Method for controlling inter-vehicle safe distance between input saturation and communication delay

Abstract

The invention provides a method for controlling the following workshop safety distance of input saturation and communication delay, which comprises the following steps of: firstly, establishing a virtual marshalling train dynamic model consisting of high-speed trains, providing a dynamic smooth hyperbolic tangent saturation function of which the saturation limit changes along with the train speed, and further designing a dynamic smooth anti-saturation compensator; secondly, considering communication delay between trains, designing a delay state prediction algorithm, further considering uncertainty of internal parameters of a system, providing an adaptive law, then introducing the adaptive law into a dynamic smooth anti-saturation compensator, designing a time delay elimination-anti-saturation robust controller, and solving the problem that the dynamic smooth anti-saturation compensator is not influenced. According to the control method, the influence of input saturation and communication delay on stable running of the multiple trains can be eliminated, and the distance between the adjacent trains is kept at the safe distance.

Description

Technical Field

[0001] The present invention relates to the technical field of train tracking control, and more specifically to a control method for a safe distance between trains under input saturation and communication delay. Background Art

[0002] With the rapid development of railway transportation systems, a single high-speed train is unable to meet the growing demand for passenger volume. Arranging multiple high-speed trains in a virtual marshaling manner can effectively increase train passenger volume and utilize railway transportation space. However, during the operation of multiple trains, due to the limitation of the maximum traction braking force output by the internal motor of the train, it is difficult to reach the ideal maximum value, resulting in input saturation of the train system. If input saturation is not considered, the train is prone to run at the maximum traction force for a long time, which can easily cause motor overload or even damage. At the same time, there is no physical rigid connection between trains in the virtual marshaling mode, and each train uses communication interaction to obtain status information, which is prone to communication delays, making it difficult to maintain a safe distance between adjacent high-speed trains. Therefore, designing a suitable anti-saturation robust control algorithm to solve the impact of input saturation and communication delay on train operation is the key to achieving safe operation of multi-train virtual marshaling systems.

[0003] For high-speed train target tracking control, sliding mode control (SMC) is widely used in train control systems due to its strong tracking performance. The literature "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 literature "Kang.Zhuanga,Jia.Li-Mina,Zuo.Xiao-Long,et al.A Novel Controller Based on Fuzzy SlidingMode Control for Train Speed ​​Tracking.IEEE Transactions on VehicularTechnology.2024;73:1-16" designs a fuzzy sliding mode controller to achieve train speed tracking. In order to improve the convergence speed of the state error on the sliding surface in SMC, terminal sliding mode control (TSMC) is proposed. The paper "Yu. Xiaodonga, Zhou. Boa, Fang. Wenjing, et al. Super-Twisting Terminal Sliding Mode Decoupling Current Control for Sinusoidal Doubly Salient Electromagnetic Machine Drives. IEEE Transactions on Energy Conversion. 2024; 1-17" proposed a new TSMC method to achieve high performance of the motor. In order to solve the non-singular phenomenon in TSMC, non-singular terminal sliding mode control (NTSMC) was proposed.The literature "Zebin.Yang, Jianfei.Sun, Xiaodong.Sun, et al. Direct Instantaneous Torque Control for Six-Phase SRM With Nonsingular Fast Terminal Sliding 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 the motor. However, the above control algorithm is difficult to adapt to the uncertainty of the internal parameters of the system. The literature ". Mustafa. A New Adaptive Terminal Sliding Mode Speed ​​Control in Flux Weakening Region for DTC Controlled Induction Motor Drive. IEEE Transactions on Power Electronics. 2024; 39: 449-458” In order to improve the control performance of the induction motor, a more robust ATSMC is proposed. Although the above sliding mode control algorithm has superior control performance, it still needs to be further studied in the field of virtual marshaling multi-train coordinated control, especially the input saturation problem that occurs in the operation of multiple trains, and it is urgent to find a more efficient and practical solution.

