Adaptive backstepping sliding mode control method for high-speed train based on auxiliary system

Abstract

The application discloses a high-speed train adaptive backstepping sliding mode control method based on an auxiliary system, relates to the train speed tracking control technical field, and comprises the following steps: a high-speed train dynamics model considering input saturation and unknown disturbance is established; based on the high-speed train dynamics model, an adaptive backstepping sliding mode control strategy based on a nonlinear auxiliary system is designed; the adaptive backstepping sliding mode control strategy based on the nonlinear auxiliary system comprises the following steps: design of the nonlinear auxiliary system, design of a backstepping sliding mode control law and design of an adaptive law; and stability analysis is carried out on the adaptive backstepping sliding mode control strategy based on the nonlinear auxiliary system. The application can effectively weaken the influence of input saturation on the system and improve the disturbance suppression capacity of the high-speed train system.

Description

Technical Field

[0001] This application relates to the field of train speed tracking control technology, and in particular to a high-speed train adaptive backstepping sliding mode control method based on an auxiliary system. Background Technology

[0002] my country's high-speed railways possess advantages such as high operating speed, high safety factor, and strong transport capacity, making them an important component of modern transportation infrastructure. With the continuous expansion of the high-speed railway network and the increasingly complex operating environment, train operation control systems face higher requirements for control performance and environmental adaptability. As train speeds continue to increase and train systems become more complex, factors such as internal nonlinearity, external environmental disturbances, and actuator saturation become increasingly coupled, making the high-speed train speed tracking control problem more complex. Therefore, studying the high-speed train speed tracking control problem under the combined effects of input saturation and external disturbances is of great significance.

[0003] Regarding the problem of high-speed train operation control, scholars both domestically and internationally have conducted extensive research, including the following methods: Adaptive control methods can improve the robustness of the system in uncertain environments and ensure accurate speed tracking of high-speed trains.

[0004] The system's anti-disturbance capability is improved by estimating and compensating for the total uncertainty during train operation using an extended state observer.

[0005] Speed ​​tracking control under multiple constraints was achieved based on model predictive control.

[0006] A novel high-precision model predictive control method is designed based on long short-term memory neural networks.

[0007] To further improve the robust tracking performance of high-speed trains under uncertain disturbance conditions and to improve the convergence speed of system errors, sliding mode control has been gradually introduced into the research of high-speed train operation control.

[0008] The train speed tracking control strategy based on nonlinear integral terminal sliding mode achieves rapid convergence of system errors.

[0009] By combining a disturbance observer with a fixed-time sliding mode control method, accurate estimation of uncertain external disturbances is achieved, ensuring that high-speed trains accurately and quickly track the target curve. The tracking error converges within a finite time.

[0010] Based on fractional integral sliding mode control, chattering in sliding mode control is reduced, and the tracking accuracy of the system is improved.

[0011] By combining iterative learning control and sliding mode control, the disturbance rejection capability is effectively improved and the tracking performance is guaranteed.

[0012] These methods have achieved good results in solving the speed tracking control problem of high-speed trains. In particular, sliding mode control has shown superior performance due to its strong robustness in dealing with uncertainties and external disturbances.

[0013] However, sliding mode control often assumes that the control input can be fully realized when facing input saturation. This assumption is easily broken in practical applications, leading to the input failing to reach the expected value, resulting in performance degradation and affecting the system's safety and stability. Therefore, effectively addressing input saturation is a major challenge in sliding mode control applications. Some studies have constructed auxiliary systems to compensate for saturation errors. For example: An auxiliary system was introduced to address the input saturation phenomenon, and an adaptive state feedback controller was designed.

[0014] Research on trajectory tracking control of robotic arm system under saturation constraints by introducing an auxiliary system.

[0015] An auxiliary system is introduced to handle the cooperative control when the actuators of high-speed trains have saturation constraints.

[0016] A second-order auxiliary system is constructed to dynamically compensate for saturation constraints.

[0017] An auxiliary system was introduced to handle the effects of actuator saturation, ensuring the fixed-time convergence of multi-vehicle coordination errors.

[0018] Introduce auxiliary systems or auxiliary dynamic systems to mitigate the impact of input saturation on control performance and closed-loop stability.

[0019] Therefore, utilizing the deviation between the actual control input and the desired control input to design a suitable auxiliary system can mitigate the impact of actuator constraints on system performance and stability, providing an effective approach for controller design under input-constrained conditions. Nevertheless, when input saturation and unknown disturbances coexist, the system must not only cope with the limited control action caused by input saturation but also handle the impact of unknown disturbances on tracking accuracy and dynamic performance. Therefore, how to balance system robustness, tracking accuracy, and control smoothness under such complex conditions still requires further research. Summary of the Invention

[0020] The purpose of this application is to provide an adaptive backstepping sliding mode control method for high-speed trains based on an auxiliary system, which can effectively reduce the impact of input saturation on the system and improve the disturbance suppression capability of the high-speed train system.

[0021] To achieve the above objectives, this application provides the following solution: In a first aspect, this application provides a high-speed train adaptive backstepping sliding mode control method based on an auxiliary system, the method comprising: Establish a high-speed train dynamics model that considers input saturation and unknown disturbances.

