Novel dynamic surface funnel control method for high-speed train with time delay and saturation

Abstract

The invention discloses a novel dynamic surface funnel control method for a high-speed train with time delay and saturation, and relates to the technical field of high-speed train control, and the method comprises the steps: constructing a high-speed train longitudinal dynamic model with input time delay and input saturation; defining a displacement tracking error and a speed tracking error of the high-speed train; respectively setting funnel boundaries for the displacement tracking error and the speed tracking error based on a dynamic funnel boundary function; constructing a Lyapunov function, and constructing a virtual control law and a nonlinear filter; determining an actual control law of the high-speed train according to the high-speed train longitudinal dynamic model with input time lag and input saturation, the filtered virtual control law and the speed tracking error; the influence of input time lag on system performance is effectively solved, high-precision tracking control of the train is achieved under the non-saturation condition, meanwhile, the system can still be kept stable when saturation occurs, and therefore the control reliability and stability of the high-speed train under different working conditions are improved.

Description

Technical Field

[0001] This application relates to the field of high-speed train control technology, and in particular to a novel dynamic surface funnel control method for high-speed trains with time delay and saturation. Background Technology

[0002] The high-speed train control system is the core of ensuring train operation safety and realizing intelligent operation and maintenance of the train system. Its performance directly affects transportation capacity and passenger experience. However, high-speed trains face many challenges in complex operating environments, such as model uncertainty, external disturbances, and actuator constraints. Among these, time delay and actuator saturation effects in the control system are particularly prominent, significantly reducing the system's response speed and control accuracy, and even threatening train operation safety. Therefore, researching train control methods under time delay and saturation constraints is of great significance for achieving accurate and reliable control of high-speed trains.

[0003] Dynamic surface control, as a recursive design framework, utilizes structured decomposition and filtering techniques to ensure system tracking accuracy and stability under parameter uncertainty and external disturbances. It also offers unique advantages in facilitating integration with other control methods. In high-speed train control systems, input time delay and parameter uncertainty significantly impact system dynamic performance. Input saturation, caused by the physical limitations of actuators, is a widespread nonlinear constraint closely related to engineering practice and can potentially worsen along with time delay issues. Therefore, designing a dynamic surface control strategy to address the simultaneous challenges of input time delay and input saturation in high-speed train operation, thereby improving the safety, reliability, and stability of high-speed trains under complex operating conditions, is essential in this field. Summary of the Invention

[0004] The purpose of this application is to provide a novel dynamic surface funnel control method for high-speed trains with time delay and saturation. This method can effectively solve the impact of input time delay on system performance, effectively compensate for and constrain the uncertainties caused by input time delay and saturation, achieve high-precision tracking control of the train in the absence of saturation, and maintain system stability when saturation occurs, thereby improving the control reliability and stability of high-speed trains under different operating conditions.

[0005] To achieve the above objectives, this application provides the following solution: This application provides a novel dynamic surface funnel control method for high-speed trains with time delay and saturation. The novel dynamic surface funnel control method for high-speed trains with time delay and saturation includes: Force analysis is performed on a high-speed train to construct a longitudinal dynamic model of the high-speed train with input time delay and input saturation. The longitudinal dynamic model of the high-speed train with input time delay and input saturation is used to characterize the relationship between the actual control law of the high-speed train, the basic resistance experienced by the high-speed train, and the running speed, displacement, and time of the high-speed train. The actual control law is the control command sent by the control system to the actuator, and the actuator generates the traction force or braking force of the high-speed train according to the control command. Based on the longitudinal dynamics model of the high-speed train with input time delay and input saturation, the displacement tracking error and speed tracking error of the high-speed train are defined, and a time delay compensation term is introduced into the speed tracking error; the displacement tracking error is used to characterize the error between the running displacement of the high-speed train and the ideal displacement curve, and the speed tracking error is used to characterize the error between the running speed of the high-speed train and the filtered virtual control law and the time delay compensation dynamic variable. Based on a dynamic funnel boundary function, funnel boundaries are set for the displacement tracking error and the velocity tracking error, respectively. The funnel boundaries are used to limit the maximum range of the displacement tracking error and the velocity tracking error. The dynamic funnel boundary function is used to adaptively adjust the boundary width of the funnel boundary according to the effectiveness of input saturation. Based on the displacement tracking error and the dynamic funnel boundary function, a Lyapunov function is constructed. When the constraint conditions are met, a virtual control law is constructed based on the Lyapunov function. A nonlinear filter is constructed based on the virtual control law, and the virtual control law is input into the nonlinear filter to obtain the filtered virtual control law. The actual control law of the high-speed train is determined based on the longitudinal dynamics model of the high-speed train with input time delay and input saturation, the filtered virtual control law, and the speed tracking error.