[0004] The current solutions to the input saturation phenomenon are: limiting the control input through a saturation function, directly considering input saturation when designing the control algorithm, and correcting the saturation deviation through an anti-saturation compensator. The literature "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 uses a saturation function to solve the input saturation of high-speed trains, and the literature "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 the input saturation phenomenon of heavy-load trains. Both of the above literatures limit input saturation through a saturation function, but mutations are prone to occur when limiting control inputs. The document "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 new anti-saturation control algorithm based on the backstepping method to solve input saturation in the controller design process, but this method is relatively complicated.The document “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 of the control system; the document “Zhang.Jianyi,Ren.Wei,Sun,Xi-Ming.Extended-State-Observer-Based Nonlinear Control for PMSM Servo SystemsWith 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 documents design a suitable anti-saturation compensator to solve input saturation after designing the controller. This method is simple and effective, but the saturation limits are fixed values. Considering the research background of multiple trains, the maximum value of the actual control input should change 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 andartificial potential field on SE(3).OceanEngineering.2022;253:111148” proposed a finite-time position and attitude tracking control algorithm based on artificial potential field and virtual formation in order to detect the motion posture of underwater robots and detect 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” proposed a distributed model predictive control scheme to achieve trajectory tracking and obstacle avoidance of multiple UAV formations. None of the above literatures have conducted research in the context of multiple trains. Aiming at the goal of achieving safe distance tracking of adjacent trains under virtual marshaling, the paper "Zhu.Lei, Li.Xuefang, Huang.Deqing, et al.Distributed Cooperative Control of VirtualCoupled High-Speed ​​Trains with Consideration of Ride Comfort.IEEE Transactions on Intelligent Vehicles.2024;1-13" proposed 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 RailwayTrains With Dynamic Coupling / Decoupling:An Accelerated Projected GradientBased Decomposition Method IEEE Transactions on Vehicular Technology.2023;72:15405-15420” In order to improve the operating efficiency of the railway transportation system, a distributed optimization control is designed based on multiple trains in a virtual formation mode; the literature “Bai.Weiqi,Lin.Zongli,Dong.Hairong,et al.DistributedCooperative Cruise Control of Multiple High-Speed ​​Trains Under aState-Dependent Information Transmission Topology.IEEE Transactions on IntelligentTransportation 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 onmulti-point model,”Arch.Transp.2019;50:35–46” discloses a traditional distributed adaptive coordination control (Distributed Adaptive Coordination Control,DACC), the literature “Xi.Wang,Hu.Mingyao,Wang,Hongwei,et al.Formation Control for Virtual Coupling 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 the tracking of multiple trains on the desired displacement and speed while keeping the distance between adjacent trains at an appropriate distance. However, the above literature does not consider the communication delay problem that occurs when multiple trains interact with each other.

[0006] Invention patent CN116118822B discloses an active collision avoidance control method, system and medium during train marshaling operation. The method of the present invention includes establishing a longitudinal dynamic model of the train containing uncertainty in combination with uncertainty factors, decomposing the parameter terms into nominal terms and time-varying uncertain terms related to uncertainty; determining safety inequality constraints, and establishing a dynamic model of inter-vehicle distance error, transforming the dynamic model of inter-vehicle distance error from a bounded range to an unbounded range, and establishing a robust controller for each train in the train marshaling to achieve active collision avoidance control during train marshaling operation. The present invention establishes a longitudinal dynamic model of the train and an inequality constraint of inter-vehicle distance error, considers the uncertainty of system parameters and performs state transformation on the inter-vehicle distance error, thereby designing a robust controller to achieve active collision avoidance of the system, so that the train marshaling operation system has active collision avoidance performance under any initial conditions, but the invention does not consider the communication delay problem that occurs when multiple trains interact with each other. Summary of the invention

[0007] Aiming at the problem in the prior art that the distance between adjacent trains is difficult to maintain within a safe distance under the conditions of input saturation and communication delay, the present invention provides a control method for the safe distance between trains under the conditions of input saturation and communication delay.

[0008] To achieve the above object, the present invention adopts the following technical solutions:

[0009] A control method for a safe distance between vehicles due to input saturation and communication delay, comprising the following steps:

[0010] S1. Perform force analysis on the pilot train L and N follower trains, and establish a dynamic model of a virtual train consisting of high-speed trains. The dynamic model of a virtual train consisting of high-speed trains is:

[0011]

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

[0013] S2. Considering the input saturation, a dynamic smooth hyperbolic tangent saturation function is designed as:

[0014]

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

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

[0017]

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

[0019] S4. Considering the delay in inter-train communication, a delay state prediction formula is designed as follows:

[0020]

[0021] in, To predict the pilot train L at time t at t+β t The position status at the moment, To predict the pilot train L at time t at t+β t The speed state at the moment, a L is the acceleration of the pilot train L that changes with time during its travel, β t is the communication delay time;

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

[0023]

[0024] The constants to be designed are r>0, m>0, d>0;

[0025] S6. Feedback the dynamic anti-saturation compensator to the adaptive law, and propose a robust controller to eliminate the delay time and anti-saturation as follows:

[0026]

[0027] Among them, p, q, k0, c i is 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 input saturation and inter-train communication delay conditions.