[0022] Based on the aforementioned high-speed train dynamics model, an adaptive backstepping sliding mode control strategy based on a nonlinear auxiliary system is designed. This strategy includes: designing the nonlinear auxiliary system, designing the backstepping sliding mode control law, and designing the adaptive law. The nonlinear auxiliary system is used to compensate for errors caused by input saturation. The backstepping sliding mode control law consists of an equivalent control law and a switching control law, used to achieve stable control of the displacement and velocity subsystems and improve the system's robustness to unknown disturbances. The adaptive law is used to perform online estimation of unknown disturbances using an adaptive algorithm.

[0023] Stability analysis is performed on the adaptive backstepping sliding mode control strategy based on the nonlinear auxiliary system.

[0024] Optionally, the expression for the high-speed train dynamics model is: ; in, , This refers to the displacement of the high-speed train; , The speed of a high-speed train; For the quality of high-speed trains; The control force that the system actually exerts; The equivalent resistance term is obtained by mass normalizing the basic operating resistance. , This represents the basic operating resistance of high-speed trains; This is the equivalent unknown disturbance term obtained after mass normalization of the unknown disturbance. , This is an unknown disturbance.

[0025] Optionally, based on the aforementioned high-speed train dynamics model, an adaptive backstepping sliding mode control strategy based on a nonlinear auxiliary system is designed, specifically including: Define saturation error.

[0026] Based on the saturation error, a nonlinear auxiliary system is designed.

[0027] Based on the aforementioned nonlinear auxiliary system, the high-speed train state tracking error is corrected to obtain the corrected high-speed train state tracking error.

[0028] Based on the corrected high-speed train state tracking error, a virtual control law is constructed according to the backstepping control design concept; and a backstepping sliding mode control law is constructed based on the backstepping design results.

[0029] An adaptive algorithm is introduced to estimate the equivalent unknown disturbance term in the backstepping sliding mode control law online, and a corresponding adaptive law is constructed.

[0030] Based on the adaptive law and the backstepping sliding mode control law, an adaptive backstepping sliding mode control strategy based on a nonlinear auxiliary system is obtained.

[0031] Optionally, the expression for the saturation error is: ; in, The control force that the system actually exerts; The control force output by the controller; This represents the saturation error.

[0032] Optionally, the expression for the nonlinear auxiliary system is: ; in, This is the first state variable of the auxiliary system; This is the second state variable of the auxiliary system; The first design parameter for the auxiliary system, The second design parameter for the auxiliary system, and satisfies... , ; For the quality of high-speed trains; This represents the saturation error.

[0033] Optionally, the expression for the corrected high-speed train state tracking error is: ; in, For the virtual control law to be designed; For the desired trajectory of the displacement, Let be the desired trajectory of the velocity, and , ; For the desired acceleration; This is the first state variable of the auxiliary system; This is the second state variable of the auxiliary system; This represents the tracking error in the first state. This represents the tracking error in the second state.

[0034] Optionally, the expression for the backstepping sliding mode control law is: ; in, This is a reverse sliding mode control law; This is an equivalent control law; To switch control laws; For the quality of high-speed trains; For sliding mode gain; It is a sliding surface; This represents the tracking error in the first state. This refers to the tracking error in the second state. This is the second state variable of the auxiliary system; The first design parameter for the auxiliary system, The second design parameter for the auxiliary system, and satisfies... , ; For the desired acceleration; This is the equivalent unknown disturbance term obtained after mass normalization of the unknown disturbance; For the virtual control law to be designed; The equivalent resistance term is obtained by mass normalizing the basic operating resistance. For feedback gain, To switch gain, The boundary layer thickness is, and , , .

[0035] Optionally, the expression for the adaptive law is: ; in, This is an estimate of the equivalent unknown disturbance term obtained after mass normalization of the unknown disturbance; For adaptive gain, and ; It is a sliding surface.

[0036] Optionally, the expression for the adaptive backstepping sliding mode control strategy based on the nonlinear auxiliary system is: ; in, The control force output by the controller; For the quality of high-speed trains; For sliding mode gain; It is a sliding surface; This represents the tracking error in the first state. This refers to the tracking error in the second state. This is the second state variable of the auxiliary system; The first design parameter for the auxiliary system, The second design parameter for the auxiliary system, and satisfies... , ; For the desired acceleration; This is an estimate of the equivalent unknown disturbance term obtained after mass normalization of the unknown disturbance; For the virtual control law to be designed; The equivalent resistance term is obtained by mass normalizing the basic operating resistance. For feedback gain, To switch gain, The boundary layer thickness is, and , , .

[0037] Optionally, the stability of the adaptive backstepping sliding mode control strategy based on the nonlinear auxiliary system can be analyzed using the Lyapunov function.

[0038] In a second aspect, this application provides a computer device, including: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the high-speed train adaptive backstepping sliding mode control method based on the auxiliary system described above.

[0039] Thirdly, this application provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the high-speed train adaptive backstepping sliding mode control method based on the auxiliary system described above.

[0040] Fourthly, this application provides a computer program product, including a computer program that, when executed by a processor, implements the high-speed train adaptive backstepping sliding mode control method based on the auxiliary system described above.

