A control method for train-to-train safety distance under input saturation and communication delay

Abstract

The application provides a control method for train-to-train safety distance under input saturation and communication delay, which comprises the following steps: firstly, a virtual marshalling train dynamics model of high-speed trains is established, a dynamic smooth hyperbolic tangent saturation function with a saturation limit changing with train speed is proposed, and a dynamic smooth anti-saturation compensator is designed; secondly, a delay state prediction algorithm is designed by considering the communication delay between trains, an adaptive law is proposed by considering the internal parameter uncertainty of the system, and then the adaptive law is introduced into the dynamic smooth anti-saturation compensator, so as to design a time delay-anti-saturation robust controller, and the control method can eliminate the influence of input saturation and communication delay on stable driving of multiple trains, and can keep the distance between adjacent trains at a safe distance.

Description

Technical Field

[0001] This invention relates to the field of train tracking control technology, and more specifically, to a method for controlling the safe distance between trains under conditions of input saturation and communication delay. Background Technology

[0002] With the rapid development of railway transportation systems, single high-speed trains can no longer meet the ever-increasing demand for passenger traffic. Arranging multiple high-speed trains in a virtual formation can effectively increase passenger capacity and utilize railway space. However, during multi-train operation, the maximum traction and braking force output of the train's internal motors is limited, making it difficult to reach the ideal maximum value, leading to input saturation in the train system. If input saturation is not considered, trains may operate at maximum traction for extended periods, potentially causing motor overload or even damage. Furthermore, the lack of physical rigid connections between trains in a virtual formation means that each train obtains status information through communication, which can lead to communication delays and make it difficult to maintain a safe distance between adjacent high-speed trains. Therefore, designing a suitable anti-saturation robust control algorithm to address the impact of input saturation and communication delays on train operation is crucial for the safe operation of a multi-train virtual formation system.

[0003] For target tracking control of high-speed trains, sliding mode control (SMC) is widely used in train control systems due to its strong tracking performance. The paper "Andrey. Polyakov. Homogeneous Unit Sliding Mode Control. IEEE Transactions on Automatic Control. 2024; 69:1157-1163" designs a uniform sliding mode control with integral action based on the concept of generalized homogeneity. The paper "Kang. Zhuanga, Jia. Li-Mina, Zuo. Xiao-Long, et al. A Novel Controller Based on Fuzzy Sliding Mode Control for Train Speed ​​Tracking. IEEE Transactions on Vehicular Technology. 2024; 73:1-16" designs a fuzzy sliding mode controller to achieve train speed tracking. To improve the convergence speed of state errors on the sliding surface in SMC, terminal sliding mode control (TSMC) has been proposed. The paper "Yu. Xiaodonga, Zhou. Boa, Fang. Wenjing, et al. Super-Twisting Terminal Sliding Mode Decoupling Current Control for Sinusoidal Double-Sliding Electromagnetic Machine Drives. IEEE Transactions on Energy Conversion. 2024; 1-17" proposes a novel TSMC method to achieve high-performance motors. To address the non-singularity phenomenon in TSMC, Non-singular Terminal Sliding Mode Control (NTSMC) is proposed.The paper "Zebin.Yang,Jianfei.Sun,Xiaodong.Sun, et al. Direct Instantaneous Torque Control for Six-Phase SRM With Nonsingular Fast TerminalSliding Mode Controller. IEEE Journal of Emerging and Selected Topics in Power Electronics. 2024;12:505-515" proposes a hybrid strategy of NTSMC and direct instantaneous torque control to improve the dynamic response of motors. However, the above control algorithm is difficult to adapt to the uncertainty of the system's internal parameters. Mustafa. To improve the control performance of induction motors, a more robust ATSMC (Automatic Terminal Sliding Mode Speed ​​Control) was proposed. (IEEE Transactions on Power Electronics, 2024; 39: 449-458). Although the above sliding mode control algorithm has superior control performance, further research is needed in the field of virtual train formation multi-train cooperative control, especially regarding the input saturation problem that occurs in multi-train operation, requiring more efficient and practical solutions.

[0004] Current solutions to input saturation include: limiting control input using saturation functions, directly considering input saturation when designing control algorithms, and correcting saturation deviations using anti-saturation compensators. The paper "Zhu. Lei, Li, Xuefang, Huang. Deqing, et al. Distributed Cooperative Fault-Tolerant Control of High-Speed ​​Trains With Input Saturation and Actuator Faults. IEEE Transactions on Intelligent Vehicles. 2023; 8:1241-1251" directly utilizes saturation functions to address input saturation in high-speed train operation. The paper "Cai. Liangcheng, Huang. Deqing. Trajectory Tracking Control of Heavy Haul Train in Whole Operation Procedure. IEEE Transactions on Vehicular Technology. 2024; 73:16225-16237" designs a saturation function to suppress input saturation in heavily loaded trains. Both of these papers limit input saturation using saturation functions, but abrupt changes are prone to occur when limiting control input. The paper “Wang.Xiaoling,Jiang.Guo-Ping,Su,Housheng, et al.Robust Global Coordination of Networked Systems With Input Saturation and External Disturbances.IEEE Transactions on Systems, Man, and Cybernetics: Systems. 2021; 51:7788-7800” constructs a novel anti-saturation control algorithm based on backstepping, which solves input saturation during controller design, but the method is relatively complex.The literature “He. Jing, Long. Yu, Zhang. Chang Fan. Anti-saturation sliding mode tracking algorithm for heavy-haul trains when actuator saturation occurs. Advances in Mechanical Engineering. 2024; 16: 1–11” designs an unbounded anti-saturation compensator to effectively solve the input saturation problem in the control system. The literature “Zhang. Jianyi, Ren. Wei, Sun, Xi-Ming. Extended-State-Observer-Based Nonlinear Control for PMSM Servo Systems With Current Constraints and Voltage Saturations. IEEE Transactions on Transportation Electrification. 2024; 10: 2713-2726” designs an anti-saturation compensator to solve the influence of voltage saturation in permanent magnet synchronous motors. Both of the above literatures design a suitable anti-saturation compensator to solve the input saturation problem after designing the controller. The method is simple and effective, but the saturation limit is a fixed value. Considering that the research background is multiple trains, the maximum and minimum values ​​of the actual control input should vary with the train speed.