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

[0030]

[0031] Among them, u L is the ideal required speed v of the leader train L As the reference control input, when the high-speed train input saturation occurs, the above formula can be transformed into:

[0032]

[0033] Among them, sat(u i0 ) is the actual control input of the train under saturation constraints.

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

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

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

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

[0038]

[0039] Under the input saturation state, the target formula for all train speeds to track the leader train speed is:

[0040]

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

[0042] Furthermore, according to the target formula 1 that the distance between adjacent high-speed trains is kept at a safe distance and the target formula 2 that all train speeds track the speed of the leader train, and considering the communication delay, the control target of the multi-train system is updated as follows:

[0043]

[0044] in, and are the position error and speed error of adjacent trains under communication delay.

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

[0046]

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

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

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

[0050] The beneficial effects of the present invention are:

[0051] The present invention designs a dynamic smooth hyperbolic tangent saturation function to solve the problem that the saturation limit in the traditional saturation function is fixed and the sudden change easily leads to the overload of the control system, and then proposes a dynamic smooth anti-saturation compensator to quickly compensate for the deviation between the actual control input and the ideal control input, so as to fully solve the problem of train input saturation.

[0052] The present invention designs a delayed state prediction formula to solve the communication delay problem that occurs when information is exchanged between trains, reasonably estimates the state information of the leader train after the communication delay, and updates the control target to the follower train tracking the leader train state information under delay.

[0053] The present invention designs a delay-eliminating anti-saturation robust controller to solve the input saturation and communication delay problems in the operation of virtual marshaling high-speed trains, and realizes the precise tracking of the speed of the leader train by the speed of each follower train, so that the position distance between adjacent high-speed trains is stably maintained at a safe distance. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 A flow chart of a control method for the following vehicle safety distance with input saturation and communication delay;

[0055] Figure 2 Schematic diagram of the distance between high-speed trains under communication delay;

[0056] Figure 3 A high-speed train control strategy diagram of the control method of the present invention;

[0057] Figure 4 It is an ideal control input curve of the control method of the present invention and the traditional anti-saturation cooperative control;

[0058] Figure 5 It is the velocity tracking trajectory diagram under the traditional anti-saturation cooperative control;

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

[0060] Figure 7 A comparison diagram of displacement errors under input saturation between the control method of the present invention and the traditional anti-saturation cooperative control;

[0061] Figure 8 A comparison diagram of speed error under input saturation between the control method of the present invention and the traditional anti-saturation cooperative control;

[0062] Fig. 9 The schematic diagram of the safe distance between the following vehicles when the control method of the present invention and the traditional anti-saturation cooperative control input are saturated;

[0063] Fig.10 It is a speed tracking curve diagram under communication delay of the control method of the present invention;

[0064] Fig.11 A comparison curve of displacement errors between the control method of the present invention and the traditional distributed adaptive coordinated control under input saturation and communication delay;

[0065] Fig.12 It is a speed error comparison curve diagram of the control method of the present invention and the traditional distributed adaptive coordinated control under input saturation and communication delay;

[0066] Fig.13 A schematic diagram of the safe distance for train derailment under input saturation and communication delay in the control method of the present invention;

[0067] Fig.14 It is a waveform diagram comparing the position error under input saturation and communication delay between the control method of the present invention and the traditional distributed adaptive coordinated control;

[0068] Fig.15 Comparison waveform of speed error between the control method of the present invention and traditional distributed adaptive coordinated control under input saturation and communication delay;

[0069] Fig.16The control method of the present invention is a waveform diagram of the safe distance between trains. DETAILED DESCRIPTION

[0070] The drawings are for illustrative purposes only and should not be construed as limiting the present patent;

[0071] In order to better illustrate the present embodiment, some parts of the drawings may be omitted, enlarged or reduced, and do not represent the actual size; for those skilled in the art, it is understandable that some well-known contents in the drawings may be omitted. The technical solution of the present invention is further explained below in conjunction with the drawings and embodiments.