[0006] In one embodiment, the step of performing force analysis on the high-speed train to construct a longitudinal dynamic model of the high-speed train with input time delay and input saturation includes: A force analysis is performed on the high-speed train, and a dynamic model of the high-speed train is constructed based on the force analysis results; wherein, the dynamic model of the high-speed train is: ; In the formula, This indicates the total mass of the high-speed train; Indicates the operating speed of high-speed trains; Indicates the displacement of a high-speed train; This indicates the traction / braking force acting on the train; This represents the basic resistance experienced by a high-speed train during operation; among which, , A coefficient representing the basic resistance; By introducing an input time delay into the high-speed train dynamics model, a high-speed train dynamics model with input time delay is obtained; wherein, the high-speed train dynamics model with input time delay is: ; In the formula, ; ; Indicates input delay. ; A saturation function is added to the high-speed train dynamics model with input time delay to limit the train's control input within the actuator's input saturation limit, thus obtaining the high-speed train longitudinal dynamics model with input time delay and input saturation; wherein, the saturation function is: ; In the formula, Represents a saturation function. Indicates the input saturation limit; The longitudinal dynamics model of the high-speed train with input time delay and input saturation is as follows: .

[0007] In one embodiment, the expression for the displacement tracking error is: ; In the formula, Indicates displacement tracking error. Represents the ideal displacement curve; The expression for the speed tracking error is: ; In the formula, Indicates speed tracking error. This represents the filtered virtual control law; This represents the time delay compensation term; where, .

[0008] In one embodiment, the dynamic funnel boundary function is: ; ; in, and Displacement tracking error and speed tracking error The funnel boundary function, , , , When the input is saturated and valid, When input saturation is invalid, .

[0009] In one embodiment, the Lyapunov function is The constraint condition is that the derivative of the Lyapunov function is less than or equal to zero.

[0010] In one embodiment, constructing the virtual control law based on the Lyapunov function includes: differentiating the Lyapunov function; when the derivative of the Lyapunov function is less than or equal to zero, the virtual control law is obtained; wherein, the virtual control law is: ; In the formula, To control the gain, .

[0011] In one embodiment, the expression for the nonlinear filter is: ; In the formula, For novel dynamic surface boundary layer errors; For filter parameters The estimated value; The time constant of the filter; Let be a positive, known, continuous, and bounded function that satisfies: ; In the formula, , It is a positive constant.

[0012] In one embodiment, the method for determining the estimated values ​​of filter parameters includes: Define compact set and The compact set and The expression is: ; In the formula, Given a positive constant, in There exists a positive one. satisfy ; Error of novel dynamic surface boundary layer Differentiate: ; In the formula, A known continuous function consisting of derivatives of a virtual control law; Using the estimated values ​​of filter parameters Estimating filter parameters ,and Adaptive law as follows: ; In the formula, The design parameters are positive.

[0013] In one embodiment, the expression for the actual control law of the high-speed train is: ; In the formula, Indicates control gain. ; This represents the unknown function to be estimated.

[0014] In one embodiment, the method further includes using an RBF neural network to estimate the unknown function. unknown function The expression is: ; in: Represents the weights of the neural network. Represents the Gaussian radial basis function vector. Let be the approximation error of the neural network; where the Gaussian radial basis function is: ; in: Let be the coordinate vector of the center point of the Gaussian radial basis function. Let be the width of the Gaussian radial basis function. These are the weights of the neural network.