[0005] Regarding virtual formation target tracking control, the literature "Qingzhe.Zhen,Lei.Wan,Yulong.Li,etal.Formation control of a multi-AUV system based on virtual structure and artificial potential field on SE(3).OceanEngineering.2022;253:111148" proposes a finite-time position and attitude tracking control algorithm based on artificial potential field and virtual formation to detect the motion attitude of underwater robots and the undulating terrain of the seabed. The literature "Yulong Li Zhihao.CAI,Longhong.WANG,Jiang.ZHAO.Virtual target guidance-based distributed model predictive controlfor formation control of multiple UAVs.2020;3:1037-1056" proposes a distributed model predictive control scheme to realize trajectory tracking and obstacle avoidance of multiple UAV formations. None of the above literatures have studied the background of multiple trains. To address the goal of achieving safe distance tracking between adjacent trains in virtual train formation, the paper "Zhu. Lei, Li. Xuefang, Huang. Deqing, et al. Distributed Cooperative Control of Virtual Coupled High-Speed ​​Trains with Consideration of Ride Comfort. IEEE Transactions on Intelligent Vehicles. 2024; 1-13" proposes a distributed model predictive control method to solve the cooperative control problem of virtual coupled high-speed trains. The paper "Yiwen. Zhang, Shukai. Li, Lixing. Yang. Distributed Optimal Control to Virtual Formation of Railway Trains With Dynamic Coupling / Decoupling: An Accelerated Projected GradientBased Decomposition Method IEEE Transactions on Vehicular Technology" further proposes a distributed model predictive control method to solve the cooperative control problem of virtual coupled high-speed trains.To improve the operational efficiency of railway transportation systems, a distributed optimization control method is designed based on multiple trains in a virtual formation mode. The literature “Bai.Weiqi, Lin.Zongli, Dong.Hairong, et al. Distributed Cooperative Cruise Control of Multiple High-Speed ​​Trains Under a State-Dependent Information Transmission Topology. IEEE Transactions on Intelligent Transportation Systems. 2019; 20:2750-2763” designs a distributed control law. The literature “T.Hou, Y.-Y.Guo, and H.-X.Niu. Research on speed control of high speed train based on multi-point model,” Arch. Transp. 2019; 50:35–46” discloses a traditional distributed adaptive coordination control (DACC). The literature “Xi.Wang, Hu.Mingyao, Wang, Hongwei, et al. Formation Control for Virtual Coupling” also presents a distributed control method. The paper "Trains With Parametric Uncertainty and Unknown Disturbances. IEEE Transactions on Circuits and Systems II: Express Briefs. 2023; 70: 3429-3433" discloses a traditional anti-saturation cooperative control (ACC) to achieve multiple trains tracking desired displacements and speeds while maintaining appropriate distances between adjacent trains. However, none of the above-mentioned literature considers the communication delay problem that occurs when multiple trains interact with each other.

[0006] Chinese patent CN116118822B discloses an active collision avoidance control method, system, and medium for train formation operation. The method includes establishing a longitudinal dynamics model of the train containing uncertainties by incorporating uncertainty factors; decomposing parameter terms into nominal terms and time-varying uncertain terms related to the uncertainties; determining safety inequality constraints; establishing a dynamic model of the train spacing error; transforming the dynamic model of the train spacing error from a bounded range to an unbounded range; and establishing robust controllers for each train in the train formation to achieve active collision avoidance control during train formation operation. This invention, by establishing a longitudinal dynamics model of the train and train spacing error inequality constraints, considers the uncertainty of system parameters and performs state transformation on the train spacing error, thereby designing a robust controller to achieve active collision avoidance, enabling the train formation operation system to have active collision avoidance performance under any initial conditions. However, this invention does not consider the communication delay problem that occurs when multiple trains interact with each other. Summary of the Invention

[0007] This invention addresses the problem in the prior art where it is difficult to maintain a safe distance between adjacent trains under conditions of input saturation and communication delay. It provides a method for controlling the safe distance between trains under conditions of input saturation and communication delay.