[0072] Example 1

[0073] like Figure 1 , a control method for the vehicle safety distance below input saturation and communication delay, comprising the following steps:

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

[0075] Assume that there is a high-speed train virtual marshaling system consisting of a leader train and N follower trains. Each train uses the CRH3 model, and the leader train is numbered L. The numbers of the virtual marshaling of the follower trains are 1, 2, ..., N. Considering the various forces acting on the train such as the basic resistance and additional resistance, the dynamic model of the virtual marshaling train consisting of multiple high-speed trains is obtained through force analysis:

[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 speed of the i-th train respectively, and u i is the driving force / braking force generated by the engine in train i. 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 ) is the aerodynamic coefficient of train i, A i ,B i ,C i are uncertain parameters that depend on the characteristics of the train. fi is the unknown composite disturbance force on the train. In engineering, it can be assumed that F fi is bounded, that is, |F fi |≤F0, F0 is a non-zero positive constant.

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

[0079]

[0080] In addition, the dynamic description of the leader train numbered L is:

[0081]

[0082] Among them, u L is the ideal required speed v of the leader train L is the reference control input.

[0083] When the input saturation of high-speed train occurs, the dynamic model of virtual marshaling train composed of multiple high-speed trains can be transformed into the following formula:

[0084]

[0085] Among them, sat(u i0 ) is the actual control input of the train under saturation constraints.

[0086] Considering that the high-speed train runs on a relatively fixed route, all carriages are in the same environment almost throughout the entire operation, so the influence of environmental factors on each carriage can be considered to be approximately the same. In order to simplify the control algorithm and enhance the feasibility of specific engineering implementation, the model uses each train as a mass point, and the resistance coefficient of each carriage in the train is the same.

[0087] S2. Considering the input saturation, a new dynamic smoothing hyperbolic tangent saturation function (DSHTSF) is designed;

[0088] During the train running, when the control system is saturated, the actual system input u i The expression is:

[0089]

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

[0091] Actual system input u i In the expression, when u i0>u max and u i0 min When the actual control input of the system is different from the ideal control input, it is easy to overload the control system. Therefore, a dynamic smoothing hyperbolic tangent saturation function (DSHTSF) is designed:

[0092]

[0093] in, and It is the maximum driving force and braking force actually output by the train.

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

[0095] A new type of dynamic smooth hyperbolic tangent saturation function designed in S2 describes the traditional saturation function, u max and u min is a fixed constant. However, in the actual running process of the train, the maximum driving force and braking force output should change with the speed. For the CRH3 model high-speed train, when the train running speed is lower than 119km / h, the train outputs a quasi-constant torque. As the speed continues to increase, the acceleration will gradually decrease. When its speed reaches 119km / h, the power P reaches a maximum value of 8800kW. Traction / braking force u i The relationship between it and power is:

[0096]

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

[0098]

[0099] ​If the controller is directly designed based on the dynamic smooth hyperbolic tangent saturation function (DSHTSF), the actual control input is smoothed by only utilizing the smoothness and boundedness of the hyperbolic tangent function, and no further substantial compensation is made for the impact of the part of the ideal control input that exceeds the saturation on the control system. Therefore, a dynamic smooth anti-saturation compensator (DSAsC) is designed based on the dynamic smooth hyperbolic tangent saturation function to solve the above problem. The dynamic smooth anti-saturation compensator (DSAsC) is:

[0100]

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

[0102] When the actual control input reaches saturation, the dynamic smoothing anti-saturation compensator (DSAsC) starts to work. When it acts to Δu=0, ρ i Converges to 0 over time, at which point |ρ i |<δ, input saturation is resolved and the dynamic smoothing anti-saturation compensator (DSAsC) stops working. If the control system has input saturation again, that is, Δu≠0, reset ρ i The dynamic smoothing anti-saturation compensator (DSAsC) is restored to work and the input saturation problem is solved again.

[0103] S4. Considering the communication delay between trains, a delay state prediction algorithm (Delay State Prediction algorithm, DSP) is designed:

[0104] Under the condition of input saturation, the control target expression that multiple high-speed trains need to achieve is as follows:

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

[0106]

[0107] All train speeds track the leader train speed, i.e.:

[0108]

[0109] Among them, X s Indicates the length of a single high-speed train, Ls Indicates the safe distance between two trains.

