0046] (1)

[0047] in, , and Respectively represent i displacement, velocity, and acceleration of the train; , and It is Davis coefficients obtained from wind tunnel tests of trains; It is Control inputs for trains; It is a lumped disturbance composed of additional resistance and unknown external interference. Additional resistance includes curve resistance, slope resistance and tunnel resistance. The relationship between the following distance and communication distance between adjacent trains is as follows: Figure 3 shown.

[0048] The spacing error between adjacent trains can be expressed as: ;

[0049] in, Indicates train exist The location at the moment, Indicates train exist The location at the moment, It's a train With train Safe distance between

[0050] The displacement error variable is: ;

[0051] Speed ​​error variable: ;

[0052] in, represents the speed error, represents the acceleration error, Indicates train speed, Indicates train speed, Indicates train The acceleration of Indicates train acceleration;

[0053] In order to describe the dynamic evolution of the error, the error state is analyzed and defined as follows:

[0054] (2)

[0055] We can further obtain:

[0056] (3)

[0057] in, It represents a coefficient. Indicates train The basic resistance Indicates train The external resistance represents the expected acceleration;

[0058] Furthermore, to fully describe the coordinated behavior of the multi-train system, the error states of each train are combined into a global state, which is defined as follows:

[0059] (4)

[0060] In the formula is the global error state vector; is the output of the train actuator; It represents the sum of the continuous bounded unknown external lumped disturbance and the reference acceleration disturbance to which the train is subjected; A and is a train system matrix with appropriate dimensions. , and The matrices are the global input matrix and the constraint matrix respectively. Represents the total basic resistance.

[0061] More specifically, ;

[0062] in:

[0063] ;

[0064] ;

[0065] ;

[0066] ;

[0067] .

[0068] Considering the train spacing displacement condition, it is assumed that the constraints satisfied by the train system state are:

[0069] (5)

[0070] in, , It is the arithmetic mean of the maximum effective communication distance and the minimum safety interval between trains.

[0071] In order to ensure that the train spacing satisfies the above design constraints and that the train spacing and tracking error converge to an equilibrium point over time, the following adaptive robust controller needs to be designed:

[0072] (6)

[0073] The block diagram of the adaptive robust control structure of high-speed train is as follows: Figure 4 As shown in Figure 2, the design steps of the adaptive robust controller are as follows:

[0074] Assumptions ( A , F ) is stabilizable for any scalar and any positive definite matrix of appropriate dimension Q and R , Be pacable and observable.

[0075] Based on the previous step, there is a unique matrix This makes the following algebraic Riccati equation true:

[0076] ;

[0077] Further definition:

[0078] (7)

[0079] Therefore, the above Riccati equation can be rewritten as:

[0080] ;

[0081] This can facilitate the subsequent derivation of controller stability.

[0082] Set the maximum effective communication distance between trains to , the minimum dynamic safety interval is , taking the arithmetic mean of the two ,Right now:

[0083] (8)

[0084] speed and its derivatives With norm boundedness, there exists an unknown positive constant , and So that:

[0085] (9)

[0086] in, , Indicates unknown parameters;

[0087] In order to achieve the control goal of high-speed trains, an adaptive robust controller in the form of formula (6) is constructed, and then the controller expression is substituted into the error system formula (4) to obtain:

[0088] ;

[0089] Under the assumption that there is an unknown constant Make Under the condition that there is always an unknown positive constant have:

[0090] (10)

[0091] Thus, we can get the adaptive robust controller , and They are:

[0092] ;

[0093] ;

[0094] ;

[0095] in, express The maximum value of To meet the conditions Any positively bounded and uniformly continuous function under , and is an unknown parameter, and They correspond to their estimated values ​​respectively and satisfy the following adaptive rates:

[0096] (11)

[0097] (12)

[0098] In the formula and is any positive constant.

[0099] The parameters and The initial values ​​of are all set to positive numbers. From equations (11) and (12), we can get the parameters and Always positive.

[0100] definition and , we can get the following error system:

[0101] (13)

[0102] (14)

[0103] After the adaptive robust controller is designed, it is necessary to find a subset in which the state of the train system is in this subsystem for any initial conditions, and its state converges asymptotically to the origin. To this end, a Lyapunov function is designed and an obstacle function is introduced to solve the problem of the maximum communication distance and the minimum safety distance. For example, Figure 2 As shown, the design steps are as follows:

[0104] S201: Redefine the closed-loop system and error system of high-speed trains;

[0105] S202: Design a Lyapunov function, set the barrier function as the first term of the function, and when the state of the train error system containing the train spacing change is in an ellipsoidal domain, the Lyapunov function value is positive;

[0106] S203: Further derivation and scaling of the Lyapunov function prove that the train system error state converges to the ellipsoid domain, thereby strictly limiting the distance between trains to an appropriate range and ensuring the safety of train operation.

