High-speed train high-order sliding mode controller design method and control method

Abstract

The application discloses a high-order sliding mode controller design method and control method of a high-speed train, relates to the field of train control, and comprises the following steps: constructing a first-order sliding mode function with displacement error and speed error as independent variables and constructing a second-order multi-power terminal sliding mode function with the first-order sliding mode function as an independent variable; the second-order multi-power terminal sliding mode function adopts a multi-power structure to adapt to different convergence stages in the sliding mode control; the function value of the second-order multi-power terminal sliding mode function at the next moment is 0; an equivalent control law is derived based on the second-order multi-power terminal sliding mode function and a first tight format dynamic linearization data model; a switching control law is derived according to the second-order multi-power terminal sliding mode function, a reaching law and the first tight format dynamic linearization data model; and the high-order sliding mode controller of the high-speed train is formed by combining the equivalent control law and the switching control law, so that the high-order sliding mode controller which can guarantee the tracking accuracy and the sliding mode chattering suppression of the high-speed train system at the same time can be obtained.

Description

Technical Field

[0001] This application relates to the field of train control, and in particular to a design method and control method for a high-order sliding mode controller for high-speed trains. Background Technology

[0002] As a core subsystem of the high-speed train automatic control system, automatic train operation plays a crucial role in ensuring the safe, punctual, and energy-efficient operation of trains, and precise train speed tracking control is the most important function realized in the automatic train operation system.

[0003] There are many high-speed train control methods currently available, but these methods cannot simultaneously guarantee the tracking accuracy and sliding mode chatter suppression of the high-speed train system. Summary of the Invention

[0004] The purpose of this application is to provide a design method and control method for a high-order sliding mode controller for high-speed trains, which can simultaneously ensure the tracking accuracy of the high-speed train system and suppress sliding mode chattering.

[0005] To achieve the above objectives, this application provides the following solution: In a first aspect, this application provides a design method for a high-order sliding mode controller for high-speed trains, including: A dynamic model describing the motion state of a high-speed train is constructed, and the displacement term is expressed by velocity and control force to obtain a MIMO discrete-time data model; the dynamic model is a continuous nonlinear model. Considering the control force constraints, based on the MIMO discrete-time data model, the first compact form dynamic linearized data model is determined by matrix update formula and adaptive extended state observer. A first-order sliding mode function with displacement error and velocity error as independent variables is constructed, and a second-order multi-power terminal sliding mode function with the first-order sliding mode function as independent variable is constructed. The second-order multi-power terminal sliding mode function adopts a multi-power structure to adapt to different convergence stages in sliding mode control. Let the function value of the second-order power-multiple terminal sliding mode function be 0 at the next time step, and derive the equivalent control law based on the second-order power-multiple terminal sliding mode function and the first tight-form dynamic linearized data model; Design a convergence law for the second-order multi-power terminal sliding mode function; The switching control law is derived based on the second-order multi-power terminal sliding mode function, the approach law, and the first tight-form dynamic linearized data model. The equivalent control law and the switching control law are combined to form the high-order sliding mode controller of the high-speed train.

[0006] Secondly, this application provides a control method for high-speed trains, including: A high-order sliding mode controller is used to control the high-speed train; The high-order sliding mode controller is obtained through the high-order sliding mode controller design method for high-speed trains described in the first aspect.

[0007] According to the specific embodiments provided in this application, the following technical effects are disclosed: On the one hand, considering control force constraints, a first-compact dynamic linearized data model is determined based on the MIMO discrete-time data model, using a matrix update formula and an adaptive extended state observer. On the other hand, a second-order multi-power terminal sliding mode function is innovatively designed, and an equivalent control law is determined based on this function. Using this equivalent control law enables faster convergence of control errors. Ultimately, this allows the high-order sliding mode controller to simultaneously guarantee the tracking accuracy and sliding mode chatter suppression of the high-speed train system. Attached Figure Description

[0008] 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.

[0009] Figure 1 This is a flowchart illustrating the design method of a high-order sliding mode controller for a high-speed train in one embodiment of this application. Figure 2 An operational status analysis diagram of a high-speed train provided in an embodiment of this application; Figure 3 This is a schematic diagram of the high-order sliding mode control of a high-speed train in one embodiment of this application; Figure 4 The following are speed-distance relationship graphs for different control schemes during the normal state experiment of this application; Figure 5 The following are speed error-distance relationship diagrams for different control schemes during normal state experiments of this application; Figure 6 The following graphs show the speed error-speed relationship of the vehicle under different control schemes during the normal state experiment of this application; Figure 7 The displacement-time relationship diagrams of the following vehicles under different control schemes in the normal state experiment of this application are shown. Figure 8 The following are control force-distance relationship diagrams for different control schemes in the normal state experiment of this application; Figure 9The acceleration-distance relationship diagrams of the following vehicles under different control schemes in the normal state experiment of this application are shown. Figure 10 The following are speed-distance relationship graphs for different control schemes in the parameter mutation experiment of this application; Figure 11 The following graphs show the speed error-distance relationship of the vehicle under different control schemes in the parameter mutation experiment of this application; Figure 12 The displacement-time relationship of the vehicle under different control schemes in the parameter mutation experiment of this application is shown in the figure. Figure 13 The figure shows the acceleration-distance relationship of the vehicle under different control schemes in the parameter mutation experiment of this application. Detailed Implementation

[0010] 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.

[0011] 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.