[0110] like Figure 2 As shown, due to the communication delay β t , the state information received by train i from the leader train L at time t should be the state information of train L at t+β t Status information at all times.

[0111] In order to eliminate the influence of delay, according to the displacement and velocity formula of variable speed motion and the time-varying characteristics of derivative integral, the estimated pilot train L at t+β t The state information at each moment is used to design the following delay state prediction formula (DSP):

[0112]

[0113] in, To predict the train L at time t+β t The position status at the moment, To predict the train L at time t+β t The speed state at the moment, a L is the acceleration of train L that changes with time during its travel, β t is the communication delay time, and β t is a known constant value.

[0114] Substituting the delayed state prediction formula (DSP) into the control target expression to be achieved by multiple high-speed trains, the control target of the multi-train system is updated as follows, considering input saturation and communication delay:

[0115]

[0116] in, and are the position error and speed error of adjacent trains under communication delay.

[0117] In the dynamic model of a virtual train consisting of multiple high-speed trains, is the corresponding variable estimation error. and A i ,B i and C i The estimated value of .

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

[0119]

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

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

[0122]

[0123] Among them, the constants to be designed are r>0, m>0, d>0.

[0124] S6. Feedback the dynamic anti-saturation compensator to the adaptive law, and propose an Eliminate Delay Timeliness-Anti-saturation Robust Controller (EDT-AsRC) as follows:

[0125]

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

[0127] For the dynamic model of a virtual train consisting of multiple high-speed trains under input saturation, under the effect of the delay time elimination-anti-saturation adaptive law, when the parameters satisfy k0>0, a i >0.5k0+0.5, under the condition of communication delay, the speed v of each following train can be achieved within a limited time i With the pilot train speed v L A consensus is reached and the distance between adjacent trains is kept stable at a safe distance.

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

[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:

[0133]

[0134] Derivative of the Lyapunov function:

[0135]

[0136]

[0137] According to the actual system input u i The expression shows that, The Lyapunov function can be differentiated and then sorted to get formula 1:

[0138]

[0139] Substituting the delay elimination time-anti-saturation robust controller (EDT-AsRC) into Formula 1, we get Formula 2:

[0140]

[0141]

[0142] Substitute the adaptive law into formula 2:

[0143]

[0144] From the above proof, it can be seen that under the action of the delay elimination-anti-saturation robust controller (EDT-AsRC), when t>T, s i →0,ρ i →0. When s i →0, within a limited time, the distance between adjacent trains is maintained at a safe distance, and the speed of each train tracks the speed of the leader train. Under the action of the adaptive law, the uncertainty parameters in the system are consistent with the estimated values. The specific virtual train control strategy is as follows: Figure 3 shown.

[0145] Example 2

[0146] In order to verify the authenticity and feasibility of the control method of the present invention, a simulation experiment is set up for verification. In this embodiment, a virtual marshaling train system is set up, including 4 high-speed trains including the leader train L. The leader train runs under ideal conditions according to the running curve, and the other 3 follower trains follow the leader according to the control algorithm. First, the experimental parameters are given, and then simulation verification is performed using MATLAB, and finally a semi-physical experiment is performed on the RT-Lab platform.

[0147] In order to make the simulation more realistic and feasible, the train data driven by L-type linear motors is used in the simulation. In the simulation, it is assumed that the mass and other parameters of the four high-speed trains are the same and unchanged, and the influence of noise is ignored. The parameters of the high-speed trains are shown in the following table:

[0148] Table 1 Parameters of virtual marshaling model for multiple heavy high-speed trains

[0149]

[0150] The controller parameter values ​​designed in the running program are: a i =1.4, k0=1.2, c i =0.8, p=5, q=3. In order to better simulate the actual operation of the virtual marshaling train, the ideal operation curve is divided into three working conditions: acceleration stage, constant speed stage, and braking stage. In the experimental setting, the mutation signal is selected to replace the unknown disturbance Φ in the train operation. i,j , the maximum communication delay is β max =0.4s. In order to simulate the input saturation phenomenon of the system, an amplitude of 5.8×10 3 The sudden signal disturbance is applied to the high-speed train, verifying that the designed controller has excellent anti-saturation performance.

[0151] First, considering the input saturation during the operation of multiple trains, the proposed EDT-ASRC is compared with the traditional anti-saturation cooperative control (ACC) to verify the superiority of the control algorithm proposed in this paper. Then, considering both input saturation and communication delay, the proposed EDT-ASRC is compared with the traditional distributed adaptive coordination control (DACC) to verify the superiority of the control algorithm proposed in this paper.