[0008] To achieve the above objectives, the present invention adopts the following technical solution:

[0009] A method for controlling the following workshop safety distances due to input saturation and communication delay includes the following steps:

[0010] S1. Perform force analysis on the lead train L and N follower trains to establish a dynamic model of the virtual train formation composed of high-speed trains; the dynamic model of the virtual train formation composed of high-speed trains is as follows:

[0011]

[0012] Where i = 1, 2, ..., N is the number of high-speed trains. m i Let x be the mass of the i-th train. i and v i u represents the displacement and velocity of the i-th train, respectively. i A is the driving / braking force generated by the engine in train i. i It is the rolling resistance of train i plus the bearing resistance coefficient, B i C is a coefficient related to air input. i Let F be the aerodynamic coefficient of train i. fi The unknown complex disturbance force experienced by the train;

[0013] S2. Considering the input saturation condition, design a dynamically smooth hyperbolic tangent saturation function as follows:

[0014]

[0015] in, and u represents the maximum driving and braking force actually output by the train. i For actual control input, u i0 For the ideal control input of the design;

[0016] S3. Based on the dynamic smooth hyperbolic tangent saturation function, a dynamic smooth anti-saturation compensator is designed as follows:

[0017]

[0018] Where, Δu=u i -u i0 a i p, q, H i All are constants to be designed, and a i >0,H i >0, s i Let ρ be the sliding mode function. i Let δ be the saturation compensation factor for the i-th high-speed train, and δ be a small positive constant.

[0019] S4. Considering the communication delay between trains, design a delay state prediction formula as follows:

[0020]

[0021] in, Predict the lead train L at time t+β. t Position status at any given moment. Predict the lead train L at time t+β. t The velocity state at time a L Let β be the acceleration of the lead train L as a function of time during its journey. t This refers to the communication delay time.

[0022] S5. Based on the delay state prediction formula, an adaptive law is proposed as follows:

[0023]

[0024] Where the design constants are r>0, m>0, and d>0;

[0025] S6. Feeding the dynamic anti-saturation compensator back to the adaptive law, a time-delay-eliminating, anti-saturation robust controller is proposed as follows:

[0026]

[0027] Where p, q, k0, c i Let be a positive constant to be designed, and 1 <p / q<2;

[0028] S7. Verify system stability to ensure that the distance between adjacent trains remains stable at a safe distance under conditions of input saturation and inter-train communication delay.

[0029] Furthermore, the dynamic model of the pilot train L is described as follows:

[0030]

[0031] Among them, u L The ideal speed required for the Navigator train, v L For reference control input, when the high-speed train experiences input saturation, the above formula can be transformed into:

[0032]

[0033] Among them, sat(u i0 ) represents the actual control input for the train under saturation limitations.

[0034] Furthermore, the virtual train dynamics model treats each train as a point mass, and the drag coefficient of each carriage in the train is the same.

[0035] Furthermore, in step 2, Δu is determined by the actual control input u. i and the ideal control input u of the design i0 Decide.

[0036] Furthermore, when the actual control input reaches saturation, the dynamic anti-saturation compensator starts to work. When it acts until Δu = 0, ρ i It converges to 0 over time, at which point |ρ i If |<δ, the input saturation is resolved, and the dynamic anti-saturation compensator stops working.

[0037] Furthermore, under input saturation conditions, the objective formula for maintaining a safe distance between adjacent high-speed trains is:

[0038]

[0039] Under input saturation conditions, the second formula for achieving the goal of all train speeds tracking the speed of the navigator train is:

[0040]

[0041] Among them, X s L represents the length of a single high-speed train. s This indicates the safe distance between two trains.

[0042] Furthermore, based on the objective formula one of maintaining a safe distance between adjacent high-speed trains and the objective formula two of ensuring all train speeds track the speed of the leader train, and considering communication delays, the multi-train system control objective is updated as follows:

[0043]

[0044] in, and This refers to the position and speed errors of adjacent trains under communication delay conditions.

[0045] Furthermore, in S3, s i The sliding mode function is:

[0046]

[0047] Among them, c i >0, p and q are positive odd numbers, and p>q.

[0048] Furthermore, in step S7, the effectiveness of this method is verified using the Lyapunov function.

[0049] Furthermore, F in S1 fi It is bounded, and |F fi |≤F0, where F0 is a non-zero positive integer.

[0050] The beneficial effects of this invention are as follows:

[0051] This invention designs a dynamic smooth hyperbolic tangent saturation function to solve the problem that the fixed saturation limit and sudden changes in the traditional saturation function can easily lead to overload of the control system. Furthermore, it proposes a dynamic smooth anti-saturation compensator to quickly compensate for the deviation between the actual control input and the ideal control input, thus fully solving the train input saturation problem.

[0052] This invention designs a delay state prediction formula to solve the communication delay problem that occurs when trains interact with each other. It reasonably estimates the state information of the navigator train after the communication delay and updates the control target to the follower train's tracking of the navigator train's state information under the delay.

[0053] This invention designs a time-delay-resistant robust controller to solve the problems of input saturation and communication delay during the operation of virtual high-speed trains, enabling each follower train to accurately track the speed of the leader train, and ensuring that the positional distance between adjacent high-speed trains remains stable at a safe distance. Attached Figure Description

[0054] Figure 1 A flowchart of a method for controlling the safe distance between workshops under input saturation and communication delay;

[0055] Figure 2 A schematic diagram of the spacing between high-speed trains under communication delays;

[0056] Figure 3 This is a diagram illustrating the high-speed train control strategy of the control method of the present invention.

[0057] Figure 4 This is the ideal control input curve for the control method of this invention and traditional anti-saturation collaborative control;

[0058] Figure 5 This is a velocity tracking trajectory diagram under traditional anti-saturation collaborative control.