[0012] The high-order sliding mode controller design method for high-speed trains provided in this application embodiment can be applied to computer equipment, which can be a terminal and a server. The terminal can be, but is not limited to, various desktop computers, laptops, smartphones, and tablets. The server can be a standalone server or a server cluster composed of multiple servers, or it can be a cloud server.

[0013] Reference Figure 1 The high-order sliding mode controller design method for high-speed trains in this application embodiment includes steps S110 to S170.

[0014] S110, a dynamic model describing the motion state of a high-speed train is constructed, and the displacement term is expressed through velocity and control force to obtain a MIMO discrete-time data model. The dynamic model is a continuous nonlinear model.

[0015] S120, under the premise of considering control force constraints, based on the MIMO discrete-time data model, the first compact scheme dynamic linearized data model is determined by using matrix update formula and adaptive extended state observer.

[0016] S130, construct a first-order sliding mode function with displacement error and velocity error as independent variables, and construct a second-order multi-power terminal sliding mode function with the first-order sliding mode function as independent variable. The second-order multi-power terminal sliding mode function adopts a multi-power structure to adapt to different convergence stages in sliding mode control.

[0017] S140, set the function value of the second-order multi-power terminal sliding mode function to 0 at the next time step, and derive the equivalent control law based on the second-order multi-power terminal sliding mode function and the first compact scheme dynamic linearized data model.

[0018] S150, design a convergence law for a second-order multi-power terminal sliding mode function.

[0019] S160, the switching control law is derived from the second-order multi-power terminal sliding mode function, the reaching law, and the first compact scheme dynamic linearized data model.

[0020] S170 combines equivalent control law and switching control law to form a high-order sliding mode controller for high-speed trains.

[0021] In the above technical solutions: First, a dynamic model describing the motion state of the high-speed train is constructed to depict its motion at various moments in time. This model can provide the velocity relationship between two adjacent moments. Expressing the displacement term through velocity and control force yields the MIMO (Multiple Input Multiple Output) discrete-time data model. The input and output of the MIMO discrete-time data model are the set of control forces of each power unit at the current moment and the set of velocities of each power unit at the next moment, respectively. The control force is represented as traction when greater than 0 and as braking force when less than 0.

[0022] Then, considering the control force constraints, based on the MIMO discrete-time data model, a first compact-form dynamic linearized data model is determined using a matrix update formula and an adaptive extended state observer. The inputs and outputs of the first compact-form dynamic linearized data model are the same as those of the MIMO discrete-time data model. It is used to determine the set of velocities of each power unit at the next time step based on the set of control force changes, the set of velocities, and the first system total uncertainty term of each power unit at the current time step. The first time-varying parameter matrix acts on the set of control force changes of each power unit at the current time step. The key point is that the above technical solution innovatively employs a matrix update formula and an adaptive extended state observer, making the estimates of the first time-varying parameters and the first system total uncertainty term in the first compact-form dynamic linearized data model more accurate.

[0023] Secondly, a first-order sliding mode function with displacement error and velocity error as independent variables is constructed, and a second-order multi-power terminal sliding mode function with the first-order sliding mode function as independent variable is also constructed. The second-order multi-power terminal sliding mode function adopts a multi-power structure to adapt to different convergence stages in sliding mode control. The function value of the second-order multi-power terminal sliding mode function is then set to 0 at the next time step, and the equivalent control law is derived based on the second-order multi-power terminal sliding mode function and the first compact scheme dynamic linearized data model. The sliding mode function is used to converge the control error. In traditional schemes, a first-order sliding mode function is usually used to determine the equivalent control law. The above technical solution innovatively designs a second-order multi-power terminal sliding mode function and determines the equivalent control law based on it. Using this equivalent control law allows the control error to converge faster.

[0024] Furthermore, a reaching law for the second-order multi-power terminal sliding mode function is designed, and the switching control law is derived based on the second-order multi-power terminal sliding mode function, the reaching law, and the first compact scheme dynamic linearized data model.

[0025] Ultimately, the equivalent control law and the switching control law are combined to form a high-order sliding mode controller for high-speed trains.

[0026] The above technical solution will be further described in detail below through a preferred embodiment.

[0027] A dynamic model describing the motion state of a high-speed train is constructed, and the displacement term is expressed through velocity and control force to obtain a MIMO discrete-time data model. Specifically, this includes: constructing a dynamic model describing the motion state of a high-speed train; using the forward Euler formula based on the dynamic model, performing dynamic linearization processing, and expressing the displacement term through velocity and control force to obtain a MIMO discrete-time data model.

[0028] Specific instructions for constructing a dynamic model describing the motion state of a high-speed train: The traction / braking system of a high-speed train consists of several distributed power units (one power unit corresponds to two motor cars). This design is beneficial for maximizing traction efficiency. Each power unit is subject to its own control and the coupler action of adjacent power units to coordinate the control of multiple power units, thereby achieving coordinated operation of the entire high-speed train. The longitudinal dynamics analysis of the high-speed train is as follows: Figure 2As shown, the middle carriage is the locomotive equipped with a power unit, and the first and last carriages are trailers. During the operation of the high-speed train, each power unit provides a certain traction force, and the extension and retraction of the couplers cause relative movement between adjacent carriages. According to Newton's laws of motion, the main forces acting on each power unit include: control force (traction force when greater than 0, braking force when less than 0), basic resistance (proportional to the square of the train speed), additional resistance, and the forces acting on the carriages. Based on the above force analysis, the following dynamic model of the high-speed train can be established: .