[0152] 1. Comparison of simulation data under input saturation:

[0153] Depend on Figure 4 Data shows that after input saturation occurs in high-speed trains, the control input under the traditional anti-saturation cooperative control (ACC) directly changes suddenly, and the motor in the train control system runs at maximum traction for a long time, which can easily cause motor overload or even damage. The control input under the Elimination of Delay Time-Anti-Saturation Robust Controller (EDT-ASRC) is smoothly limited to the saturation value, effectively solving the input saturation phenomenon.

[0154] Depend on Figure 5 The data shows that under the traditional anti-saturation cooperative control (ACC), the speed of each follower train tracks the speed of the leader train in 1.3s. When input saturation occurs at 10s, the speed trajectory of each follower train begins to deviate until the saturation disappears and then tracks the speed of the leader train again. Figure 6 The data show that under the action of the Elimination of Delay Timing-Anti-saturation Robust Controller (EDT-ASRC), the speed of each follower train tracks 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 The data shows that when input saturation is considered during the operation of multiple high-speed trains, the maximum displacement error peak is 1.25m under the traditional anti-saturation coordinated control (ACC), and the displacement error converges to 0 after the train runs for 20s. Under the Elimination of Delay Temporal Anti-saturation Robust Controller (EDT-ASRC), the maximum displacement error peak is 0.2m, and the displacement error stably converges to 0 after the train runs for 5s.

[0156] Depend on Figure 8 The data shows that during the operation of multiple high-speed trains, under the action of traditional anti-saturation coordinated control (ACC), the maximum speed error peak is 1.0 km / h, and when input saturation occurs, the maximum speed error peak is 0.08 km / h. After the train runs for 22 seconds, the displacement error converges to 0. Under the action of the Elimination of Delay Temporal-Anti-saturation Robust Controller (EDT-ASRC), the maximum displacement error peak is 0.08 km / h, and when input saturation occurs, the maximum displacement error peak is 0.01 km / h, with almost no error offset.

[0157] Combination Figures 4 to 8 The data shows that when input saturation occurs in multiple high-speed trains, the Elimination of Delay Time-Anti-saturation Robust Controller (EDT-ASRC) algorithm designed in this paper has better tracking performance and anti-saturation performance than the traditional anti-saturation cooperative control (ACC) algorithm.

[0158] Depend on Fig. 9 The data show that due to the starting acceleration and deceleration braking of the train at the beginning of the tracking phase, the train spacing fluctuates within 0s≤t≤40s. After the train runs for 40s, under the action of the delay elimination-anti-saturation robust controller (EDT-ASRC), the train returns to stable operation, and the spacing between high-speed trains is maintained at a safe distance.

[0159] 2. Comparison of simulation data under input saturation and communication delay:

[0160] Depend on Fig.10 The data shows that there is a communication delay β in the multi-train systemt The delay state prediction formula can predict the leader train L at t+β t Speed ​​status The EDT-ASRC controller designed with the delayed state prediction formula as the control target can quickly and stably track the speed of the leader train.

[0161] Depend on Fig.11 The data shows that under the action of traditional distributed adaptive coordinated control DACC, due to the influence of input saturation, the maximum displacement error peak is 1.7m, and the jitter is large. Under the influence of communication delay, since traditional distributed adaptive coordinated control DACC cannot predict the delay information state, the follower train cannot track the leader train L at t+β t The position state at the moment, that is, the position error cannot converge to 0. Under the action of the Elimination of Delay Temporal-Anti-Saturation Robust Controller (EDT-ASRC), when the train faces input saturation, the maximum position error peak is 0.1m, and under the influence of communication delay, the position error can stably converge to 0.

[0162] Depend on Fig.12 The data shows that under the action of traditional distributed adaptive coordinated control DACC, due to the influence of input saturation, the maximum speed error peak is 1.8km / h, and the jitter is large. Under the influence of communication delay, the traditional distributed adaptive coordinated control DACC cannot make the follower train track the leader train L at t+β t The speed state at the moment, that is, the speed error cannot converge to 0. Under the action of the delay elimination time-anti-saturation robust controller (EDT-ASRC), when the train faces input saturation, the maximum speed error peak is 0.1km / h, and under the influence of communication delay, the speed error can stably converge to 0. Figures 10 to 12 It can be seen that compared with the traditional distributed adaptive coordinated control DACC algorithm, the delay-eliminating temporal-anti-saturation 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 Fig.13 It can be seen that when multiple trains in the virtual marshaling mode face input saturation and communication delay, under the action of the delay elimination time-anti-saturation robust controller (EDT-ASRC), the train returns to stable operation after 10s of operation, and the distance between each high-speed train is maintained at a safe distance.