[0059] Figure 6 This is a speed tracking trajectory diagram under the control method of the present invention;

[0060] Figure 7 This is a comparison chart of the displacement error under input saturation between the control method of this invention and the traditional anti-saturation collaborative control.

[0061] Figure 8 This is a comparison chart of the speed error under input saturation between the control method of this invention and the traditional anti-saturation collaborative control.

[0062] Figure 9 The following diagram illustrates the safe distance between workshops and the input saturation of the control method of this invention and the traditional anti-saturation collaborative control.

[0063] Figure 10 This is a speed tracking curve under communication delay for the control method of the present invention;

[0064] Figure 11 This is a comparison curve of the displacement error under input saturation and communication delay between the control method of the present invention and the traditional distributed adaptive coordinated control.

[0065] Figure 12 This is a comparison curve of the speed error of the control method of the present invention with that of traditional distributed adaptive coordinated control under input saturation and communication delay;

[0066] Figure 13 A schematic diagram illustrating the input saturation and communication delay of the control method of the present invention, showing the safe distance between vehicles.

[0067] Figure 14 The waveform diagram shows a comparison of the position error under input saturation and communication delay between the control method of this invention and the traditional distributed adaptive coordinated control.

[0068] Figure 15 Waveform comparison of the speed error under input saturation and communication delay in the control method of this invention with that of traditional distributed adaptive coordinated control;

[0069] Figure 16Waveform diagram of the safe distance between trains in the control method of the present invention. Detailed Implementation

[0070] The accompanying drawings are for illustrative purposes only and should not be construed as limiting the scope of this patent.

[0071] To better illustrate this embodiment, some parts of the accompanying drawings may be omitted, enlarged, or reduced, and do not represent actual dimensions. It is understandable for those skilled in the art that some well-known content may be omitted in the drawings. The technical solution of the present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0072] Example 1

[0073] like Figure 1 A method for controlling the following workshop safety distances due to input saturation and communication delay includes the following steps:

[0074] S1. Perform force analysis on the lead train L and N follower trains to establish a dynamic model of a virtual train formation composed of high-speed trains;

[0075] Suppose there exists a virtual high-speed train formation system consisting of one lead train and N follower trains. All trains are CRH3 model. The lead train is numbered L, and the subsequent trains in the virtual formation are numbered 1, 2, ..., N. Considering the various forces acting on the trains, including basic and additional resistance, the dynamic model of the virtual train formation composed of multiple high-speed trains is obtained through force analysis as follows:

[0076]

[0077] Where i = 1, 2, ..., N is the number of high-speed trains, mi is the mass of the i-th train, xi and vi represent the displacement and velocity of the i-th train, respectively, and u i It refers to the driving force / braking force generated by the engine in train i. A i (N) is the rolling resistance of train i plus the bearing resistance coefficient, B i (Ns / m) is a coefficient related to air input, C i (Ns 2 / m 2 Let A be the aerodynamic coefficient of train i. i B i C i These are all uncertain parameters that depend on the characteristics of the train. fi For the unknown complex disturbance force experienced by the train, in engineering, it can be assumed that F fi For it to be bounded, i.e., |F fi |≤F0, where F0 is a non-zero positive integer.

[0078] Will Substituting these values ​​into a virtual train formation dynamics model consisting of multiple high-speed trains, the results are summarized as follows:

[0079]

[0080] Additionally, the dynamic description of the Navigator train, designated L, is as follows:

[0081]

[0082] Among them, u L The ideal speed required for the Navigator train, v L For reference, the control input.

[0083] When a high-speed train experiences input saturation, the dynamics model of a virtual train formation consisting of multiple high-speed trains can be transformed into the following equation:

[0084]

[0085] Among them, sat(u i0 ) represents the actual control input for the train under saturation limitations.

[0086] Considering that high-speed trains operate on relatively fixed routes, and all carriages are in almost the same environment throughout the entire journey, the influence of environmental factors on each carriage can be considered approximately the same. To simplify the control algorithm and enhance the feasibility of specific engineering implementation, the model treats each train as a point mass, and the drag coefficient of each carriage in the train is the same.

[0087] S2. Considering the input saturation condition, design a novel Dynamic Smoothing Hyperbolic Tangent Saturation Function (DSHTSF).

[0088] During train operation, when the control system experiences input saturation, the actual system input u i The expression is:

[0089]

[0090] Among them, u i For actual control input, u i0 For the ideal control input of the design, u max and u min These are the maximum and minimum values ​​that the controller can achieve under physical constraints.

[0091] Actual system input u i In the expression, when u i0>u max and u i0 min At times, there is a sudden change between the actual control input and the ideal control input of the system, which can easily cause the control system to overload. Therefore, a Dynamic Smoothing Hyperbolic Tangent Saturation Function (DSHTSF) is designed:

[0092]

[0093] in, and This refers to the maximum driving force and braking force actually output by the train.

[0094] S3. Based on the dynamic smooth hyperbolic tangent saturation function, design a dynamic smooth anti-saturation compensator (DSAsC).