[0041] According to the specific embodiments provided in this application, this application has the following technical effects: This application provides an adaptive backstepping sliding mode control method for high-speed trains based on an auxiliary system. By constructing a high-speed train dynamics model that takes into account both input saturation and unknown disturbances, it can fully reproduce the constraints and disturbances encountered during actual train operation. This lays a reliable model foundation for the subsequent controller to accurately match the actual operating characteristics of the train and avoid the theoretical control scheme deviating from engineering practice. The method involves modularly designing and combining a nonlinear auxiliary system, a backstepping sliding mode control law, and an adaptive law to form an overall control strategy. This strategy can rely on the auxiliary system to offset the negative impact of input saturation, rely on the dual-structure control law to ensure the accuracy of displacement and speed regulation and the ability to resist disturbances, and utilize the adaptive... The system should identify unknown disturbances in real time, and the three aspects should work together to simultaneously suppress multiple adverse factors, thereby improving the dynamic control performance of the train traction and braking process. Stability analysis of the entire control strategy can theoretically verify the closed-loop convergence and global stability of the control scheme, eliminate the instability risks caused by control parameters and structural defects, and ensure the operational reliability of the control algorithm after its implementation. This application solves two core control problems of high-speed train input saturation and external unknown disturbances. Under the premise of ensuring the global stability of the system, it optimizes the tracking accuracy and operational robustness of train displacement and speed, and adapts to the safe and stable traction and braking control requirements of high-speed trains under complex track conditions. Attached Figure Description

[0042] 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.

[0043] Figure 1 This is an application environment diagram of an adaptive backstepping sliding mode control method for high-speed trains based on an auxiliary system, as described in one embodiment of this application. Figure 2 A flowchart illustrating an adaptive backstepping sliding mode control method for high-speed trains based on an auxiliary system, provided in an embodiment of this application; Figure 3 This is a schematic diagram of the overall structure of a control system provided in an embodiment of this application; Figure 4 This is a schematic diagram of the desired train speed curve provided in one embodiment of this application; Figure 5 This is a schematic diagram of the expected displacement curve of a train operation provided in an embodiment of this application; Figure 6 A schematic diagram of the speed tracking and error curve without considering input saturation is provided for one embodiment of this application; Figure 7 This is a schematic diagram of an embodiment of the present application, without considering input saturation displacement tracking and error curves. Figure 8 A schematic diagram of speed tracking and error curves without auxiliary systems when considering input saturation is provided for one embodiment of this application; Figure 9 A schematic diagram of displacement tracking and error curves without the use of an auxiliary system when considering input saturation is provided for one embodiment of this application; Figure 10 A schematic diagram of speed tracking and error curves using an auxiliary system considering input saturation is provided for one embodiment of this application; Figure 11 A schematic diagram of displacement tracking and error curves using an auxiliary system considering input saturation is provided for one embodiment of this application; Figure 12 A schematic diagram of the control force curve provided in an embodiment of this application; Figure 13 A schematic diagram illustrating external disturbances and their estimation provided in an embodiment of this application; Figure 14 This is a schematic diagram of the structure of a computer device provided in an embodiment of this application. Detailed Implementation

[0044] 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.

[0045] To address the issues of actuator input saturation and unknown time-varying disturbances during high-speed train operation, this application proposes an adaptive backstepping sliding mode control method for high-speed trains based on an auxiliary system. First, a high-speed train dynamic model considering input saturation and unknown disturbances is established. Second, within the backstepping sliding mode control framework, a nonlinear auxiliary system is introduced to compensate online for the equivalent error caused by saturation, and an adaptive law is designed to estimate the unknown disturbance online. Simultaneously, a hyperbolic tangent function is used to replace the sign function to reduce chattering, thereby achieving stable speed-displacement tracking. Finally, simulation results using a CRH380A high-speed train demonstrate that the proposed method can still guarantee the stability of the closed-loop system under conditions of input constraints and unknown disturbances, and effectively mitigate the adverse effects of input saturation on the system's tracking performance. When the actuators are desaturated, the system gradually recovers good speed and displacement tracking performance, verifying the feasibility and effectiveness of the method.

[0046] Its innovations mainly lie in the following three aspects: 1) Construct a nonlinear auxiliary system to effectively compensate for the error caused by input saturation, thereby reducing the impact of input limitation on the speed tracking performance of high-speed trains.

[0047] 2) Design a controller by combining backstepping and sliding mode control methods to improve the robustness, tracking accuracy and dynamic response performance of the system.

[0048] 3) Introduce an adaptive law to estimate disturbances online, so that the system can still maintain stable tracking of the desired velocity curve even in the presence of unknown disturbances and input saturation.