[0015] According to the specific embodiments provided in this application, the following technical effects are disclosed: This application provides a novel dynamic funnel control method for high-speed trains with time delay and saturation. First, a longitudinal dynamic model of the high-speed train with input time delay and saturation is established through force analysis. Second, dynamic compensation is designed by defining the displacement tracking error and speed tracking error of the high-speed train, and a constraint mechanism is designed based on the boundary function of the dynamic funnel, solving the dual constraint problem of time delay and saturation. Then, by constructing a Lyapunov function and a virtual control law, the tracking error is always limited within the dynamic funnel boundary, and asymptotic tracking is achieved after saturation is removed. This method effectively addresses the impact of input time delay on system performance, effectively compensates for and constrains the uncertainties caused by input time delay and saturation, achieves high-precision tracking control of the train in the absence of saturation, and maintains system stability even when saturation occurs, thereby improving the control reliability and stability of high-speed trains under different operating conditions. Attached Figure Description

[0016] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0017] Figure 1 This is a flowchart illustrating a novel dynamic surface funnel control method for high-speed trains with time delay and saturation in one embodiment of this application. Figure 2 The displacement tracking and error curves of a high-speed train simulation experiment without input saturation in the application scenario of this application; Figure 3 The speed tracking and error curves of a high-speed train simulation experiment without input saturation in the application scenario of this application; Figure 4 The train input signal curve for a high-speed train simulation experiment without input saturation in the application scenario of this application; Figure 5 The displacement tracking and error curves of the high-speed train simulation experiment in the application scenario of this application do not consider input saturation; Figure 6 The application scenario in this application does not consider the speed tracking and error curves of high-speed train simulation experiments under input saturation. Figure 7 The displacement tracking and error curve of the high-speed train simulation experiment under input saturation in the application scenario of this application; Figure 8 The application scenario of this application considers the speed tracking and error curve of a high-speed train simulation experiment under input saturation. Figure 9 The train input signal curve is shown in the high-speed train simulation experiment considering input saturation in the application scenario of this application. Detailed Implementation

[0018] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0019] To make the above-mentioned objectives, features and advantages of this application more apparent and understandable, the application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0020] like Figure 1 As shown, this application provides a novel dynamic surface funnel control method for high-speed trains with time delay and saturation. In the embodiments of this application, the novel dynamic surface funnel control method for high-speed trains with time delay and saturation includes the following steps S101 to S106. Wherein: Step S101: Perform force analysis on the high-speed train to construct a longitudinal dynamic model of the high-speed train with input time delay and input saturation. The longitudinal dynamic model of the high-speed train with input time delay and input saturation is used to characterize the relationship between the actual control law of the high-speed train, the basic resistance experienced by the high-speed train, and the running speed, displacement, and time of the high-speed train. The actual control law is the control command sent by the control system (controller) to the execution system (actuator). The execution system (actuator) generates the traction force or braking force of the high-speed train according to the control command.

[0021] In step S101 of this application embodiment, the step of performing force analysis on the high-speed train to construct a longitudinal dynamic model of the high-speed train with input time delay and input saturation includes the following steps S201 to S203. Wherein: Step S201: Perform a force analysis on the high-speed train and construct a dynamic model of the high-speed train based on the force analysis results; wherein, the dynamic model of the high-speed train is: ; In the formula, This indicates the total mass of the high-speed train; Indicates the operating speed of high-speed trains; Indicates the displacement of a high-speed train; This indicates the traction / braking force acting on the train; This represents the fundamental resistance experienced by a high-speed train during operation. It can be understood that the forces acting on a high-speed train during operation are the fundamental resistance and the train's traction / braking force; the resultant force of these two determines the train's motion state. Then, by analyzing the relationship between the forces acting on the train and its speed, displacement, and time, a dynamic model of the high-speed train's operation is obtained. Furthermore, the fundamental resistance experienced by the high-speed train during operation is related to the train's speed... The relationship is quadratic, and the specific expression is: , A coefficient representing the basic resistance.

[0022] Step S202: Introduce an input time delay into the high-speed train dynamics model to obtain a high-speed train dynamics model with input time delay; wherein, the high-speed train dynamics model with input time delay is: ; In the formula, ; ; Indicates input delay. .