[0107] The specific steps for designing the barrier function are as follows:

[0108] The high-speed train closed-loop system and error system are defined as , and then design the following Lyapunov function:

[0109] (15)

[0110] The first term on the right side of the equal sign in formula (15) is the barrier function. represents the Lyapunov function.

[0111] Combining formula (4) with formulas (9)-(10), the derivative of the Lyapunov function is obtained:

[0112] (16)

[0113] Considering formula (16), the following inequality can be obtained by scaling:

[0114] (17)

[0115] (18)

[0116] From the error system formula (13) and formula (14), we can know that:

[0117] (19)

[0118] as well as:

[0119] (20)

[0120] According to formulas (17)-(20), formula (16) can be rewritten as the following inequality:

[0121] (twenty one)

[0122] in ; .

[0123] Choose any positive constant c , define the following set:

[0124] (twenty two)

[0125] (twenty three)

[0126] According to formulas (22) and (23), we can know that , as well as .

[0127] In the interval Integrating formula (21) above yields:

[0128] (twenty four)

[0129] We can further obtain:

[0130] (25)

[0131] (26)

[0132] According to formula (25), we can know that the function is uniformly bounded, and we can get The formula is uniformly continuous. Combining formula (26) and Barbalat's lemma, we can obtain:

[0133]

[0134] Obviously, .

[0135] So far, the initial conditions are satisfied , then the solution is uniformly bounded, and the train system state satisfies the constraints , , the train state converges asymptotically to the origin.

[0136] Simulation verification and analysis

[0137] 1) Simulation equipment and platform:

[0138] The computer CPU is 11th Gen Intel(R) Core(TM) i5-1135G7, 2.42GHz, Windows 10 Professional operating system, and the simulation platform is MATLAB R2024a

[0139] 2) To verify the effectiveness of the high-speed train tracking control method proposed in this embodiment under the dual constraints of train communication and safety distance based on the barrier function, simulation experiments are conducted on the performance of the proposed adaptive robust controller and the results of the simulation experiments are analyzed.

[0140] The basic parameters of the simulated high-speed train are shown as follows.

[0141] Table 1 Basic parameters of high-speed trains

[0142]

[0143] Assume that the total disturbance to which the high-speed train is subjected during operation is Has the following form:

[0144] ;

[0145] in , and They represent the slope resistance, tunnel resistance and curve resistance of the train, and , as well as ; The external unknown disturbance is set to ;" rand "express A random value between ; gravitational acceleration g =9.8N / kg.

[0146] Select , select , use MATLAB to solve the Riccati equation and solve the matrices P and K.

[0147] Assume that the initial state of the train spacing is , which means that the initial train spacing fluctuates up and down (within the maximum communication distance threshold constrained by the Radio Block Center (RBC) communication protocol) , and the minimum safety distance threshold derived from the multi-vehicle cooperative system dynamics model at a cruising speed of 350 km / h ), it is necessary to stabilize it to the stable range through automatic adjustment control. In addition, the parameter , , , , .

[0148] Figure 5 is the expected speed tracking trajectory diagram of the high-speed train, Figure 6 The expected displacement tracking trajectory of the high-speed train is obtained through simulation. The curves of the train spacing change, speed tracking error, and system state trajectory change under the adaptive control method are as follows: Figure 7-10 As shown. Figure 7 and Figure 8 As can be seen from the figure, the proposed control method effectively ensures that the train spacing meets the constraints. Even if the train spacing is initially too large or too small, it will eventually converge to a near-equilibrium point over time under the proposed adaptive control method. The train can adjust the spacing based on actual operating conditions, ensuring the coordination and consistency of the overall train operation. High-precision tracking can be achieved even under uncertain environmental factors, providing passengers with a smoother and more comfortable ride.

[0149] from Figure 9-10 As can be seen from the figure, for a given target speed, the proposed control method can accurately track the train spacing and converge to zero in a short period of time. The speed tracking error under the proposed control method fluctuates very little, which can ensure the smoothness of the train during operation to a certain extent. It has strong anti-interference ability and can effectively ensure the safety of train operation.