[0164] Example 3

[0165] In order to further verify the engineering practicability of the control method for the vehicle safety distance under input saturation and communication delay designed by the present invention, the present embodiment uses the RT-LAB semi-physical platform to conduct experiments to simulate the actual operation of multiple trains, and the parameters are consistent with those used in Example 2.

[0166] Depend on Fig.14 The experimental waveform shown in the figure shows that under the influence of traditional distributed adaptive coordinated control DACC, due to the influence of input saturation, the maximum displacement error peak is 1.56m, and the jitter is large. Under the influence of communication delay, since the traditional distributed adaptive coordinated control DACC cannot predict the delayed information state, the follower train still tracks the position state of the leader train L at time t. Under the influence of the delay-eliminating temporal-anti-saturation robust controller (EDT-ASRC), when the train faces input saturation, the maximum position error peak is 1m, and under the influence of communication delay, the follower train can track the leader train L at t+β t The position state at the moment, the position error can stably converge to 0.

[0167] Depend on Fig.15 The experimental waveforms shown in the figure show that under the action of the traditional distributed adaptive coordinated control DACC, due to the influence of input saturation, the maximum speed error peak is 1.8km / h, and the jitter is large. Under the influence of communication delay, DACC cannot converge the speed error to 0. Under the action of the delay-eliminating temporal-anti-saturation robust controller (EDT-ASRC), when the train faces input saturation, the maximum speed error peak is 0.1km / h, and under the influence of communication delay, the speed error can stably converge to 0.

[0168] Depend on Fig.16 The experimental waveforms shown in the figure show that when multiple high-speed trains in the virtual marshaling mode face input saturation and communication delay, under the action of the delay elimination time-anti-saturation robust controller (EDT-ASRC), each train can quickly recover to stable operation, and the distance between each high-speed train is maintained at a safe distance. Figures 14 to 16 It can be seen that the Elimination of Delay Timing-Anti-saturation 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, the present invention aims at the problem that the distance between adjacent trains is difficult to maintain at a safe distance under the condition of input saturation and communication delay for virtual marshaling high-speed trains. A control method that can predict the delay state of the leader train and solve the problem of input saturation is proposed, and the superiority of the control method is verified through simulation comparison and experimental comparison. The main conclusions are as follows:

[0170] (1) Aiming at the problem that the saturation limit in the traditional saturation function is fixed and the sudden change easily leads to the overload of the control system, a new dynamic smooth hyperbolic tangent saturation function DSHTSF is proposed. In this function, the actual control input is smoothed close to the maximum traction braking force that changes with the train speed. Based on DSHTSF, a new anti-saturation compensator DSASC is further designed, which makes the controlled traction force smoothly limited within the saturation limit. In contrast, the traction braking force in the ACC designed based on the traditional saturation function undergoes a sudden change during operation. Therefore, the dynamic smooth anti-saturation compensator has a better anti-saturation effect.

[0171] (2) Aiming at the communication delay problem when multiple trains interact with each other under the virtual marshaling mode, a delay state prediction algorithm DSP is proposed. Through simulation verification, the algorithm effectively predicts the state information of the leader train when the communication delay occurs, and the follower high-speed train will track the estimated leader state. Therefore, the algorithm is effective in solving the communication delay problem of multiple trains during driving.

[0172] (3) In order to solve the problem that adjacent trains cannot maintain a safe distance due to input saturation and communication delay, a dynamic smoothing anti-saturation compensator DSASC is fed back into the designed adaptive law, and then an EDT-ASRC algorithm with delay elimination can be proposed. Compared with DCAA, this algorithm can track the speed of the leader train within 5 seconds when input saturation and communication delay occur simultaneously, and quickly keep the distance between adjacent trains at a safe distance. Therefore, an EDT-ASRC algorithm with delay elimination can have superior performance in solving the problems of input saturation and communication delay.