[0029] in, i The serial number indicates the index of the power unit. n Indicates the total number of power units. i The value range is [1, ...]. n ], , and These represent the speed, control force, and unknown environmental disturbance of power unit i, respectively. and These represent the resultant force and acceleration coefficient of power unit i, respectively; This represents the additional resistance of dynamic unit i caused by gradient, curves, and tunnels, which is usually treated as a disturbance term in train dynamics models. and Let i represent the basic resistance and the coupler force, respectively. Their specific forms are as follows: .

[0030] in, , and Both represent the time-varying drag coefficient of power unit i. , and These represent the displacement, elastic coefficient, and damping coefficient of the dynamic unit, respectively.

[0031] The dynamic model is transformed using the forward Euler formula: .

[0032] in, This represents the nonlinear time-varying function corresponding to dynamic unit i. , and Let i and i+1 represent the velocities of power units i-1, i, and i+1 at time t, respectively. , and These represent the displacements of power units i-1, i, and i+1 at time t, respectively. and These represent the control force and generalized disturbance of power unit i at time t, respectively. The generalized disturbance is related to additional drag and unknown environmental disturbances, such as... It is a with and The relevant generalized disturbances This represents the velocity of the power unit at time t+1.

[0033] The above nonlinear model determines the velocity of a power unit at time t+1 based on its own velocity at time t, the velocities of adjacent power units, its own control force, its own displacement, the displacements of adjacent power units, and its own generalized disturbance.

[0034] Based on the actual situation, we can introduce hypothesis 1: generalized perturbation in the nonlinear model It is bounded. That is: ; It is a constant.

[0035] High-speed train systems are affected by environmental factors and changes in railway sections, resulting in inherent uncertainties in model parameters such as train mass, drag coefficient, and elastic constants. Furthermore, as can be seen from the basic drag, nonlinear terms become more significant at higher speeds, making it difficult to construct an accurate train model. To facilitate subsequent dynamic linearization, all displacement terms in the nonlinear model are converted into expressions including velocity and control force. The transformed formula can be restated as the following MIMO discrete-time data model: .

[0036] in, Represents a nonlinear time-varying function. , and Let each of these represent the set of velocity, control force, and generalized disturbance of each power unit at time t. These three represent the output, input, and uncertainty of the train control execution system, respectively. The output of the controller designed in this method is used to determine the input of the control execution system. , , and Let these represent the orders of the sets of velocity, control force, and generalized disturbance, respectively. This represents the set of velocities of each power unit at time t+1.

[0037] Considering the actual operational constraints of high-speed trains, namely that the motor output torque is limited by the motor power, the following control force and its rate of change constraints are introduced: .

[0038] in, and These represent the maximum traction force and the maximum braking force, respectively. The constraints represent the control components; the above parameters can be determined from the traction and braking characteristic curves of the corresponding train model.

[0039] After obtaining the MIMO discrete-time data model, and considering the control force constraints, the first compact scheme dynamic linearized data model is determined using the matrix update formula and the adaptive extended state observer.

[0040] The process specifically includes: under the premise of considering control force constraints, the MIMO discrete-time data model is equivalent to the second compact form dynamic linearized data model; the second compact form dynamic linearized data model contains the second system total uncertainty term.

[0041] The second time-varying parameter matrix is ​​determined using a matrix update formula based on the second compact scheme dynamic linearized data model.

[0042] Based on the idea of ​​perturbation decoupling, the second time-varying parameter matrix is ​​decomposed into the first time-varying parameter matrix and the perturbation matrix; the first time-varying parameter matrix is ​​the diagonal parameter matrix of the second time-varying parameter matrix.

[0043] The perturbation matrix is ​​introduced into the total uncertainty term of the second system to form the total uncertainty term of the first system; the total uncertainty term of the first system is estimated using an adaptive extended state observer; and the first compact form dynamic linearized data model is determined based on the first time-varying parameter matrix and the estimated total uncertainty term of the first system.

[0044] The above steps effectively model the high-speed train operation process, considering input constraints, as a virtual data decoupling model, achieving dynamic linearization transformation and coupling separation of the nonlinear system. Specifically: For MIMO discrete-time data models that satisfy the constraints of control force and its rate of change, assumptions 2 and 3 can be introduced.

[0045] Assumption 2: Nonlinear time-varying function Input to the control execution system The partial derivatives of exist, are not zero, and remain unchanged in sign.

[0046] Assumption 3: The MIMO discrete-time data model satisfies the generalized Lipschitz condition.

[0047] It should be noted that Assumption 2 represents a typical constraint in the design of nonlinear control systems. Assumption 3 constitutes a quasi-linearization condition, which is also the most commonly used generalized Lipschitz condition. Many practical control systems satisfy these two conditions, including single-input single-output, multi-input multi-output, and high-speed train systems based on multi-agent theory.

[0048] For a MIMO discrete-time data model that satisfies Assumptions 1-3, when If there exists a time-varying parameter matrix, then there must exist a time-varying parameter matrix. This makes the MIMO discrete-time data model equivalent to the following compact form dynamic linearization (CFDL) data model, which is defined as the second compact form dynamic linearization data model: .

[0049] .

[0050] .