[0023] Considering that the input time delay in the control system originates from dynamically changing internal and external conditions during train operation: firstly, the quality of vehicle-to-ground wireless communication varies with the environment, causing fluctuations in information transmission delay; secondly, the response characteristics of the traction / braking system change with train speed, load, and equipment status (such as temperature). These factors collectively contribute to the total control input time delay. It manifests as a quantity that varies over time, and its range and pattern of variation can be estimated through historical data or mechanistic analysis. To ensure consistency with traditional control systems, this application uses... To represent control input signals Furthermore, in order to represent time-varying and time-delay input signals, this paper applies to further... Revised to , Thus, the high-speed train dynamics model with input time delay in step S202 is obtained.

[0024] Furthermore, given the physical limitations of the actuators during high-speed train operation, this application adds a saturation function to the aforementioned high-speed train dynamics model with input time delay, so that the control input of the high-speed train is limited within the input saturation limit of the actuator, as shown in step S203.

[0025] Step S203: Add a saturation function to the high-speed train dynamics model with input time delay, so that the train's control input is limited within the actuator's input saturation limit, to obtain the high-speed train longitudinal dynamics model with input time delay and input saturation; wherein, the saturation function is: ; In the formula, Represents a saturation function. This indicates the input saturation limit.

[0026] The longitudinal dynamics model of the high-speed train with input time delay and input saturation is as follows: .

[0027] Step S102: Define the displacement tracking error and speed tracking error of the high-speed train according to the longitudinal dynamics model of the high-speed train with input time delay and input saturation, and introduce a time delay compensation term into the speed tracking error; the displacement tracking error is used to characterize the error between the running displacement of the high-speed train and the ideal displacement curve, and the speed tracking error is used to characterize the error between the running speed of the high-speed train and the filtered virtual control law and the time delay compensation dynamic variable.

[0028] In step S102 of this embodiment, the expression for the displacement tracking error is: ; In the formula, Indicates displacement tracking error. Represents the ideal displacement curve; The expression for the speed tracking error is: ; In the formula, Indicates speed tracking error. This represents the filtered virtual control law; This represents the time delay compensation term; where, , This represents a time-delay compensation dynamic variable that can be updated online, and it is directly used to update the system's velocity tracking error. .

[0029] Step S103: Set funnel boundaries for the displacement tracking error and the velocity tracking error respectively based on the dynamic funnel boundary function. The funnel boundaries are used to limit the maximum range of the displacement tracking error and the velocity tracking error. The dynamic funnel boundary function is used to adaptively adjust the boundary width of the funnel boundary according to the effectiveness of input saturation.

[0030] In step S103 of this application embodiment, the dynamic funnel boundary function is: ; ; in, and Displacement tracking error and speed tracking error The funnel boundary function, , , , When the input is saturated and valid, When input saturation is invalid, .

[0031] Since the displacement tracking error of high-speed trains is affected by the speed tracking error, and the speed variation of high-speed trains is determined by the power system, this application designs a dynamic funnel boundary that can change with the tracking error to ensure that the increased tracking error when the system input is saturated is still confined within the funnel boundary in order to ensure that the tracking error remains within the funnel boundary. Funnel boundary function In The effectiveness of saturation is determined when satisfy When saturation is effective, then the value is positive. make funnel The boundary is widened, thus making it more compatible with... Coupled funnel The boundary is forced to widen, thus ensuring that displacement and speed tracking errors under train input saturation conditions are limited within the funnel's boundary. If the system does not experience saturation, Then the funnel boundary reverts to the classic funnel shape: When a system saturation shock occurs, the dynamic funnel boundary design causes the funnel boundary to widen instantaneously to buffer the impact, thereby improving the stability of the controller during saturation.

[0032] Step S104: Construct a Lyapunov function based on the displacement tracking error and the dynamic funnel boundary function. When the constraint conditions are met, construct a virtual control law based on the Lyapunov function.

[0033] In step S104 of this application embodiment, the Lyapunov function is The constraint condition satisfied by the Lyapunov function is that the derivative of the Lyapunov function is less than or equal to zero. It should be noted that when the displacement tracking error... Approaching the boundary of the funnel hour, It tends towards infinity; therefore, as long as the derivative of the Lyapunov function is negative, the displacement tracking error is naturally guaranteed. Unable to reach the edge of the funnel This will reduce displacement tracking error. It is strictly confined inside the funnel.