[0049] To make the above-mentioned objectives, features and advantages of this application more apparent and understandable, this application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0050] The adaptive backstepping sliding mode control method for high-speed trains based on auxiliary systems provided in this application can be applied to, for example... Figure 1In the application environment shown, terminal 102 communicates with server 104 via a network. A data storage system can store the data that server 104 needs to process. The data storage system can be set up separately, integrated into server 104, or placed in the cloud or on another server. Terminal 102 can send a high-speed train dynamics model considering input saturation and unknown disturbances to server 104. After receiving the high-speed train dynamics model, server 104 designs an adaptive backstepping sliding mode control strategy based on a nonlinear auxiliary system. The adaptive backstepping sliding mode control strategy based on the nonlinear auxiliary system includes: the design of the nonlinear auxiliary system, the design of the backstepping sliding mode control law, and the design of the adaptive law. The nonlinear auxiliary system is used to compensate for errors caused by input saturation. The backstepping sliding mode control law consists of an equivalent control law and a switching control law, used to achieve stable control of the displacement and velocity subsystems and improve the system's robustness to unknown disturbances. The adaptive law is used to estimate unknown disturbances online using an adaptive algorithm. A stability analysis is performed on the adaptive backstepping sliding mode control strategy based on the nonlinear auxiliary system. Server 104 can feed back the obtained adaptive backstepping sliding mode control strategy based on the nonlinear auxiliary system to terminal 102. Furthermore, in some embodiments, the high-speed train adaptive backstepping sliding mode control method based on the auxiliary system can also be implemented independently by server 104 or terminal 102. For example, terminal 102 can directly perform high-speed train adaptive backstepping sliding mode control based on the auxiliary system for a high-speed train dynamics model considering input saturation and unknown disturbances; alternatively, server 104 can obtain a high-speed train dynamics model considering input saturation and unknown disturbances from the data storage system and perform high-speed train adaptive backstepping sliding mode control based on the auxiliary system for that model.

[0051] The terminal 102 can be, but is not limited to, various desktop computers, laptops, smartphones, and tablets. The server 104 can be implemented using a standalone server or a server cluster consisting of multiple servers, or it can be a cloud server.

[0052] In one exemplary embodiment, such as Figure 2 As shown, a high-speed train adaptive backstepping sliding mode control method based on an auxiliary system is provided. This method is executed by computer equipment, specifically by a terminal or server alone, or by both a terminal and a server. In this embodiment, the method is applied to... Figure 1 Taking server 104 as an example, the explanation includes the following steps S1 to S3.

[0053] S1: Establish a high-speed train dynamics model that considers input saturation and unknown disturbances; S2: Based on the aforementioned high-speed train dynamics model, an adaptive backstepping sliding mode control strategy based on a nonlinear auxiliary system is designed. This strategy includes: design of the nonlinear auxiliary system, design of the backstepping sliding mode control law, and design of the adaptive law. The nonlinear auxiliary system is used to compensate for errors caused by input saturation. The backstepping sliding mode control law consists of an equivalent control law and a switching control law, used to achieve stable control of the displacement and velocity subsystems and improve the system's robustness to unknown disturbances. The adaptive law is used to perform online estimation of unknown disturbances using an adaptive algorithm. S3: Perform stability analysis on the adaptive backstepping sliding mode control strategy based on the nonlinear auxiliary system.

[0054] Implementing steps S1 to S3 above can accurately overcome the control challenges caused by actuator input saturation and unknown external disturbances during high-speed train operation. It relies on a dynamic model that closely matches the actual train operating conditions to ensure the engineering adaptability of the control algorithm. It also uses a nonlinear auxiliary system to compensate for saturation errors, backstepping sliding mode to achieve accurate displacement and velocity tracking, and an adaptive law to identify disturbances online to enhance anti-disturbance performance. Furthermore, stability analysis provides theoretical evidence for the reliable convergence of the closed-loop system. Ultimately, it comprehensively improves the tracking accuracy, anti-interference capability, and control stability of high-speed train operation, meeting the requirements for smooth, accurate, and safe traction and braking control of trains in complex operating environments.

[0055] As an optional implementation, in step S1, firstly, the coupling relationship between vehicles inside the train is ignored, and the high-speed train is equivalent to a rigid point moving along the track direction for force analysis. Since the high-speed train is mainly affected by traction / braking force and basic running resistance during operation, the traction / braking force is provided by the actuator. During the traction phase, the high-speed train experiences a traction force in the same direction as the train's movement, and during the braking phase, it experiences a braking force in the opposite direction. The basic running resistance consists of mechanical resistance and aerodynamic resistance, and it always exists during train operation. The resultant force of these two components determines the running state of the high-speed train. Therefore, according to Newton's dynamics principles, the dynamic model of the high-speed train is expressed as: (1); in, This refers to the displacement of the high-speed train; The speed of a high-speed train; For the quality of high-speed trains; For the control force acting on the train, and Indicates traction force. Indicates braking force; The basic operating resistance of a high-speed train is represented by the following mathematical model: (2); in, This is the first drag coefficient; This is the second drag coefficient; This is the third drag coefficient.

[0056] Since there are unknown disturbances during the actual operation of the train and the physical output capability of the actuator is limited, the influence of input saturation and unknown disturbances is further considered on the basis of the high-speed train dynamics model (1), and a high-speed train dynamics model with input saturation and unknown disturbances is established.

[0057] In actual operation of high-speed trains, the output control force of the actuators is bounded. If the commands calculated by the controller exceed this physical limit, the system will fail to achieve the expected performance. This saturation effect will severely impact the tracking accuracy, operational stability, and safety of the high-speed train. Furthermore, high-speed trains are also affected by changes in the external environment during operation, which can be considered as unknown disturbances. ,and The following bounded conditions must be met: (3); in, The given positive constant is .

[0058] Therefore, considering the input saturation constraint and unknown disturbance of the actuator, equation (1) can be rewritten as: (4); In the formula, It can be represented as: (5); in, and These represent the maximum and minimum values ​​of the control input, respectively. The control force output by the controller; The control force that the system actually operates under.

[0059] Set system state , , , Establish a high-speed train dynamics model that considers input saturation and unknown disturbances: (6); in, The equivalent resistance term is obtained by mass normalizing the basic operating resistance. The equivalent unknown disturbance term is obtained by mass normalization of the unknown disturbance.