[0095] The novel dynamically smooth hyperbolic tangent saturation function designed in S2 describes the traditional saturation function, u. max and u min It is a fixed constant value. However, during actual train operation, the maximum driving force and braking force output should vary with speed. For the CRH3 high-speed train, when the train speed is below 119 km / h, the train outputs a quasi-constant torque. As the speed increases, the acceleration gradually decreases. When the speed reaches 119 km / h, the power P reaches its maximum value of 8800 kW. Traction / braking force u i The relationship between power and equation is:

[0096]

[0097] Based on traction / braking force u i The relationship between power and dynamic smooth hyperbolic tangent saturation function (DSHTSF) can be derived from this. and The detailed expression is related to train speed:

[0098]

[0099] ​If a controller is directly designed based on the Dynamically Smoothed Hyperbolic Tangent Saturation Function (DSHTSF), it only utilizes the smooth and bounded property of the hyperbolic tangent function to smooth the actual control input, without further compensating for the impact of the ideal control input exceeding saturation on the control system. Therefore, a Dynamically Smoothed Anti-Saturation Compensator (DSAsC) is designed based on the Dynamically Smoothed Hyperbolic Tangent Saturation Function to solve the above problem. This Dynamically Smoothed Anti-Saturation Compensator (DSAsC) is as follows:

[0100]

[0101] Where, Δu=u i -u i0 a i ,p,q,H i All are constants to be designed, and a i >0,H i >0. s i Let ρ be the sliding mode function. i Let δ be the saturation compensation factor for the i-th high-speed train, and δ be a small normal number.

[0102] When the actual control input reaches saturation, the Dynamic Smoothing Anti-Saturation Compensator (DSAsC) starts working. When it reaches Δu = 0, ρ i It converges to 0 over time, at which point |ρ i If |<δ, input saturation is resolved, and the Dynamic Smoothing Anti-Saturation Compensator (DSAsC) stops working. If input saturation reappears in the control system (i.e., Δu≠0), then ρ is reset. i This restores the Dynamic Smoothing Anti-Saturation Compensator (DSAsC) to its working state, resolving the input saturation problem once again.

[0103] S4. Considering the communication delay between trains, design a delay state prediction algorithm (DSP):

[0104] Under input saturation conditions, the control objective expression to be achieved by multiple high-speed trains is as follows:

[0105] The distance between adjacent high-speed trains is always maintained at a safe distance, that is:

[0106]

[0107] All train speeds are tracked to the speed of the navigator train, that is:

[0108]

[0109] Among them, X s L represents the length of a single high-speed train.s This indicates the safe distance between two trains.

[0110] like Figure 2 As shown, due to the communication delay β t Given the existence of train i, the state information received by train i from the navigator train L at time t should be that train L at time t+β t Status information at any given moment.

[0111] To eliminate the effect of delay, the displacement and velocity formulas for variable-speed motion and the time-varying characteristics of derivative integrals are used to estimate the time of delay for the navigator train L at t+β. t Based on the state information at each moment, design the following delay state prediction formula (DSP):

[0112]

[0113] in, Predict train L at time t+β t Position status at any given moment. Predict train L at time t+β t The velocity state at time a L Let β be the acceleration of train L as it travels over time. t Let β be the communication delay time. t It is a known constant value.

[0114] Substituting the Delayed State Prediction (DSP) formula into the control objective expression to be achieved for multiple high-speed trains, the control objective update for the multi-train system, considering input saturation and communication delay, is as follows:

[0115]

[0116] in, and This refers to the position and speed errors of adjacent trains under communication delay conditions.

[0117] In a virtual train dynamics model consisting of multiple high-speed trains, let This represents the estimation error for the corresponding variable. Wherein, and A respectively i B i and C i The estimated value.

[0118] For high-speed train virtual formation systems, the non-singular terminal sliding surface is designed as follows:

[0119]

[0120] Among them, c i>0, p and q are positive odd numbers, and p>q.

[0121] S5. Based on the delay state prediction formula, an adaptive law is proposed as follows:

[0122]

[0123] The design constants are r>0, m>0, and d>0.

[0124] S6. By feeding the dynamic anti-saturation compensator back to the adaptive law, a delay timeliness-anti-saturation robust controller (EDT-AsRC) is proposed:

[0125]

[0126] Where p, q, k0, c i Let be a positive constant to be designed, and 1 <p / q<2。

[0127] For a virtual train dynamics model consisting of multiple high-speed trains under input saturation, under the action of eliminating time delay and anti-saturation adaptive law, when the parameter satisfies k0>0, a i When the value is greater than 0.5k0+0.5, under the condition of communication delay, the speeds v of each following train can be realized within a finite time. i With the speed v of the Navigator train L An agreement was reached, and the distance between adjacent trains was kept consistently at a safe level.

[0128] S7. Verify system stability to ensure that the distance between adjacent trains remains stable at a safe distance under conditions of input saturation and inter-train communication delay:

[0129] The definition is as follows:

[0130] x = [x1, x2, ..., x N ] T v = [v1, v2, ..., v N ] T ,ρ=[ρ1,ρ2,…,ρ N ] T H1=L=H i =LH n

[0131] s = [s1, s2, ..., s N ] T ,

[0132] Choose a positive definite Lyapunov function as follows:

[0133]

[0134] Differentiate the Lyapunov function:

[0135]

[0136]

[0137] According to the actual system input u i As can be seen from the expression, Formula 1 can be obtained by differentiating the Lyapunov function and rearranging the equation:

[0138]

[0139] Substituting the time-delay-resistant robust controller (EDT-AsRC) into Equation 1, we obtain Equation 2:

[0140]

[0141]

[0142] Substituting the adaptive law into Formula 2:

[0143]

[0144] As demonstrated above, under the action of the Delay-Induced Time-Resistant Robust Controller (EDT-AsRC), when t > T, s i →0,ρ i →0. When s i After →0, within a limited time, the distance between adjacent trains is kept at a safe distance, and the speed of each train tracks the speed of the navigator train. Under the action of the adaptive law, the uncertain parameters and estimated values ​​within the system are made consistent. Specific virtual train formation control strategies include... Figure 3 As shown.