[0051] in, and These represent the sets of velocities of each power unit at time t and time t+1, respectively. The second time-varying parameter matrix at time t, for any time... Both are bounded. yes The element in the i-th row and j-th column, This represents the set of changes in control force of each power unit at time t. Let represent the total uncertainty of the second system at time t. The total uncertainty of the second system is the set of the second uncertainties of each dynamic unit. Represents a nonlinear time-varying function. This represents the set of control forces of each power unit at time t-1. and Let represent the sets of uncertainties for each dynamic unit at time t and time t-1, respectively. This represents the set of control forces of each power unit at time t. This represents the set of generalized perturbations of each dynamic unit at time t. , and These represent the order of the sets of velocity, control force, and generalized disturbance, respectively.

[0052] To further improve the system's dynamic performance, based on the idea of ​​perturbation decoupling, the second time-varying parameter matrix in the second compact scheme dynamic linearized data model is decomposed into a diagonal parameter matrix and a perturbation matrix containing unknown terms and coupling effects. This allows the second compact scheme dynamic linearized data model to be rewritten as the first compact scheme dynamic linearized data model. .

[0053] .

[0054] .

[0055] .

[0056] in, This represents the first time-varying parameter matrix at time t. This represents the total uncertainty term of the first system at time t. and Let i represent the first and second uncertainties of the power unit i at time t, respectively. express The element in the i-th row and j-th column, and Let represent the changes in control force of power units i and j at time t, respectively. The total uncertainty term of the first system is a generalized bounded disturbance that includes system coupling effects. This represents the diagonal matrix operator.

[0057] Matrix update formula: .

[0058] Output observer: .

[0059] For the observer's output error, For observation gain, it is required It is located inside the unit circle, thus ensuring the stability of the observer itself.

[0060] Since the output error of the observer at time t cannot be calculated normally for the next time step, i.e. Therefore, a two-step delay estimation method is adopted: the core theory is that when the system sampling time is sufficiently small, the estimation error of the observer output will be minimized. Considered a slowly time-varying signal, its first-order difference changes very little, and its second-order difference is approximately zero: that is... ,get . This represents the output error of the observer at the previous moment.

[0061] To enhance system robustness, a parameter reset algorithm is further presented: .

[0062] .

[0063] and They represent and The initial value is set, and when the condition is met, it is adjusted accordingly. and Perform initialization and reset.

[0064] Due to total uncertainty The unknown, in this embodiment, uses AESO (an enhanced or extended form of "extended state observer"), which integrates extended state observer theory and dynamic linearization methods, for estimation. The adaptive extended state observer is: .

[0065] in, and They represent and The estimated value, and They represent and The estimated value, and Both represent the gain of the adaptive extended state observer, and the state variables are defined respectively. and state variable observations They are respectively and .

[0066] Furthermore, the constructed first-order sliding mode function for: .

[0067] .

[0068] .

[0069] in, , and Let these represent the first-order sliding mode function value, velocity error, and displacement error at time t, respectively. and These represent the actual position and the ideal position at time t, respectively. and Let these represent the velocity and ideal velocity of each power unit at time t, respectively. This represents the coefficient of the sliding surface to be designed.

[0070] The constructed second-order multi-power terminal sliding mode function is as follows: .

[0071] in, This represents the value of the second-order power-law terminal sliding mode function at time t. , , , , , and All of these represent sliding mode parameters. Specifically, .

[0072] It should be noted that the second-order multi-power terminal sliding mode function adopts a multi-power structure to adapt to different convergence stages in sliding mode control: when hour, enlarge ,and Shrink .when hour, Shrink ,and enlarge Therefore, in a large error band, and It plays a dominant role, forcing the tracking error to decrease rapidly. Within the small error band, It plays a leading role in achieving finite step size convergence and high-precision tracking.

[0073] make The equivalent control law can be derived as follows: .

[0074] When the initial state of the system is not on the sliding surface or external disturbances occur during motion, independent equivalent control cannot drive the system trajectory to the sliding surface. To mitigate chattering and improve system robustness, the following improved reaching law is designed: .

[0075] in, , and as well as Both represent approaching parameters. Specifically, , , .

[0076] , This indicates the computation of symbolic functions. It is also referred to as sliding mode parameters. This represents the value of the first-order sliding mode function at time t; For the first A first-order sliding surface function; For serial number, The number; Let be the first-order sliding surface function at time t; For time t, the first A first-order sliding surface function.

[0077] The switching control law is derived by combining the second-order multi-power terminal sliding mode function, the reaching law, and the first compact scheme dynamic linearized data model: .

[0078] It should be noted that, It is designed in integral form. It becomes continuous by using the integral of discontinuous sign functions. Therefore... Chattering can be significantly reduced without sacrificing robustness. Furthermore, the improved reaching law... exist When taking a larger value, it should be close to 0 to avoid integral saturation, while... Increase the value to 1 when the value is small to improve tracking accuracy.

[0079] Ultimately, the control law (higher-order sliding mode controller) takes the following form: .

[0080] It should be noted that, in order to ensure To achieve convergence within a finite time, sliding mode parameters , , , and The selection must meet the following conditions: .

[0081] .

[0082] .

[0083] .

[0084] .

[0085] in, The initial values ​​for the first-order sliding surface; For the first The absolute value of a first-order sliding surface function; , as well as All are intermediate variables.

[0086] The above is a preferred embodiment of the high-order sliding mode controller design method for high-speed trains in this application. It has the following technical features: 1. A discrete-time, two-layer, multi-power sliding mode structure and integral-form switching control are adopted to replace the linear sliding surface and sign function switching term in traditional SMC. This not only achieves high-precision tracking of system dynamics but also promotes the development of recursive high-order sliding mode control in high-speed train systems. Furthermore, by addressing the issue of overly conservative switching gain selection, integral saturation is avoided while effectively suppressing controller chattering.