[0060] According to the established high-speed train dynamics model (6), there are two key factors affecting control performance. First, the actuator has input saturation constraints, which means that the ideal control force output by the controller cannot fully act on the system, thus weakening the control effect. Second, there are unknown disturbances, which cause the ideal dynamic characteristics of the system to be destroyed, thus affecting the tracking accuracy and stability.

[0061] As an optional implementation, in step S2, based on the high-speed train dynamics model, an adaptive backstepping sliding mode control strategy based on a nonlinear auxiliary system is designed, specifically including: S21: Define saturation error.

[0062] S22: Based on the saturation error, design a nonlinear auxiliary system.

[0063] S23: Based on the aforementioned nonlinear auxiliary system, the high-speed train state tracking error is corrected to obtain the corrected high-speed train state tracking error.

[0064] S24: Based on the corrected high-speed train state tracking error, construct a virtual control law according to the backstepping control design concept; construct a backstepping sliding mode control law according to the backstepping design results.

[0065] S25: Introduce an adaptive algorithm to estimate the equivalent unknown disturbance term in the backstepping sliding mode control law online, and construct the corresponding adaptive law.

[0066] S26: Based on the adaptive law and the backstepping sliding mode control law, an adaptive backstepping sliding mode control strategy based on a nonlinear auxiliary system is obtained.

[0067] Specifically, for the high-speed train dynamics model (6) established in step S1, an adaptive backstepping sliding mode control strategy based on a nonlinear auxiliary system is designed to weaken the adverse effects of input saturation and external disturbances on system performance, and to achieve asymptotic tracking of speed and displacement. The overall structure of the control system is as follows: Figure 3 As shown.

[0068] The design of an adaptive backstepping sliding mode control strategy based on a nonlinear auxiliary system can be divided into three parts: nonlinear auxiliary system design, backstepping sliding mode control law design, and adaptive law design, as detailed in steps S2.1 to S2.3.

[0069] S2.1: Design a nonlinear auxiliary system to compensate for saturation error and reduce the adverse effects of input saturation on the closed-loop system.

[0070] When the actuator has input saturation constraints, the actual input after the control input passes through the saturation stage is not equal to the ideal control input. In this case, the actual control force exerted by the system is... The control force output by the controller is There is a deviation between the two, and the saturation error is defined as follows: (7); in, This represents the saturation error.

[0071] At this point, the saturation effect can be equivalent to the system dynamics caused by... The introduced additional terms affect the closed-loop performance and stability analysis. Therefore, a nonlinear auxiliary system is designed to address the input saturation problem.

[0072] To suppress the adverse effects of saturation error on error convergence when system saturation occurs, the nonlinear auxiliary system is designed as follows: (8); in, This is the first state variable of the auxiliary system; This is the second state variable of the auxiliary system; The first design parameter for the auxiliary system, The second design parameter for the auxiliary system, and satisfies... , .

[0073] When the actuator is not saturated The auxiliary system did not function; conversely, when the actuator saturated, The auxiliary system will express the influence of saturation error as a state variable. and Introduced into the tracking error of high-speed trains.

[0074] S2.2: Based on the nonlinear auxiliary system formula (8) established in step S2.1, the tracking error is redefined, and on this basis, the backstepping sliding mode control law is designed to achieve stable control of the displacement and velocity subsystems while improving the system's robustness to unknown disturbances.

[0075] Due to the introduction of a nonlinear auxiliary system To address the equivalent error caused by input saturation, the corrected high-speed train state tracking error is defined as follows: (9); in, For the virtual control law to be designed; For the desired trajectory of the displacement, Let be the desired trajectory of the velocity, and , ; For the desired acceleration; This represents the tracking error in the first state. This represents the tracking error in the second state.

[0076] The design of the backstepping sliding mode control law consists of two steps: First, constructing a virtual control law based on the backstepping control design concept; second, constructing the backstepping sliding mode control law based on the backstepping design results. The specific design steps are as follows: Step 1: Based on the first-order subsystem (displacement) and first-state tracking error of the system. , can be obtained The dynamic equations are as follows: (10); Substituting equations (8) and (9) into equation (10), we get: (11); According to equation (11), the virtual control law of the first-order subsystem can be designed as follows: (12); Substituting equation (12) into equation (11), we get: (13); Therefore, under the action of the virtual control law, the first-order error subsystem is rearranged into a system containing stable terms. and recursive variables This standard form lays the foundation for the subsequent construction of the sliding surface and the design of the final control law.

[0077] Step 2: Track the error using the system's second-order subsystem (velocity) and second state. , can be obtained The dynamic equations are as follows: (14); Substituting equations (6), (7), and (8) into equation (14), we get: (15); According to sliding mode control theory, the sliding surface is defined as follows: (16); In the formula, For sliding mode gain; It is a sliding surface.

[0078] right Differentiating, we get: (17); Based on the concept of equivalent control, let Then the equivalent control law is: (18); in, This is the equivalent control law.

[0079] To make the system more stable and reduce controller output chatter, the switching control law is designed as follows: (19); in, To switch control laws; For feedback gain, To switch gain, The boundary layer thickness is, and , , .