[0034] In this embodiment of the application, the construction of the virtual control law based on the Lyapunov function includes: Differentiating the Lyapunov function, the virtual control law is obtained when the derivative of the Lyapunov function is less than or equal to zero; where: Differentiating the Lyapunov function yields: ; In order to make The virtual control law designed in this application is as follows: ; In the formula, To control the gain, The dynamic gain and displacement tracking error and dynamic funnel By linking these elements, the core feedback mechanism of the dynamic surface is upgraded from "linear" to "non-linear," enabling the controller to self-optimize based on the system's real-time displacement tracking error. When input saturation occurs, and The ratio decreases, making The gain is reduced to prevent the controller from saturating further.

[0035] Step S105: Construct a nonlinear filter based on the virtual control law, input the virtual control law into the nonlinear filter, and obtain the filtered virtual control law.

[0036] In step S105 of this embodiment, the expression for the nonlinear filter is: ; In the formula, For novel dynamic surface boundary layer errors; For filter parameters The estimated value; The time constant of the filter; Let be a positive, known, continuous, and bounded function that satisfies: ; In the formula, , It is a positive constant.

[0037] To avoid "differential explosion" and prove that the derivative of the virtual control law is bounded, the method for determining the estimated values ​​of the filter parameters in this application embodiment includes: Define compact set and The compact set and The expression is: ; In the formula, Given a positive constant, in There exists a positive one. satisfy ; Error of novel dynamic surface boundary layer Differentiate: ; In the formula, A known continuous function consisting of derivatives of a virtual control law; Using the estimated values ​​of filter parameters Estimating filter parameters ,and ; According to the lemma: for any and There is an inequality: It can be known that ; For online estimation of upper bound Adaptive law as follows: : In the formula, The design parameter is positive. This formula enables the novel dynamic surface to quickly and stably suppress boundary layer errors. This ensures that the system tracking error asymptotically converges to zero, thereby improving the transient control performance.

[0038] Step S106: Determine the actual control law of the high-speed train based on the longitudinal dynamics model of the high-speed train with input time delay and input saturation, the filtered virtual control law, and the speed tracking error.

[0039] Since the definition of train speed tracking error is: Among them, time delay compensation item satisfy Differentiating the definition of train speed tracking error yields: ; Based on the derivative, the expression for the actual control law of the high-speed train can be obtained as follows: ; In the formula, Indicates control gain. ; This represents the unknown function to be estimated.

[0040] In step S106 of the embodiments of this application, the unknown function is estimated using an RBF neural network. unknown function The expression is: ; in: Represents the weights of the neural network. Represents the Gaussian radial basis function vector. Let be the approximation error of the neural network; where the Gaussian radial basis function is: ; in: Let be the coordinate vector of the center point of the Gaussian radial basis function. Let be the width of the Gaussian radial basis function. These are the weights of the neural network.

[0041] Therefore, the actual control law in step S106 can be rewritten as: ; The adaptive law design for neural network weights and neural network error is as follows: ; ;in, , These are positive design parameters. , for , The estimated value, and , .

[0042] By implementing steps S101 to S106 above, this application first establishes a longitudinal dynamic model of a high-speed train with input time delay and saturation through force analysis. Second, by defining the displacement tracking error and speed tracking error of the high-speed train and designing dynamic compensation, and by designing a constraint mechanism based on the dynamic funnel boundary function, the dual constraint problem of time delay and saturation is solved. Then, by constructing a Lyapunov function and a virtual control law, the tracking error is always limited within the dynamic funnel boundary, and asymptotic tracking is achieved after saturation is removed. This method effectively solves the impact of input time delay on system performance, effectively compensates for and constrains the uncertainties caused by input time delay and saturation, and achieves high-precision tracking control of the train in the absence of saturation, while maintaining system stability even when saturation occurs, thereby improving the control reliability and stability of the high-speed train under different operating conditions.