[0173] The embodiments are merely examples for clearly illustrating the present invention, and are not intended to limit the embodiments of the present invention. For those skilled in the art, other different forms of changes or modifications can be made based on the above description. It is not necessary and impossible to list all the embodiments here. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the claims of the present invention.

Claims

1. A control method for the safe distance between vehicles under input saturation and communication delay, characterized in that: The following steps are involved: S1. Perform force analysis on the pilot train L and N follower trains, and establish a dynamic model of a virtual train consisting of high-speed trains. The dynamic model of a virtual train consisting of high-speed trains is: Where i=1,2,...,N is the number of high-speed trains, mi is the mass of the ith train, xi and vi represent the displacement and velocity of the ith train respectively, u i is the driving force / braking force generated by the engine in train i, A i is the rolling resistance of train i plus the bearing resistance coefficient, B i is a coefficient related to air input, C i is the aerodynamic coefficient of train i, F fi is the unknown composite disturbance force acting on the train; S2. Considering the input saturation, a dynamic smooth hyperbolic tangent saturation function is designed as: in, and is the maximum driving force and braking force actually output by the train, u i is the actual control input, u i0 is the ideal control input for the design; S3. Based on the dynamic smooth hyperbolic tangent saturation function, a dynamic smooth anti-saturation compensator is designed as: Where Δu=u i -u i0 , a i , p, q, H i are constants to be designed, and a i >0,H i >0,s i is the sliding mode function, ρ i is the saturation compensation factor of the i-th high-speed train, δ is a small positive constant; S4. Considering the delay in inter-train communication, a delay state prediction formula is designed as follows: in, To predict the pilot train L at time t at t+β t The position status at the moment, To predict the pilot train L at time t at t+β t The speed state at the moment, a L is the acceleration of the pilot train L that changes with time during its travel, β t is the communication delay time; S5. Based on the delay state prediction formula, an adaptive law is proposed: The constants to be designed are r>0, m>0, d>0; S6. Feedback the dynamic anti-saturation compensator to the adaptive law, and propose a robust controller to eliminate the delay time and anti-saturation as follows: Among them, p, q, k0, c i is 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 input saturation and inter-train communication delay conditions.

2. The method for controlling the vehicle safety distance due to input saturation and communication delay according to claim 1, characterized in that: The dynamic model of pilot train L is described as: Among them, u L is the ideal required speed v of the leader train L As the reference control input, when the high-speed train input saturation occurs, the above formula can be transformed into: Among them, sat(u i0 ) is the actual control input of the train under saturation constraints.

3. The method for controlling the vehicle safety distance due to input saturation and communication delay according to claim 1, characterized in that: The virtual train dynamics model takes each train as a mass point, and the resistance coefficient of each carriage in the train is the same.

4. The method for controlling the vehicle safety distance due to 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 i0 Decide.

5. The method for controlling the vehicle safety distance due to 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 to work. When it acts to Δu=0, ρ i Converges to 0 over time, at which point |ρ i |<δ, the input saturation is resolved and the dynamic anti-saturation compensator stops working.

6. The method for controlling the vehicle safety distance under input saturation and communication delay according to claim 1, characterized in that: Under the condition of input saturation, the target formula for maintaining a safe distance between adjacent high-speed trains is: Under the input saturation state, the target formula for all train speeds to track the leader train speed is: Among them, X s Indicates the length of a single high-speed train, L s Indicates the safe distance between two trains.

7. The method for controlling the vehicle safety distance due to input saturation and communication delay according to claim 6, characterized in that: According to the target equation 1 that the distance between adjacent high-speed trains is kept at a safe distance and the target equation 2 that all train speeds track the speed of the leader train, and considering the communication delay, the control target of the multi-train system is updated as follows: in, and are the position error and speed error of adjacent trains under communication delay.

8. The method for controlling the vehicle safety distance due to input saturation and communication delay according to claim 1, characterized in that: In S3s i The sliding mode function is: Among them, c i >0, p, q are positive odd numbers, and p>q.

9. The method for controlling the vehicle safety distance due to input saturation and communication delay according to claim 1, characterized in that: In step S7, the effectiveness of this method is verified by using the Lyapunov function.

10. The method for controlling the vehicle safety distance due to input saturation and communication delay according to claim 1, characterized in that: The S1 F fi is bounded, and |F fi |≤F0, F0 is a non-zero positive constant.

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