[0087] 2. The introduction of the Adaptive Extended State Observer (AESO) enables the proposed solution to achieve stronger robustness and reaching performance with a smaller switching gain. Its combination satisfies the system's requirements for chattering elimination and disturbance suppression, thus achieving efficient decoupled control. Unlike existing methods, the gains of both AESO and data-driven sliding mode control are dynamically updated through parameter estimation algorithms, rather than relying on system state information, enhancing the solution's adaptability to uncertainties.

[0088] 3. All components of the proposed technical solution—including parameter estimation and parameter reset algorithms, data-driven sliding mode control, and AESO—are designed entirely based on the system's input and output data.

[0089] Based on the high-order sliding mode controller design method for high-speed trains provided in the above embodiments, this application also provides a control method for high-speed trains, specifically including: using a high-order sliding mode controller to control the high-speed train; wherein, the high-order sliding mode controller is obtained through the high-order sliding mode controller design method for high-speed trains provided in the above embodiments.

[0090] The technical effectiveness of the above-mentioned high-speed train control method will be verified through a set of experimental data.

[0091] 1. Simulation experimental platform.

[0092] The proposed control method was experimentally verified on a high-speed train operation control and optimization semi-physical simulation test platform independently developed by the team. This platform integrates three core modules: an actual train controller, a real-time simulator, and a virtual environment simulation platform, forming a highly efficient and accurate testing system. The platform first uses the actual train controller to calculate and optimize train operation control commands, ensuring consistency with actual operation. Then, the real-time simulator fully simulates the train operation process, achieving seamless integration of the virtual and real environments. Simultaneously, the environment simulation platform performs hardware circuit simulation, reproducing diverse operating scenarios and providing a more realistic testing environment. During the semi-physical simulation test, the system can automatically generate a series of optimized train control curves and speed limit curves based on specific operating commands, ground system signals, and track information. Users can input control strategies into the system through the platform's programming interface and use the simulator to generate real-time safety impact factors, ensuring the safe operation of high-speed trains. At the same time, the virtual display device provides real-time feedback on train speed, position, distance from the target point, and other operating data, supporting operators in real-time monitoring of the train's status. The system is also equipped with efficient monitoring equipment to continuously track the train's operating status, ensuring the train arrives at its destination safely and on time. Through this series of meticulous testing and optimization processes, the platform not only improves the operating efficiency of high-speed trains, but also provides reliable data support and technical assurance for the future deployment of data-driven algorithms in practical applications.

[0093] 2. Simulation parameter settings.

[0094] The CRH380A high-speed train has three traction power units, each with one transformer, two converters, and four traction motors. First, the actual operating curves and traction characteristic curves of the CRH380A high-speed train were imported into the simulation platform. Then, various control strategies were implemented into the platform, and noise and cosine signals were introduced to simulate the total uncertainty faced by the high-speed train under real-world track conditions. Under this setup, the platform can compare and evaluate the performance of various control strategies. Finally, the platform provides real-time feedback and monitoring of key data such as train speed and position for each scheme.

[0095] Four methods were compared in this experiment. Besides the high-speed train control method (SO-MTSMDC scheme) proposed in this application, the other three control strategies were, in order: Model-Free Adaptive Sliding Mode Control (MFASMC) based on dynamic linearization, Improved Model-Free Adaptive Control (iMFAC), and Model-Based Generalized Predictive Control (GPC). The parameters of the CRH380A high-speed train are detailed in Table 1. The parameters of each control scheme were set according to the experimental requirements.

[0096] Table 1. CRH380A High-Speed ​​Train Model Parameters

[0097] 3. Experiment 1: Normal operating status.

[0098] The speed-distance relationship under the four control schemes is as follows: Figure 4 As shown, the corresponding speed error-distance relationship is as follows: Figure 5 As shown. From Figure 4 It can be seen that the tracking results of all four schemes do not exceed the system speed limit curve, indicating that all four schemes meet the most basic operational safety requirements. And from... Figure 5 The speed error versus distance relationship shown indicates that the SO-MTSMDC and MFASMC methods exhibit more stable tracking performance throughout the entire operation. The errors of each power unit remain below ±0.167 km / h and ±0.445 km / h, respectively, demonstrating a significant advantage over the maximum errors of 0.928 km / h and 0.822 km / h of the iMFAC and GPC methods. Due to the introduction of the second-order sliding surface and AESO, SO-MTSMDC significantly outperforms the MFASMC scheme in terms of interference suppression and convergence speed.

[0099] The speed limit curve was drawn based on the train speed error requirements of CTCS-3. Figure 6 The speed error level verification results of four control schemes were compared. (Comprehensive Analysis) Figure 6 It can be seen that both the SO-MTSMDC and MFASMC methods meet the speed error requirements throughout the entire train operation. In particular, the SO-MTSMDC method strictly adheres to the error boundaries at all speed levels, demonstrating better environmental adaptability and control precision, which helps ensure the operational stability of high-speed trains under different operating conditions. The MFASMC method, however, experiences larger speed error fluctuations under interference such as crosswinds and heavy rain, exhibiting relatively weak anti-interference performance and potentially posing operational risks. Conversely, the iMFAC and GPC methods show speed errors exceeding operational limits at low speeds, failing to meet the error allowable standards of the high-speed train control system.