[0043] This application also provides an application scenario in which the aforementioned novel dynamic surface funnel control method for high-speed trains exhibiting time delay and saturation is applied. Specifically, this embodiment uses a CRH380AL EMU as the controlled object for simulation verification. The parameter table of the CRH380AL EMU is shown in Table 1. This application selects the actual displacement of a CRH380AL EMU from Jinan to Xuzhou. With speed The curve serves as the target curve. For example... Figure 2 As shown, the total simulation run time is 3160 seconds. Figure 3 As shown, there are three operating conditions during train operation: traction, constant speed, and braking.

[0044] Table 1: Simulation parameters of CRH380AL EMU

[0045] In this embodiment, the simulation experiments include high-speed train simulation experiments without input saturation, high-speed train simulation experiments without considering input saturation, and high-speed train simulation experiments considering input saturation; the simulation results include displacement curves, displacement error curves, speed curves, speed error curves, and train input signal curves. Wherein: High-speed train simulation experiment without input saturation: From simulation results Figure 2It can be seen that, without saturation, the train displacement tracking error remains stable within the centimeter level; from Figure 3 It can be seen that the speed tracking error is stable within the millimeter level; from Figure 4 As can be seen, the train input signal remains smooth and continuous, further demonstrating the good operating condition of the control system. Based on the above simulation results... Figure 2 , Figure 3 and Figure 4 As can be seen, this application effectively suppresses the negative impact of input time delay, and the system tracking error can quickly converge to the ideal range and remain dynamically stable, verifying the effectiveness of the time delay compensation method.

[0046] High-speed train simulation experiment without considering input saturation: To fully verify the robustness and engineering applicability of the control strategy proposed in this application, the input time delay of the control system was set to... The design is based on two main considerations: First, the time delay amplitude varies periodically between 0 and 0.2 seconds, simulating the time-varying delay caused by communication and signal processing in actual control systems; second, absolute value calculation ensures the non-negativity of the time delay, and the 0.2-second amplitude corresponds to a time delay magnitude with significant impact in high-speed train control, constituting a rigorous verification condition. This time-varying time delay condition is more complex than a constant time delay, enabling a more comprehensive test of the dynamic adaptability of the designed compensation mechanism, thus demonstrating the effectiveness and superiority of this application in dealing with creep time delays. Therefore, the dynamic variable for input time delay compensation is designed as follows: The nonlinear filter design parameters are as follows: , The parameters of the dynamic funnel are designed as follows: , , , , The adaptive law parameters are designed as follows: , , .

[0047] Simulation experiments were conducted based on the controller parameters mentioned above: When the train actuator malfunctions and can provide a maximum force of 200,000 N, the saturation ratio reaches 11.4% compared to the input value before saturation. If the input saturation signal is not processed, the following simulation results of train tracking error are obtained.

[0048] from Figure 5 It can be seen that after a slight input saturation occurred during the train traction phase, the train displacement tracking error increased significantly. During the constant speed operation phase, the displacement tracking error reached the kilometer level; upon entering the braking phase, the displacement error further increased to approximately five kilometers, indicating that the train had completely deviated from the desired position. From Figure 6As can be seen, even slight input saturation during the traction phase leads to a significant deterioration in train speed tracking: the speed tracking error fluctuates continuously around 20 m / s during the constant speed phase, and the peak error during the braking phase approaches 40 m / s; furthermore, the train does not stop even when the desired speed drops to zero. These simulation results demonstrate that without active handling of input saturation, its nonlinear effects severely damage the tracking capability and stability of the closed-loop system. To verify the effectiveness of this strategy, simulation results under the same conditions will be presented and analyzed below.

[0049] High-speed train simulation experiment considering input saturation: The simulation results from the high-speed train simulation experiment without considering input saturation show that without addressing input saturation, the system's tracking performance will severely deteriorate, directly jeopardizing train operation safety. To verify the effectiveness of the control strategy proposed in this application in handling time delay and saturation problems, a simulation experiment was conducted using this controller under the same operating conditions. The simulation results are as follows: Figures 7 to 9 As shown.

[0050] In the case of input time delay and saturation coexisting in high-speed train systems, from Figure 7 The displacement tracking and error curves show that even during the brief period of mild saturation in the traction phase and the deep saturation lasting up to 77 seconds in the braking phase, the system remained stable. Although the displacement tracking error increased during the saturation period, with the peak error exceeding 40 m in the braking phase, the displacement tracking error quickly converged to the centimeter level once the saturation was released, indicating that the controller still possesses rapid recovery and high-precision tracking capabilities under saturation constraints.