[0145] Example 2

[0146] To verify the authenticity and feasibility of the control method of this invention, a simulation experiment was conducted. This embodiment sets up a virtual train formation system including four high-speed trains, including a leader train L. The navigator train operates under ideal conditions according to the running curve, while the other three follower trains are controlled by the control algorithm to track the leader train. First, the experimental parameters are given, then simulation verification is performed using MATLAB, and finally, a semi-physical experiment is conducted on the RT-Lab platform.

[0147] To make the simulation more realistic and feasible, the simulation uses train data driven by an L-shaped linear motor. The simulation assumes that the mass and other parameters of the four high-speed trains are identical and constant, and ignores the influence of noise. The high-speed train parameters are shown in the table below:

[0148] Table 1 Parameters of the Virtual Formation Model for Multiple High-Speed ​​Trains

[0149]

[0150] The controller parameter values ​​designed in the running program are as follows: a i =1.4, k0=1.2, c i =0.8, p=5, q=3. To better simulate the actual operation of the virtual train formation, an ideal operating curve was set up with three conditions: acceleration, constant speed, and braking. In the experimental setup, a sudden change signal was selected to replace the unknown disturbance Φ in the train operation. i,j The maximum communication delay is β max =0.4s. To simulate input saturation in the system, an amplitude of 5.8 × 10⁻⁶ was added. 3 The sudden signal disturbance was applied to the high-speed train to verify that the designed controller has excellent anti-saturation performance.

[0151] First, considering input saturation during multi-train operation, the proposed Delay-Avoiding Time-Restricted Robust Controller (EDT-ASRC) is compared with the traditional Anti-saturation Cooperative Control (ACC) to verify the superiority of the proposed control algorithm. Then, considering both input saturation and communication delay, the proposed EDT-ASRC is compared with the traditional Distributed Adaptive Coordination Control (DACC) to further verify the superiority of the proposed control algorithm.

[0152] I. Comparison of simulation data under input saturation conditions:

[0153] Depend on Figure 4 Data shows that when high-speed trains experience input saturation, the control input under traditional anti-saturation cooperative control (ACC) exhibits abrupt changes. This causes the motors in the train control system to operate at maximum traction for extended periods, potentially leading to motor overload or even damage. The control input under the elimination of time delay – anti-saturation robust controller (EDT-ASRC) – is smoothly limited within the saturation value, effectively resolving the input saturation phenomenon.

[0154] Depend on Figure 5 Data shows that under traditional anti-saturation cooperative control (ACC), the speeds of each follower train catch up with the leader train in 1.3 seconds. When input saturation occurs at 10 seconds, the speed trajectories of each follower train begin to deviate until saturation disappears, at which point they re-track the leader train's speed. Figure 6 Data shows that under the action of the Delay-Avoided Saturation Robust Controller (EDT-ASRC), the speed of each follower train tracks the speed of the leader train within 0.3s. When input saturation occurs, the speed tracking trajectory of each follower train basically does not deviate.

[0155] Depend on Figure 7 Data shows that, considering input saturation during the operation of multiple high-speed trains, the maximum peak displacement error under traditional anti-saturation cooperative control (ACC) is 1.25m, and the displacement error converges to 0 after 20 seconds of train operation. Under the elimination of time delay-anti-saturation robust controller (EDT-ASRC), the maximum peak displacement error is 0.2m, and the displacement error stably converges to 0 after 5 seconds of train operation.

[0156] Depend on Figure 8 Data shows that during the operation of multiple high-speed trains, under the traditional anti-saturation cooperative control (ACC), the maximum peak speed error is 1.0 km / h, and when input saturation occurs, the maximum peak speed error is 0.08 km / h. After 22 seconds of train operation, the displacement error converges to 0. Under the time-delay-eliminated anti-saturation robust controller (EDT-ASRC), the maximum peak displacement error is 0.08 km / h, and when input saturation occurs, the maximum peak displacement error is 0.01 km / h, with almost no error offset.

[0157] Combination Figures 4 to 8 Data shows that when multiple high-speed trains experience input saturation, the proposed Delay-Avoidance Robust Controller (EDT-ASRC) algorithm exhibits better tracking and anti-saturation performance compared to the traditional Anti-Saturation Cooperative Control (ACC) algorithm.

[0158] Depend on Figure 9 Data shows that due to the acceleration, deceleration, and braking during the initial tracking phase, the train spacing fluctuates within 0s≤t≤40s. After 40s of train operation, under the action of the Delay-Avoided Time-Resistant Robust Controller (EDT-ASRC), the train returns to stable operation, and the spacing between each high-speed train remains at a safe distance.

[0159] II. Comparison of simulation data under input saturation and communication delay conditions:

[0160] Depend on Figure 10 Data shows that communication delay β occurs in multi-train systems.t At that time, the delay state prediction formula can predict the navigator train L at t+β t speed state The Delay-Avoided Time-Resistant Robust Controller (EDT-ASRC), designed with the delay state prediction formula as the control objective, can quickly and stably track the speed of the Navigator Train.