[0080] The backstepping sliding mode control law consists of an equivalent control law and a switching control law. The design of the backstepping sliding mode control law is as follows: (20); in, This is a reverse sliding mode control law.

[0081] S2.3: The equivalent unknown disturbance term obtained after mass normalization of the unknown disturbance in the backstepping sliding mode control law (20) constructed in step S2.2. An adaptive law is designed for online estimation, thereby realizing the design of an adaptive backstepping sliding mode control strategy based on a nonlinear auxiliary system.

[0082] Since the external disturbances experienced by high-speed trains in actual operation are usually unknown, these disturbances are difficult to obtain through precise modeling. Using robust gains with fixed upper bounds is not only difficult to select reasonably, but also leads to excessive control input, exacerbating actuator saturation and chattering. Therefore, this application employs an adaptive algorithm to obtain the equivalent unknown disturbance term after mass normalization of the unknown disturbance. Perform online estimation, for The estimated value. Let. To estimate the error, and .

[0083] Based on this, the adaptive law is designed as follows: (twenty one); in, For adaptive gain, and .

[0084] The estimated value of the equivalent unknown disturbance term obtained by mass normalization of the unknown disturbance using the designed adaptive law (21) Perform real-time updates and obtain the equivalent unknown disturbance term from the unknown disturbance in the backstep sliding mode control law after quality normalization. Replace with estimated value The adaptive backstepping sliding mode control strategy based on the nonlinear auxiliary system can be obtained as follows: (twenty two); As an optional implementation, in step S3, the Lyapunov function is used to perform stability analysis on the adaptive backstepping sliding mode control strategy based on the nonlinear auxiliary system designed in step S2.

[0085] First, design Lyapunov functions. as follows: (twenty three); right Differentiating, we get: (twenty four); Substituting equations (13), (16), (17), and (22) into equation (24), we get: (25); Define the system error vector Then the above inequality can be transformed into the following quadratic form: (26); Where the matrix The definition is as follows: (27); Due to the matrix Given a second-order real symmetric matrix, the control parameters satisfy the Sylvester criterion. and At that time, matrix Positive definite. Furthermore, according to the properties of quadratic forms of positive definite matrices, we can obtain: .

[0086] Therefore, by selecting appropriate design parameters, it can be ensured that all signals of the closed-loop system are bounded, and that the velocity tracking error and displacement tracking error asymptotically converge to zero.

[0087] In summary, the control strategy described in this application can still ensure the stability of the closed-loop system under conditions of input constraints and disturbances, and effectively mitigate the adverse effects of input saturation on the system's tracking performance. When the actuator is desaturated, the system can gradually recover good speed and displacement tracking performance, verifying the feasibility and effectiveness of the strategy.

[0088] S4: Simulation verification.

[0089] To verify the effectiveness of the proposed control strategy, a CRH380A high-speed train was selected as the control object, and simulation verification was carried out in conjunction with an actual route.

[0090] S41: Simulation conditions.

[0091] The simulation parameters of the CRH380A high-speed train are shown in Table 1. The expected operating curve of the high-speed train is shown in Table 1. Figure 4 and Figure 5 As shown, the total simulation duration is 3160 seconds, including three operating conditions: traction, cruise, and braking.

[0092] Table 1 Simulation parameters of CRH380A high-speed train

[0093] External disturbances are defined as gust interference. Gusts begin at... For any given time, its mathematical model is as follows: (28); in, The amplitude of the gust is... Random numbers within, , These represent the start and end times of the gusts.

[0094] To verify the effectiveness of the control strategy designed in this embodiment in high-speed train speed and displacement tracking, the controller parameters were set as follows: the nonlinear auxiliary system parameters were designed as follows. , The sliding gain of the sliding surface is designed as follows: The switching control law feedback gain is designed as The switching gain is designed as The boundary layer thickness is designed to be Adaptive gain design for The actuator limit is .

[0095] S42: Simulation results without considering input saturation.

[0096] To verify the tracking capability of the designed controller under ideal conditions, simulations were conducted without considering input saturation. In this case, it was assumed that the actuator could fully output the control force generated by the controller. By analyzing the tracking errors of the high-speed train's speed and displacement, the tracking performance of the controller under ideal conditions was verified.

[0097] from Figure 6 It can be seen that, without considering input saturation, the actual train speed can accurately track the desired speed. Overall, the speed response is continuous and stable, and the speed error is always kept within the millimeter level.

[0098] from Figure 7 It can be seen that, without considering input saturation, the actual displacement of the train can maintain a high degree of consistency with the expected displacement, and the displacement error is always kept within the centimeter level. This indicates that the control system, on the basis of precise speed tracking, further ensures the accuracy of displacement tracking.

[0099] Furthermore, based on the error data, the root mean square error of speed tracking can be calculated as follows: The root mean square error of displacement tracking is Therefore, the error between the actual output and the desired trajectory is extremely small, and the designed controller has high tracking accuracy.

[0100] S43: Simulation results considering input saturation.

[0101] To verify the impact of actuator input saturation on the tracking control performance of high-speed trains and to further verify the compensation capability of the designed auxiliary system for input saturation, simulations were conducted under the condition of limited actuator output. In this case, the actual actuator output is the control input after amplitude limiting. By comparing the speed, displacement, and error responses with and without the auxiliary system, the effectiveness of the auxiliary system in handling input saturation was analyzed.

[0102] S431: Simulation results without the use of auxiliary systems.