[0051] from Figure 8 As can be seen from the speed tracking and error curves, the speed tracking error converges rapidly during the traction phase. Although the error fluctuation increases due to the increased input saturation during the train braking phase, with a peak value of about 4 m / s, the speed tracking error converges to the centimeter level within 22 seconds after the input saturation is released, which once again verifies the strong robustness of this application under time-varying saturation conditions.

[0052] from Figure 9 As can be seen from the train input signal curve, under the constraint condition that the train actuator provides a maximum of 200,000 N, the controller always strictly limits the input signal within the actuator's saturation amplitude. This further proves that the controller designed in this application not only actively avoids oversaturation, but also maintains system stability during saturation and quickly restores tracking performance after saturation is released.

[0053] In summary, the simulation results consistently demonstrate that this application achieves high-performance control under complex constraints through the synergistic design of time delay compensation and saturation suppression: the system can still maintain closed-loop stability when input saturation occurs; and the tracking error can quickly converge to centimeter-level accuracy after saturation is removed.

[0054] In one exemplary embodiment, a computer device is also provided, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps in the above-described method embodiments.

[0055] In one exemplary embodiment, a computer-readable storage medium is provided storing a computer program that, when executed by a processor, implements the steps in the above-described method embodiments.

[0056] In one exemplary embodiment, a computer program product is provided, including a computer program that, when executed by a processor, implements the steps in the above-described method embodiments.

[0057] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, data stored, data displayed, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties, and the collection, use and processing of the relevant data must comply with relevant regulations.

[0058] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium. When executed, the computer program can include the processes of the embodiments described above. Any references to memory, databases, or other media used in the embodiments provided in this application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM can take many forms, such as Static Random Access Memory (SRAM) or Dynamic Random Access Memory (DRAM).

[0059] The databases involved in the embodiments provided in this application may include at least one type of relational database and non-relational database. Non-relational databases may include, but are not limited to, blockchain-based distributed databases. The processors involved in the embodiments provided in this application may be general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic devices, quantum computing-based data processing logic devices, etc., and are not limited to these.

[0060] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0061] This document uses specific examples to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this application. Furthermore, those skilled in the art will recognize that, based on the ideas of this application, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A novel dynamic surface funnel control method for high-speed trains with time delay and saturation, characterized in that, The novel dynamic surface funnel control method for high-speed trains with time delay and saturation includes: Force analysis is performed on a high-speed train to construct a longitudinal dynamic model of the high-speed train with input time delay and input saturation. The longitudinal dynamic model of the high-speed train with input time delay and input saturation is used to characterize the relationship between the actual control law of the high-speed train, the basic resistance experienced by the high-speed train, and the running speed, displacement, and time of the high-speed train. The actual control law is the control command sent by the control system to the actuator, and the actuator generates the traction force or braking force of the high-speed train according to the control command. Based on the longitudinal dynamics model of the high-speed train with input time delay and input saturation, the displacement tracking error and speed tracking error of the high-speed train are defined, and a time delay compensation term is introduced into the speed tracking error; the displacement tracking error is used to characterize the error between the running displacement of the high-speed train and the ideal displacement curve, and the speed tracking error is used to characterize the error between the running speed of the high-speed train and the filtered virtual control law and the time delay compensation dynamic variable. Based on a dynamic funnel boundary function, funnel boundaries are set for the displacement tracking error and the velocity tracking error, respectively. The funnel boundaries are used to limit the maximum range of the displacement tracking error and the velocity tracking error. The dynamic funnel boundary function is used to adaptively adjust the boundary width of the funnel boundary according to the effectiveness of input saturation. Based on the displacement tracking error and the dynamic funnel boundary function, a Lyapunov function is constructed. When the constraint conditions are met, a virtual control law is constructed based on the Lyapunov function. A nonlinear filter is constructed based on the virtual control law, and the virtual control law is input into the nonlinear filter to obtain the filtered virtual control law. The actual control law of the high-speed train is determined based on the longitudinal dynamics model of the high-speed train with input time delay and input saturation, the filtered virtual control law, and the speed tracking error.