[0100] Figure 7The displacement tracking performance of each power unit of the high-speed train under four different schemes is presented. The stopping errors at intermediate stops are as follows: SO-MTSMDC scheme 0.125 meters, MFASMC scheme 0.545 meters, iMFAC scheme 3.68 meters, and GPC scheme 19.6 meters. Among these, the SO-MTSMDC scheme consistently maintains a low and safe displacement error; while the MFASMC, iMFAC, and GPC schemes have larger errors, making them more prone to repeated speed corrections for subsequent trains, thus interfering with the overall line operation plan. The stopping errors at the final stop are 0.482 meters, 1.260 meters, 2.73 meters, and 19.7 meters, respectively. The comparison shows that the SO-MTSMDC scheme has the smallest displacement error during the stopping phase, meeting the requirements for precise stopping of high-speed trains (errors are typically controlled within 0.5 meters), demonstrating outstanding positioning performance.

[0101] To evaluate the stability and safety of different control methods, Figure 8 The control force response of the HST power unit under four schemes was compared. The results show that the SO-MTSMDC scheme performs excellently in the start-up, braking, and coasting phases: the traction force is smoothly engaged, suppressing the abrupt changes in traditional control, and the braking force transition is smooth, significantly alleviating train bumps and passenger discomfort; the system control force is stable throughout the entire process, with the overall control force strictly limited within [-48.8, 47.5] kN, and the acceleration changes are also smoother. In contrast, the control force fluctuation of the other schemes, MFASMC, is more drastic than that of SO-MTSMDC (range [-58.5, 48.3] kN); iMFAC and GPC exhibit large and frequent fluctuations during the start-stop phase (ranges [-59.1, 49.1] kN and [-65.2, 45.7] kN, respectively), posing a safety risk to operations.

[0102] Acceleration variation curve ( Figure 9 This further confirms the above conclusion: the acceleration changes of the MFASMC, iMFAC, and GPC schemes are rapid, with amplitudes of [-0.580, 0.532], [-0.588, 0.587], and [-0.604, 0.514], respectively, while the acceleration changes of the SO-MTSMDC scheme are more gradual (except during the start-up phase), with an amplitude of only [-0.559, 0.474]. While meeting passenger comfort standards, it also demonstrates better system stability.

[0103] To more intuitively and reasonably evaluate the merits of the four schemes, five performance indicators are used for evaluation: mean squared error (MSE), integral absolute error (IAE), maximum acceleration (MA), control input peak-to-peak value (PP), and energy index (EI).

[0104] Table 2 shows the calculation results for each performance index. Clearly, compared to the other three schemes, the SO-MTSMDC scheme has lower IAE and MSE values. The MA of the high-speed train using the SO-MTSMDC method is 0.578 m·s. -2 The changes were relatively small; while the MA of the MFASMC and GPC schemes were higher, at 0.592 and 0.610 m·s, respectively. -2 Furthermore, the peak control input values ​​and energy consumption indicators reflect the degree of jitter and energy consumption levels of each scheme. The peak-to-peak control input values ​​for the four schemes are 98.9, 106.5, 106.4, and 121.2 kN, respectively. In terms of total energy consumption, the SO-MTSMDC scheme achieves energy savings of 7.2%, 8.7%, and 20.0% compared to MFASMC, iMFAC, and GPC, respectively.

[0105] Table 2 Performance Indicators of Four Control Schemes under Normal Test

[0106] 4. Experiment 2: System parameter mutation experiment.

[0107] This experiment evaluates the robustness of various control schemes under uncertain environments by simulating abrupt parameter changes (such as changes in the train's total mass and tunnel wind resistance). The disturbance conditions are set as follows: (At 57.1km) Simulated mass reduction or entry into a narrow tunnel, At 115.6 km, the simulated mass increases or encounters strong headwinds, corresponding to a decrease and an increase in system parameters, respectively. Simultaneously, the amplitude of interference (white noise and sinusoidal signals) is increased to 1.5 times the reference value throughout the process to enhance the anti-interference capabilities of the four methods.

[0108] Trajectory tracking performance under extreme conditions ( Figure 10 , Figure 11 and Figure 12The results show that the SO-MTSMDC method exhibits significant robustness and high tracking accuracy. Its speed error can be controlled within ±0.364 km / h, a 32.9% reduction compared to MFASMC (±0.543 km / h). Parking accuracy is also significantly superior, with mid-range and end-point displacement errors of 0.44 m and 0.97 m, respectively (MFASMC: 0.45 m and 1.46 m). This advantage is attributed to its multi-layered anti-interference design: real-time compensation of the system's total uncertainty is achieved through online updates of the control gain, combined with an integral sliding surface, a higher-order fast approach law, and AESO. In contrast, the iMFAC method, although based on AESO, suffers from a speed error of ±1.863 km / h and a relatively large displacement error (0.63 m mid-range and 4.17 m end-point). The traditional GPC method, due to its fixed gain, recovers slowly (>5 seconds) after parameter abrupt changes, with a maximum speed error of ±2.76 km / h and significant displacement errors (8.34 m mid-range and 11.24 m end-point), highlighting its insufficient adaptability.