[0103] To verify the impact of actuator limiting on train tracking performance without addressing input saturation, simulations were performed considering input saturation but without using auxiliary systems.

[0104] from Figure 8 and Figure 9 It can be seen that within most operating sections, the actual train speed and displacement can basically track the desired trajectory; however, during the braking phase, due to amplitude constraints on the actuator output, the system error increases significantly and oscillations occur. At this point, the maximum speed tracking error is approximately... The maximum displacement tracking error is approximately Furthermore, the speed and displacement errors could not converge stably to near zero. This indicates that input saturation disrupted the ideal tracking characteristics of the original controller, thereby affecting the train's tracking performance for the desired speed and displacement, causing the train to fail to reduce its speed to zero within the specified time and to fail to stop precisely at the desired position.

[0105] Therefore, it is evident that without an auxiliary system, input saturation severely impacts the closed-loop system performance, causing velocity and displacement errors to fail to converge. Thus, it is necessary to introduce an auxiliary system to address input saturation.

[0106] S432: Simulation results using the auxiliary system.

[0107] To verify the effectiveness of the designed auxiliary system in handling input saturation, simulations were conducted using the same actuator saturation boundary.

[0108] from Figure 10 and Figure 11 It can be seen that, with the help of the auxiliary system, the train's actual speed and displacement can basically track the desired trajectory accurately. Especially during the braking phase, the fluctuations in speed tracking error and displacement tracking error are significantly reduced, ensuring that the train stops on time and also achieving precise stopping.

[0109] Compared with the system without the auxiliary system, the speed error and displacement error can gradually converge to near 0 after a short period of fluctuation during the braking phase. This indicates that the auxiliary system can effectively reduce error oscillations under strong saturation conditions, reduce the adverse effects of input saturation on the dynamic performance of the closed-loop system, and improve the overall tracking accuracy of the system.

[0110] from Figure 12 It can be seen that when the actuator is limited to Under the constraints, the control force output by the controller is always within the constraint range, indicating that the designed controller can meet the actuator saturation constraint requirements.

[0111] from Figure 13 It can be seen that the disturbance change can be mainly divided into two stages. In the initial and final stages of the simulation, the disturbance amplitude experiences a momentary increase. Due to the deviation between the actual control input and the ideal control force when considering saturation constraints, this deviation is uniformly represented as a disturbance and included in the disturbance estimation, resulting in a significant increase in the initial disturbance amplitude. As the auxiliary system plays a compensating role, this equivalent disturbance rapidly decays and tends to stabilize. In the later stages of the simulation, the disturbance amplitude amplifies again. This corresponds to random gust disturbances. The results from the local magnification show that the disturbance estimate can quickly and accurately track the actual disturbance change, with a small estimation error. Combined with... Figure 10 and Figure 11 It can be seen that when external disturbances and input saturation exist simultaneously, the system error remains bounded and converges rapidly, verifying the robustness of the proposed control method.

[0112] The technical effects of this application are as follows: To address the speed tracking control problem of high-speed trains under external disturbances and actuator input saturation constraints, this application proposes an adaptive backstepping sliding mode control method based on an auxiliary system. This method effectively mitigates the impact of input saturation on the system and improves the disturbance suppression capability of the high-speed train system. By establishing a dynamic model incorporating running resistance and designing a nonlinear auxiliary system to compensate for saturation deviations caused by actuator physical constraints in real time, this method effectively solves the system performance degradation problem caused by input constraints. Furthermore, combining the recursive design advantages of the backstepping method with the strong robustness of sliding mode control, and introducing an adaptive law for online estimation of unknown disturbances, the global asymptotic stability of the closed-loop system is rigorously proven using Lyapunov theory. Simulation verification based on the CRH380A train shows that this strategy, while handling saturation constraints and suppressing sliding mode chattering, ensures the speed tracking accuracy and operational stability of the high-speed train.

[0113] In one exemplary embodiment, a computer device is provided, which may be a server or a terminal, and its internal structure diagram may be as follows. Figure 14 As shown, this computer device includes a processor, memory, input / output (I / O) interfaces, and a communication interface. The processor, memory, and I / O interfaces are connected via a system bus, and the communication interface is also connected to the system bus via the I / O interfaces. The processor provides computational and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system, computer programs, and a database. The internal memory provides the environment for the operating system and computer programs stored in the non-volatile storage media. The database stores a high-speed train dynamics model considering input saturation and unknown disturbances. The I / O interfaces are used for information exchange between the processor and external devices. The communication interface is used for communication with external terminals via a network connection. When the computer program is executed by the processor, it implements a high-speed train adaptive backstepping sliding mode control method based on an auxiliary system.

[0114] Figure 14 The structures shown are merely block diagrams of some structures related to the present application and do not constitute a limitation on the computer device to which the present application is applied. Specific computer devices may include more or fewer components than shown in the figures, or combine certain components, or have different component arrangements. In an exemplary embodiment, a computer device is provided, including a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the steps in the above-described method embodiments.

[0115] 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.

[0116] 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.

[0117] 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 related data must comply with relevant regulations and be authorized by the owner of the corresponding device.

[0118] 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).

[0119] 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.

[0120] 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.