2. The novel dynamic surface funnel control method for high-speed trains with time delay and saturation as described in claim 1, characterized in that, The force analysis of the high-speed train to construct a longitudinal dynamic model of the high-speed train with input time delay and input saturation includes: A force analysis is performed on the high-speed train, and a dynamic model of the high-speed train is constructed based on the force analysis results; wherein, the dynamic model of the high-speed train is: ； In the formula, This indicates the total mass of the high-speed train; Indicates the operating speed of high-speed trains; Indicates the displacement of a high-speed train; This indicates the traction / braking force acting on the train; This represents the basic resistance experienced by a high-speed train during operation; among which, , A coefficient representing the basic resistance; By introducing an input time delay into the high-speed train dynamics model, a high-speed train dynamics model with input time delay is obtained; wherein, the high-speed train dynamics model with input time delay is: ； In the formula, ; ; Indicates input delay. ; A saturation function is added to the high-speed train dynamics model with input time delay to limit the train's control input within the actuator's input saturation limit, thus obtaining the high-speed train longitudinal dynamics model with input time delay and input saturation; wherein, the saturation function is: ； In the formula, Represents the saturation function. Indicates the input saturation limit; The longitudinal dynamics model of the high-speed train with input time delay and input saturation is as follows: 。 3. The novel dynamic surface funnel control method for high-speed trains with time delay and saturation as described in claim 2, characterized in that, The expression for the displacement tracking error is: ； In the formula, Indicates displacement tracking error. Represents the ideal displacement curve; The expression for the speed tracking error is: ； In the formula, Indicates speed tracking error. This represents the filtered virtual control law; This represents the time delay compensation term; where, .

4. The novel dynamic surface funnel control method for high-speed trains with time delay and saturation as described in claim 1, characterized in that, The boundary function of the dynamic funnel is: ； ； in, and Displacement tracking error and speed tracking error The funnel boundary function, , , , When the input is saturated and valid, When input saturation is invalid, .

5. The novel dynamic surface funnel control method for high-speed trains with time delay and saturation as described in claim 4, characterized in that, The Lyapunov function is The constraint condition is that the derivative of the Lyapunov function is less than or equal to zero.

6. The novel dynamic surface funnel control method for high-speed trains with time delay and saturation as described in claim 5, characterized in that, The construction of the virtual control law based on the Lyapunov function includes: differentiating the Lyapunov function; when the derivative of the Lyapunov function is less than or equal to zero, the virtual control law is obtained; wherein, the virtual control law is: ； In the formula, To control the gain, .

7. The novel dynamic surface funnel control method for high-speed trains with time delay and saturation as described in claim 6, characterized in that, The expression for the nonlinear filter is: ； In the formula, For novel dynamic surface boundary layer errors; For filter parameters The estimated value; The time constant of the filter; Let be a positive, known, continuous, and bounded function that satisfies: ； In the formula, , It is a positive constant.

8. The novel dynamic surface funnel control method for high-speed trains with time delay and saturation as described in claim 7, characterized in that, Methods for determining the estimated values ​​of filter parameters include: Define compact set and The compact set and The expression is: ； In the formula, Given a positive constant, in There exists a positive one. satisfy ; Error of novel dynamic surface boundary layer Differentiate: ； In the formula, A known continuous function consisting of derivatives of a virtual control law; Using the estimated values ​​of filter parameters Estimating filter parameters ,and Adaptive law as follows: ； In the formula, The design parameters are positive.

9. The novel dynamic surface funnel control method for high-speed trains with time delay and saturation as described in claim 8, characterized in that, The expression for the actual control law of the high-speed train is: ； In the formula, Indicates control gain. ; This represents the unknown function to be estimated.

10. The novel dynamic surface funnel control method for high-speed trains with time delay and saturation as described in claim 9, characterized in that, It also includes using RBF neural networks to estimate unknown functions. unknown function The expression is: ； in: Represents the weights of the neural network. Represents the Gaussian radial basis function vector. Let be the approximation error of the neural network; where the Gaussian radial basis function is: ； in: Let be the coordinate vector of the center point of the Gaussian radial basis function. Let be the width of the Gaussian radial basis function. These are the weights of the neural network.

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