[0109] In the comparative experimental results of acceleration ( Figure 13 The four control schemes exhibited significant performance differences. The SO-MTSMDC scheme, employing a discrete-time fast second-order integral sliding mode function combined with AESO disturbance estimation compensation, demonstrated the best overall control quality: its acceleration fluctuation amplitude was the lowest (±0.558). Furthermore, it remains stable even under conditions of parameter abrupt changes and strong disturbances, highlighting the robustness provided by the composite anti-interference mechanism. In contrast, the MFASMC method utilizes sliding surface dynamics to adjust the strategy, controlling the acceleration amplitude within ±0.593. Within a certain range. Although it has some effect in suppressing chattering, the overall system oscillation level is still higher than that of SO-MTSMDC due to limited disturbance rejection capability. The acceleration responses of the iMFAC and GPC schemes show significant fluctuations, with amplitudes reaching ±0.595 and ±0.813, respectively. .

[0110] Based on five evaluation indicators, as shown in Table 3, the SO-MTSMDC scheme maintains stable system control performance even under complex conditions such as abrupt changes in model parameters, nonlinear coupling, and external disturbances. Specifically, this scheme demonstrates significant advantages in key performance indicators, such as error tracking accuracy, disturbance suppression capability, maximum acceleration / deceleration control, and energy economy. In contrast, although the MFASMC method shows some local optimization capability under specific operating conditions, its overall control quality still lags behind the SO-MTSMDC scheme.

[0111] Table 3 Performance Indicators of Four Control Schemes under Parameter Mutation Test

[0112] In summary, this application proposes a novel data-driven second-order sliding mode control method for multiple-input multiple-output (MIMO-HST) train systems. This method, based on dynamic linearization and adaptive enhanced sliding mode control (AESO) design, achieves stable control under complex operating conditions involving external disturbances, coupling effects, and input constraints. Through a virtual data decoupling model, the system achieves dynamic linearization and coupling separation; by combining a fast terminal sliding surface and an enhanced exponential reaching law, it ensures rapid convergence of tracking errors while effectively suppressing chattering. Theoretical analysis rigorously proves the existence of the sliding mode and the convergence characteristics of the closed-loop system.

[0113] Comparative simulations conducted on the CRH380A train hardware on a ring-based platform demonstrate that the proposed second-order fast sliding mode control scheme SO-MTSMDC has the following advantages over MFASMC, iMFAC, and GPC methods: 1. It performs well in speed and displacement tracking, with errors controlled within ±0.167 km / h and ±0.482 m respectively, meeting the requirements for safe operation.

[0114] 2. The generated control force and acceleration curves are smoother, with amplitudes limited to the ranges of [-48.8, 47.5] kN and [-0.559, 0.474], meeting passenger comfort standards.

[0115] 3. Based on the AESO design, combined with a novel recursive nonlinear sliding mode function and an enhanced exponential arrival law, the convergence speed of the system is further improved and chattering is significantly reduced.

[0116] 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.

[0117] 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.

[0118] 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.

[0119] 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.

[0120] 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).

[0121] 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.

[0122] 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.

[0123] 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 design method for a high-order sliding mode controller for high-speed trains, characterized in that, include: A dynamic model describing the motion state of a high-speed train is constructed, and the displacement term is expressed by velocity and control force to obtain a MIMO discrete-time data model; The dynamic model is a continuous nonlinear model; Considering the control force constraints, based on the MIMO discrete-time data model, the first compact form dynamic linearized data model is determined by matrix update formula and adaptive extended state observer. A first-order sliding mode function with displacement error and velocity error as independent variables is constructed, and a second-order multi-power terminal sliding mode function with the first-order sliding mode function as independent variable is constructed. The second-order multi-power terminal sliding mode function adopts a multi-power structure to adapt to different convergence stages in sliding mode control. Let the function value of the second-order power-multiple terminal sliding mode function be 0 at the next time step, and derive the equivalent control law based on the second-order power-multiple terminal sliding mode function and the first tight-form dynamic linearized data model; Design a convergence law for the second-order multi-power terminal sliding mode function; The switching control law is derived based on the second-order multi-power terminal sliding mode function, the approach law, and the first tight-form dynamic linearized data model. The equivalent control law and the switching control law are combined to form the high-order sliding mode controller of the high-speed train.

2. The design method for a high-order sliding mode controller for high-speed trains according to claim 1, characterized in that, A dynamic model describing the motion state of a high-speed train is constructed, and the displacement term is expressed through velocity and control force, resulting in a MIMO discrete-time data model, specifically including: Construct a dynamic model to describe the motion state of a high-speed train; Based on the aforementioned dynamic model, the forward Euler formula is used for dynamic linearization, and the displacement term is expressed through velocity and control force to obtain the MIMO discrete-time data model.

3. The design method for a high-order sliding mode controller for high-speed trains according to claim 2, characterized in that, The dynamic model is as follows: ； ； in, , and Representing the power unit Speed, control, and interference from unknown environments; and Representing the power unit The resultant force and acceleration coefficient; Indicates power unit Additional resistance caused by gradients, curves, and tunnels; and Representing the power unit The basic resistance and coupler force; , and All represent power units The time-varying drag coefficient; , and Representing the power unit Displacement, elastic modulus, and damping modulus; Indicates the first The coupler force of each power unit; For serial numbers; Indicates the first The displacement of each power unit; Indicates the first The speed of each power unit; The MIMO discrete-time data model is as follows: ； in, This represents the set of velocities of each power unit at time t+1. Represents a nonlinear time-varying function. , and Let each represent the set of velocity, control force, and generalized disturbance of each power unit at time t. , and These represent the order of the set of the velocity, the control force, and the generalized disturbance, respectively. Let be the velocity of the first power unit at time t; For power unit The velocity at time t; For transpose; The control force of the first power unit at time t; For power unit Control force at time t; This represents the generalized perturbation of the first dynamic unit at time t; For power unit The generalized perturbation at time t.