[0161] Depend on Figure 11 Data shows that under traditional distributed adaptive coordinated control (DAC), the maximum displacement error peaks at 1.7m due to input saturation, and the jitter is significant. Under the influence of communication delay, because traditional DAC cannot predict the delay information state, the follower train cannot track the navigator train L at t+β. t The position state at any given time, i.e., the position error cannot converge to 0. Under the action of the Delay-Avoided Time-Saturation Robust Controller (EDT-ASRC), when the train faces input saturation, the maximum peak position error is 0.1m, and under the influence of communication delay, the position error can stably converge to 0.

[0162] Depend on Figure 12 Data shows that under traditional distributed adaptive coordinated control (DAC), due to input saturation, the maximum speed error peaks at 1.8 km / h, and the jitter is significant. Under the influence of communication delay, traditional DAC cannot enable the follower train to track the leader train L at t+β. t The speed state at a given moment, i.e., the speed error cannot converge to zero. Under the action of the Delay-Eliminating Time-Anti-Saturation Robust Controller (EDT-ASRC), when the train faces input saturation, the maximum peak speed error is 0.1 km / h, and under the influence of communication delay, the speed error can stably converge to zero. Combined with... Figures 10 to 12 As can be seen, compared with the traditional distributed adaptive coordinated control (DAC) algorithm, the time-delay-resistant robust controller (EDT-ASRC) algorithm designed in this paper can effectively solve the problems of input saturation and communication delay, and has better tracking control performance and anti-saturation performance.

[0163] Depend on Figure 13 It can be seen that, under the virtual formation mode, when faced with input saturation and communication delay, the trains return to stable operation after 10 seconds of operation thanks to the Delay Elimination Time-Anti-Saturation Robust Controller (EDT-ASRC), and the distance between each high-speed train is maintained at a safe distance.

[0164] Example 3

[0165] To further verify the engineering applicability of the control method for safe distance between workshops under input saturation and communication delay designed in this invention, this embodiment uses the RT-LAB hardware platform to conduct an experimental simulation of the actual operation of multiple trains, with parameters consistent with those used in Embodiment 2.

[0166] Depend on Figure 14 The experimental waveforms show that under the traditional Distributed Adaptive Coordinated Control (DAC), the maximum displacement error peak value is 1.56m due to input saturation, and the jitter is significant. Under the influence of communication delay, because the traditional DAC cannot predict the delay information state, the follower train still tracks the position state of the navigator train L at time t. Under the Delay-Eliminating Time-Anti-Saturation Robust Controller (EDT-ASRC), when the train faces input saturation, the maximum position error peak value is 1m, and under the influence of communication delay, the follower train can track the navigator train L at time t+β. t The position state at any given time, the position error can be stably converged to 0.

[0167] Depend on Figure 15 The experimental waveforms show that under the traditional Distributed Adaptive Coordinated Control (DACC) system, the maximum peak speed error is 1.8 km / h due to input saturation, and the fluctuations are significant. Under the influence of communication delay, DACC cannot bring the speed error to zero. Under the Delay-Eliminating Time-Averse-Saturation Robust Controller (EDT-ASRC) system, when the train faces input saturation, the maximum peak speed error is 0.1 km / h, and under the influence of communication delay, the speed error can stably converge to zero.

[0168] Depend on Figure 16 The experimental waveforms show that, under the virtual train formation mode, when faced with input saturation and communication delays, the delay-eliminating time-based anti-saturation robust controller (EDT-ASRC) enables each high-speed train to quickly return to stable operation, and the distance between each high-speed train remains at a safe level. Combined with... Figures 14 to 16 As can be seen, the Delay-Avoided Time-Resistant Robust Controller (EDT-ASRC) algorithm designed in this paper can effectively solve the problems of input saturation and communication delay, and has excellent tracking control performance and anti-saturation performance.

[0169] In summary, this invention addresses the problem of maintaining a safe distance between adjacent trains in virtual high-speed train formations under conditions of input saturation and communication delay. It proposes a control method that can both predict the delay state of the leader train and resolve input saturation. The superiority of this control method is verified through simulation and experimental comparisons. The main conclusions are as follows:

[0170] (1) To address the problem that fixed saturation limits and abrupt changes in traditional saturation functions can easily lead to control system overload, a novel dynamic smooth hyperbolic tangent saturation function, DSHTSF, is proposed. In this function, the actual control input smoothly approaches the maximum traction braking force that varies with train speed. Based on DSHTSF, a novel anti-saturation compensator, DSASC, is further designed, which smoothly limits the control traction force within the saturation limit, while the ACC, designed based on the traditional saturation function, experiences abrupt changes in the traction braking force during operation. Therefore, the dynamic smooth anti-saturation compensator has a better anti-saturation effect.

[0171] (2) To address the communication delay problem during information exchange among multiple trains in virtual train formation, a delay state prediction algorithm (DSP) is proposed. Simulation results demonstrate that this algorithm effectively predicts the state information of the navigator train during communication delays, and the following high-speed trains will track the predicted navigator state. Therefore, this algorithm can effectively solve the communication delay problem during the operation of multiple trains.