[0121] 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 high-speed train adaptive backstepping sliding mode control method based on an auxiliary system, characterized in that, The method includes: Establish a high-speed train dynamics model that considers input saturation and unknown disturbances; Based on the aforementioned high-speed train dynamics model, an adaptive backstepping sliding mode control strategy based on a nonlinear auxiliary system is designed. This strategy includes: designing the nonlinear auxiliary system, designing the backstepping sliding mode control law, and designing the adaptive law. The nonlinear auxiliary system is used to compensate for errors caused by input saturation. The backstepping sliding mode control law consists of an equivalent control law and a switching control law, used to achieve stable control of the displacement and velocity subsystems and improve the system's robustness to unknown disturbances. The adaptive law is used to perform online estimation of unknown disturbances using an adaptive algorithm. Stability analysis is performed on the adaptive backstepping sliding mode control strategy based on the nonlinear auxiliary system. The expression for the nonlinear auxiliary system is: ； in, This is the first state variable of the auxiliary system; This is the second state variable of the auxiliary system; The first design parameter for the auxiliary system, The second design parameter for the auxiliary system, and satisfies... , ; For the quality of high-speed trains; This is the saturation error; The expression for the adaptive backstepping sliding mode control strategy based on the nonlinear auxiliary system is: ； in, The control force output by the controller; For the quality of high-speed trains; For sliding mode gain; It is a sliding surface; This represents the tracking error in the first state. This refers to the tracking error in the second state. This is the second state variable of the auxiliary system; The first design parameter for the auxiliary system, The second design parameter for the auxiliary system, and satisfies... , ; For the desired acceleration; This is an estimate of the equivalent unknown disturbance term obtained after mass normalization of the unknown disturbance; For the virtual control law to be designed; The equivalent resistance term is obtained by mass normalizing the basic operating resistance. For feedback gain, To switch the gain, Where is the boundary layer thickness, and , , .

2. The high-speed train adaptive backstepping sliding mode control method based on an auxiliary system according to claim 1, characterized in that, The expression for the high-speed train dynamics model is as follows: ； in, , This refers to the displacement of the high-speed train; , The speed of a high-speed train; For the quality of high-speed trains; The control force that the system actually exerts; The equivalent resistance term is obtained by mass normalizing the basic operating resistance. , This represents the basic operating resistance of high-speed trains; This is the equivalent unknown disturbance term obtained after mass normalization of the unknown disturbance. , This is an unknown disturbance.

3. The high-speed train adaptive backstepping sliding mode control method based on an auxiliary system according to claim 1, characterized in that, Based on the aforementioned high-speed train dynamics model, an adaptive backstepping sliding mode control strategy based on a nonlinear auxiliary system is designed, specifically including: Define saturation error; Based on the saturation error, a nonlinear auxiliary system is designed; Based on the aforementioned nonlinear auxiliary system, the high-speed train state tracking error is corrected to obtain the corrected high-speed train state tracking error. Based on the corrected high-speed train state tracking error, a virtual control law is constructed according to the backstepping control design concept; and a backstepping sliding mode control law is constructed based on the backstepping design results. An adaptive algorithm is introduced to estimate the equivalent unknown disturbance term in the backstepping sliding mode control law online, and a corresponding adaptive law is constructed. Based on the adaptive law and the backstepping sliding mode control law, an adaptive backstepping sliding mode control strategy based on a nonlinear auxiliary system is obtained.

4. The high-speed train adaptive backstepping sliding mode control method based on an auxiliary system according to claim 3, characterized in that, The expression for the saturation error is: ； in, The control force that the system actually exerts; The control force output by the controller; This represents the saturation error.

5. The high-speed train adaptive backstepping sliding mode control method based on an auxiliary system according to claim 3, characterized in that, The expression for the corrected high-speed train state tracking error is as follows: ； in, For the virtual control law to be designed; For the desired trajectory of the displacement, Let be the desired trajectory of the velocity, and , ; For the desired acceleration; This is the first state variable of the auxiliary system; This is the second state variable of the auxiliary system; This represents the tracking error in the first state. This represents the tracking error in the second state.

6. The high-speed train adaptive backstepping sliding mode control method based on an auxiliary system according to claim 3, characterized in that, The expression for the backstepping sliding mode control law is: ； in, This is a reverse sliding mode control law; This is an equivalent control law; To switch control laws; For the quality of high-speed trains; For sliding mode gain; It is a sliding surface; This represents the tracking error in the first state. This refers to the tracking error in the second state. This is the second state variable of the auxiliary system; The first design parameter for the auxiliary system, The second design parameter for the auxiliary system, and satisfies... , ; For the desired acceleration; This is the equivalent unknown disturbance term obtained after mass normalization of the unknown disturbance; For the virtual control law to be designed; The equivalent resistance term is obtained by mass normalizing the basic operating resistance. For feedback gain, To switch the gain, Where is the boundary layer thickness, and , , .

7. The high-speed train adaptive backstepping sliding mode control method based on an auxiliary system according to claim 3, characterized in that, The expression for the adaptive law is: ； in, This is an estimate of the equivalent unknown disturbance term obtained after mass normalization of the unknown disturbance; For adaptive gain, and ; It is a sliding surface.

8. The high-speed train adaptive backstepping sliding mode control method based on an auxiliary system according to claim 1, characterized in that, The stability of the adaptive backstepping sliding mode control strategy based on the nonlinear auxiliary system is analyzed using the Lyapunov function.

Images