Claims

1. A high-speed train group control method based on tracking and communication distance constraints, characterized in that The steps include: Establish a dynamic model of the high-speed train in equilibrium state, and based on this dynamic model, construct an error system model of the high-speed train; Considering the constraints of train running distance and setting the constraints that the train system state must meet, an adaptive robust controller is designed; The barrier function is introduced into the Lyapunov function to solve the problem of limited running distance of high-speed trains; The design method of the adaptive robust controller includes the following steps: Establish A single-mass dynamics model of a high-speed train is proposed, and the position and speed signals of each train are measurable; Construct high-speed train position error variables and speed error variables; Convert the defined error variables into train error state space equations; Considering the dual constraints of the maximum communication distance and the minimum safety distance of the train, the constraints that the train system state must meet are set; Based on the designed train system and state constraints, an adaptive robust controller is designed to ensure that the maximum communication distance and minimum safety distance of the train group meet the constraints, and that the train spacing and tracking error converge to an equilibrium point over time. The single-particle dynamic model of a high-speed train is: ； in, , and denote the displacement, velocity and acceleration of the i-th train respectively; , and It is Davis coefficients obtained from wind tunnel tests of trains; It is Control inputs for trains; It is the lumped disturbance composed of additional resistance and unknown external disturbance. The additional resistance includes curve resistance, slope resistance and tunnel resistance. By comparing the position, velocity and acceleration differences of adjacent trains, an error variable is defined : ； Indicates train exist The location at the moment, Indicates train exist The location at the moment, It's a train With train Safe distance between In order to analyze its dynamic changes, the velocity error and acceleration error are further defined as follows: ； in, represents the speed error, represents the acceleration error, Indicates train speed, Indicates train speed, Indicates train The acceleration of Indicates train acceleration; In order to describe the dynamic evolution of the error, the error state is analyzed and defined as follows: ； Further we get: ； ； It represents a coefficient. Indicates train The basic resistance Indicates train The external resistance represents the expected acceleration; The error states of each train are combined into a global state, and the train error state space equation is constructed, which is defined as follows: ； in, is the global error state vector; is the output of the train actuator; represents the sum of the continuous bounded unknown external lumped disturbance and the reference acceleration disturbance to which the train is subjected; A and is a train system matrix of appropriate dimension, where , and The matrices are the global input matrix and the constraint matrix, represents the total basic resistance; The method for designing an adaptive robust controller includes the following steps: Assume that the constraints satisfied by the train system state are: ， ； Among them, the collection , It is the arithmetic mean of the maximum effective communication distance and the minimum safety interval between trains; To ensure that the train spacing satisfies the constraints of the above design and that the train spacing and tracking error converge to the equilibrium point over time, the following adaptive robust controller is designed: ； in, It is adaptive by design; The method for designing an adaptive robust controller includes the following steps: set up( A , F ) is stabilizable for any scalar and any positive definite matrix of appropriate dimension Q and R , is pacifiable and observable; There exists a unique matrix , so that the following algebraic Riccati equation holds: ； Further definition: ； The above Riccati equation can be reformulated as: ； Set the maximum effective communication distance between trains to , the minimum dynamic safety interval is , taking the arithmetic mean of the two ,Right now: ； speed and its derivatives With norm boundedness, there exists an unknown positive constant , and So that: ； in, , Indicates unknown parameters; Construct an adaptive robust controller: ； Then, the controller expression is substituted into the error state equation to obtain: ； In the presence of an unknown constant Make Under the condition that there is always an unknown positive constant have: ； in, express The maximum value of Get the controller , and They are: ； ； ； in To meet the conditions Any positively bounded and uniformly continuous function under , and is an unknown parameter, and They correspond to their estimated values ​​respectively and satisfy the following adaptive rates: ； ； in, and is any positive constant; The parameters and The initial values ​​of are all set to positive numbers, and the parameters and is always positive; definition and , we can get the following error system: ； 。 2. The high-speed train group control method based on tracking and communication distance constraints according to claim 1, characterized in that: Find a subset in which the state of the train system is in this subsystem for any initial conditions, and its state converges asymptotically to the origin. For this purpose, a Lyapunov function is designed and an obstacle function is introduced to solve the problem of the maximum communication distance and the minimum safety distance being limited.

3. The high-speed train group control method based on tracking and communication distance constraints according to claim 2, characterized in that: The method for solving the problem of the maximum communication distance and the minimum safety distance being limited includes the following steps: Redefine the closed-loop system and error system of high-speed trains; A Lyapunov function is designed, and the barrier function is set as the first term of the Lyapunov function. When the state of the train error system containing the train spacing variation is in an ellipsoidal domain, the Lyapunov function value is positive. By derivatizing and scaling the Lyapunov function, it is proved that the error state of the train system converges to the ellipsoid domain, and the distance between trains is strictly limited to an appropriate range.

4. The high-speed train group control method based on tracking and communication distance constraints according to claim 3, characterized in that: Find a subset , so that any initial condition , the state of the high-speed train error system always remains in the subset and can converge asymptotically to the origin; Design the Lyapunov function to find the above ellipsoidal domain: ； The designed Lyapunov function is as follows: ； The first term on the right side of the equal sign is the barrier function. represents the Lyapunov function.

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