4. The design method for a high-order sliding mode controller for high-speed trains according to claim 1, characterized in that, Considering control constraints, based on the aforementioned MIMO discrete-time data model, the first compact scheme dynamically linearized data model is determined using a matrix update formula and an adaptive extended state observer, specifically including: Considering the control force constraints, the MIMO discrete-time data model is equivalent to a second compact scheme dynamic linearized data model; the second compact scheme dynamic linearized data model includes a second system total uncertainty term; The second time-varying parameter matrix is ​​determined based on the second compact scheme dynamic linearized data model using a matrix update formula; Based on the idea of ​​perturbation decoupling, the second time-varying parameter matrix is ​​decomposed into a first time-varying parameter matrix and a perturbation matrix; the first time-varying parameter matrix is ​​the diagonal parameter matrix of the second time-varying parameter matrix; The disturbance matrix is ​​introduced into the total uncertainty term of the second system to form the total uncertainty term of the first system. An adaptive extended state observer is used to estimate the total uncertainty of the first system, and the first compact scheme dynamic linearized data model is determined based on the first time-varying parameter matrix and the estimated total uncertainty of the first system.

5. The design method for a high-order sliding mode controller for high-speed trains according to claim 4, characterized in that, The control force constraint is: ； in, and These represent the maximum traction force and the maximum braking force, respectively. Represents constraints that control the components; For power unit Control force at time t; For power unit At any moment Control; The second compact form of the dynamically linearized data model is: ； ； ； in, and These represent the sets of velocities of each power unit at time t and time t+1, respectively. This represents the second time-varying parameter matrix at time t. This represents the set of changes in control force of each power unit at time t. Let represent the total uncertainty of the second system at time t. The total uncertainty of the second system is the set of the second uncertainties of each dynamic unit. Represents a nonlinear time-varying function. This represents the set of control forces of each power unit at time t-1. and Let represent the sets of uncertainties for each dynamic unit at time t and time t-1, respectively. This represents the set of control forces of each power unit at time t. This represents the set of generalized perturbations of each dynamic unit at time t. , and These represent the orders of the sets of velocity, control force, and generalized disturbance, respectively. The first compact form of dynamically linearized data model is: ； ； ； ； in, This represents the first time-varying parameter matrix at time t. This represents the total uncertainty term of the first system at time t. and Let i represent the first and second uncertainties of the power unit i at time t, respectively. express The element in the i-th row and j-th column, and These represent the changes in control force of power units i and j at time t, respectively. This represents the first uncertainty term of the first power unit at time t; Indicates power unit The first uncertainty term at time t; For transpose; express The element in the first row and first column of the middle; express The Middle Line number Column elements; This represents the diagonal matrix operator.

6. The design method for a high-order sliding mode controller for high-speed trains according to claim 5, characterized in that, The mathematical expression for the output observer is: ； The matrix update formula is determined based on the output observer: ； ； ； in, For a moment The second time-varying parameter matrix; for The estimated value; for The estimated value; , This is an adjustable step size factor; For each power unit at any time The set of changes in control forces; For the output observer at time The output estimation error; For observation gain; For the output observer at time The output estimation error; , It is an adjustable weighting factor; The square of the Euclidean norm; for The element in the i-th row and i-th column; for The initial value; Indicates a pre-defined positive number; for The element in the i-th row and j-th column; for The initial value; for The estimated value; for The element in the first row and first column of the middle; for The Middle Line number Column elements; The adaptive extended state observer is: ； in, and They represent and The estimated value, and They represent and The estimated value, and Both represent the gain of the adaptive extended state observer; Indicates time The first system total uncertainty term.

7. The design method for a high-order sliding mode controller for high-speed trains according to claim 6, characterized in that, The first-order sliding mode function for: ； ； ； in, , and Let these represent the first-order sliding mode function value, velocity error, and displacement error at time t, respectively. and These represent the actual position and the ideal position at time t, respectively. and Let these represent the velocity and ideal velocity of each power unit at time t, respectively. Indicates the sliding surface coefficient to be designed; The second-order power-law terminal sliding mode function is: ； in, This represents the value of the second-order power-law terminal sliding mode function at time t; The increment of the first-order sliding mode function value at time t; , Indicates time The first-order sliding mode function value; , , , , and All represent sliding mode parameters; The equivalent control law is: ； in, This is an equivalent control law; Let be the ideal velocity of each power unit at time t; The sampling period.

8. The design method for a high-order sliding mode controller for high-speed trains according to claim 7, characterized in that, The reaching law is as follows: ； in, For a moment The law of convergence of time; , , and Both represent approach parameters; For a moment The law of convergence of time; The switching control law is: ； in, To switch the control law increment; for The estimated value; Indicates time The first time-varying parameter matrix; for The estimated value; for The input for switching between different times.

9. The design method for a high-order sliding mode controller for high-speed trains according to claim 8, characterized in that, The high-order sliding mode controller is: .

10. A control method for a high-speed train, characterized in that, include: A high-order sliding mode controller is used to control the high-speed train; The high-order sliding mode controller is obtained by the high-order sliding mode controller design method for high-speed trains according to any one of claims 1-9.

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