[0172] (3) To address the problem of adjacent trains struggling to maintain a safe distance due to input saturation and communication delays, a dynamic smoothing anti-saturation compensator (DSAsC) is fed back into the adaptive law of the design, leading to the proposal of an anti-delay time-dependent robust controller algorithm (EDT-ASRC). Compared to DCAA, this algorithm can track the speed of the lead train within 5 seconds even when input saturation and communication delays occur simultaneously, and quickly maintains a safe distance between adjacent trains. Therefore, this anti-delay time-dependent robust controller algorithm demonstrates superior performance in solving the problems of input saturation and communication delays.

[0173] The embodiments described are merely examples to clearly illustrate the present invention and are not intended to limit the implementation of the invention. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is neither necessary nor possible to exhaustively describe all possible implementations. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the claims of the present invention.

Claims

1. A method for controlling the safe distance between workshops under the following conditions: input saturation and communication delay, characterized in that: Includes the following steps: S1. Perform force analysis on the lead train L and N follower trains to establish a dynamic model of the virtual train formation composed of high-speed trains; the dynamic model of the virtual train formation composed of high-speed trains is as follows: Where i = 1, 2, ..., N is the number of high-speed trains. mi is the mass of the i-th train, xi and vi represent the displacement and velocity of the i-th train, respectively, and u i A is the driving / braking force generated by the engine in train i. i It is the rolling resistance of train i plus the bearing resistance coefficient, B i C is a coefficient related to air input. i Let F be the aerodynamic coefficient of train i. fi The unknown complex disturbance force experienced by the train; S2. Considering the input saturation condition, design a dynamically smooth hyperbolic tangent saturation function as follows: in, and u represents the maximum driving and braking force actually output by the train. i For actual control input, u i0 For the ideal control input of the design; S3. Based on the dynamic smooth hyperbolic tangent saturation function, a dynamic smooth anti-saturation compensator is designed as follows: Where, Δu=u i -u i0 a i p, q, H i All are constants to be designed, and a i >0,H i >0, s i Let ρ be the sliding mode function. i Let δ be the saturation compensation factor for the i-th high-speed train, and δ be a small positive constant. S4. Considering the communication delay between trains, design a delay state prediction formula as follows: in, Predict the lead train L at time t+β. t Position status at any given moment. Predict the lead train L at time t+β. t The velocity state at time a L Let β be the acceleration of the lead train L as a function of time during its journey. t This refers to the communication delay time. S5. Based on the delay state prediction formula, an adaptive law is proposed as follows: Where the design constants are r>0, m>0, and d>0; S6. Feeding the dynamic anti-saturation compensator back to the adaptive law, a time-delay-eliminating, anti-saturation robust controller is proposed as follows: Where p, q, k0, c i Let be a positive constant to be designed, and 1 <p / q<2; S7. Verify system stability to ensure that the distance between adjacent trains remains stable at a safe distance under conditions of input saturation and inter-train communication delay.

2. The method for controlling the safe distance between workshops under the conditions of input saturation and communication delay according to claim 1, characterized in that: The dynamic model of the pilot train L is described as follows: Among them, u L The ideal speed required for the Navigator train, v L For reference control input, when the high-speed train experiences input saturation, the above formula can be transformed into: Among them, sat(u i0 ) represents the actual control input for the train under saturation limitations.

3. The method for controlling the safe distance between workshops under the conditions of input saturation and communication delay according to claim 1, characterized in that: The virtual train dynamics model uses each train as a point mass, and the drag coefficient of each carriage in the train is the same.

4. The method for controlling the safe distance between workshops under the conditions of input saturation and communication delay according to claim 1, characterized in that: In step 2, Δu is the actual control input u i and the ideal control input u of the design i0 Decide.

5. The method for controlling the safe distance between workshops under the conditions of input saturation and communication delay according to claim 1, characterized in that: When the actual control input reaches saturation, the dynamic anti-saturation compensator starts working. When it reaches Δu = 0, ρ i It converges to 0 over time, at which point |ρ i If |<δ, the input saturation is resolved, and the dynamic anti-saturation compensator stops working.

6. The method for controlling the safe distance between workshops under the following conditions of input saturation and communication delay as described in claim 1, characterized in that: Under input saturation conditions, the objective formula for maintaining a safe distance between adjacent high-speed trains is: Under input saturation conditions, the second formula for achieving the goal of all train speeds tracking the speed of the navigator train is: Among them, X s L represents the length of a single high-speed train. s This indicates the safe distance between two trains.

7. The method for controlling the safe distance between workshops under the following conditions of input saturation and communication delay as described in claim 6, characterized in that: Based on the objective formula one of maintaining a safe distance between adjacent high-speed trains and the objective formula two of ensuring that all train speeds track the speed of the leader train, and considering communication delays, the multi-train system control objectives are updated as follows: in, and This refers to the position and speed errors of adjacent trains under communication delay conditions.

8. The method for controlling the safe distance between workshops under the following conditions of input saturation and communication delay as described in claim 1, characterized in that: In S3, s i The sliding mode function is: Among them, c i >0, p and q are positive odd numbers, and p>q.

9. The method for controlling the safe distance between workshops under the conditions of input saturation and communication delay according to claim 1, characterized in that: In step S7, the effectiveness of this method is verified using the Lyapunov function.

10. The method for controlling the safe distance between workshops under the conditions of input saturation and communication delay according to claim 1, characterized in that: F in S1 fi It is bounded, and |F fi |≤F0, where F0 is a non-zero positive integer.

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