Virtual marshalling multi-train cooperative adaptive sliding mode control method based on extended state observer

Abstract

The invention discloses a virtual marshalling multi-train cooperative adaptive sliding mode control method based on an extended state observer, and the method comprises the steps: firstly constructing an urban rail multi-train tracking error dynamic model based on a unit train dynamic equation; secondly, establishing a nonsingular terminal sliding mode surface according to the urban rail multi-train tracking error dynamical model to obtain an equivalent control law, combining the equivalent control law with a switching control law to obtain a nonsingular terminal sliding mode control law, and introducing a gain adaptive law and a saturation function into the nonsingular terminal sliding mode control law to obtain an adaptive nonsingular terminal sliding mode control law; and finally, an extended state observer is adopted to estimate external interference, an observation value of the interference is added to the output of the adaptive nonsingular terminal sliding mode controller to serve as feed-forward compensation, and the adaptive nonsingular terminal sliding mode control method based on the extended state observer is constructed. According to the method, the multi-train cooperative operation tracking control precision and stability can be remarkably improved under the external interference condition.

Description

Technical Field

[0001] The present invention belongs to the technical field of train control, and in particular relates to a collaborative adaptive sliding mode control method for virtual marshaling multiple trains based on an extended state observer. Background Art

[0002] Virtual Coupling (VC) technology has a good effect in solving the problems that the existing urban rail trains are prone to large differences in full load rates during peak and off-peak periods due to fixed marshaling modes, making it difficult to adapt to the unbalanced characteristics of passenger flow demand, resulting in waste of resources and transportation capacity. Therefore, train control technology under virtual marshaling conditions is a hot topic in urban rail transit research. Virtual marshaling technology enables multiple unit trains to operate in coordination to form a virtual formation through communication and active control between vehicles, thereby improving operation efficiency, reducing energy consumption, and improving the safety and stability of the rail transit system. Combining the dynamic characteristics of urban rail transit trains and effective control methods, an efficient train operation system controller is designed to achieve the coordinated operation of multiple trains at a predetermined speed and position, so that a virtual marshaling operation strategy with information sharing and collaborative decision-making characteristics can be realized. Therefore, studying the virtual marshaling multi-train collaborative tracking operation control method is of great significance to the realization of flexible marshaling and intelligent dynamic scheduling strategies under vehicle-to-vehicle communication technology.

[0003] The coordinated tracking operation control of multiple trains in urban rail is affected by the real-time performance of the train ATO (Automatic Train Operation) curve. It is necessary to adopt a control algorithm with fast response speed and high robustness to meet the control requirements of the coordinated tracking operation of multiple trains in urban rail in real time. The sliding mode control algorithm (SMC) has the characteristics of fast response speed and high robustness. However, when the traditional sliding mode control algorithm is used in the coordinated operation control system of multiple trains in urban rail, problems such as slow system error convergence speed, low control accuracy, and large jitter will occur. In order to solve this problem, some scholars have proposed the following related research: using the non-singular terminal sliding mode control (NTSM) method to improve the convergence speed of the system error while avoiding the singular phenomenon of the traditional sliding mode control near the zero point; by designing an adaptive reaching law, the train tracking error converges while achieving the purpose of improving the control accuracy; using the positive and negative tangent functions to construct the non-singular terminal sliding surface, improve the system robustness, and solve the jitter problem in the sliding mode control.

[0004] The above studies mostly focus on improving the convergence speed of multi-train cooperative control systems and reducing control output jitter, but do not consider the problem that urban rail multi-train cooperative tracking operation is easily affected by external interference, which reduces the anti-interference performance of the sliding mode controller and affects the tracking accuracy and stability between trains. Summary of the invention

[0005] In view of the problems existing in the above-mentioned background technology, the purpose of the present invention is to provide a virtual marshaling multi-train collaborative adaptive sliding mode control method based on an extended state observer, which can complete the rapid coordination of multi-train operation in urban rail on the basis of estimating external interference, solve the tracking error and control force jitter problems during multi-train coordination, and improve the steady-state performance of the train control system.

[0006] In order to achieve the above object, the present invention adopts the following technical solution: The method for cooperative adaptive sliding mode control of multiple trains in virtual marshaling based on extended state observer includes the following steps: S1. Construct a multi-train tracking error dynamics model for urban rail based on the unit train dynamics equation; S2. Establish a non-singular terminal sliding surface based on the urban rail multi-train tracking error dynamics model to obtain the equivalent control law of the virtual marshaling multi-train cooperative control system : Where: , and is a positive odd number and satisfies , is the speed error, is the sliding surface weight coefficient and >0, is the mass of the train, is the basic resistance of the unit train, ,in, , , are Davis coefficients, for Train Schedule speed, is the expected acceleration, Due to external uncertain interference and ,in is the upper bound of the external uncertain interference; S3. Design of switching control law : Where: And they are all switching gains, is the sliding surface; S4. The equivalent control law and the switching control law are summed to obtain a non-singular terminal sliding mode control law: S5. Design the adaptive law of switching gain in the virtual marshaling multi-train cooperative control system: Where: and All are adaptive variable gains. , , , are all positive real numbers, is the gain boundary of the adaptive law; S6. Establish saturation function: Where: The boundary layer is used; outside the boundary layer, switching control is used to make the system state quickly tend to the sliding mode. Inside the boundary layer, feedback control is used to reduce the chattering generated when the sliding mode switches quickly and ensure Always within the boundary layer; S7. Uncertain interference from the outside world Expand to a new variable , design the extended state observer: Where: , , are the extended state observer pairs , , The observed value of For trains The displacement of For trains speed; , , are all positive real numbers, is the observer parameter; is the observation error; the extended state observer can be used to achieve hour, , , ; The extended state observer is used to estimate the external uncertain interference and obtain the observed value of the interference; S8, introducing the adaptive law and saturation function into the non-singular terminal sliding mode control law, and adding the observed value of the disturbance instead of the actual disturbance value to the output of the adaptive non-singular terminal sliding mode controller as feedforward compensation, to construct an adaptive non-singular terminal sliding mode control law based on an extended state observer: Where: is the observed value of the interference.

[0007] Furthermore, in S1, the urban rail multi-train tracking error dynamics model is: Where: is the displacement tracking error; is the speed tracking error; For trains displacement; For trains Displacement of the preceding vehicle; For trains speed; For trains The speed of the vehicle ahead; is a fixed safety distance between trains. is the number of trains; when =1, is the expected displacement, is the expected speed, =0.

[0008] Further, in S3, the calculation formula of the sliding surface is: .

[0009] Compared with the shortcomings and deficiencies of the prior art, the present invention has the following beneficial effects: The adaptive non-singular terminal sliding mode control model constructed based on the extended state observer in the present invention effectively solves the problems of low tracking accuracy and insufficient stability of multi-train cooperative control caused by external interference in the virtual marshaling operation environment. The purpose of converging the multi-train cooperative tracking error to the minimum neighborhood near the origin within a limited time is achieved. At the same time, the present invention uses the result of estimating external interference by the extended state observer to compensate for the control force output of the adaptive non-singular terminal sliding mode controller, further improving the anti-interference performance of the multi-train cooperative control system. Through theoretical analysis and simulation verification, the present invention shows significant advantages in improving tracking accuracy, weakening jitter and enhancing system stability, which is of great significance to the realization of the virtual marshaling operation strategy of urban rail transit. BRIEF DESCRIPTION OF THE DRAWINGS

[0010] Figure 1 It is a flow chart for constructing a virtual marshaling multi-train cooperative adaptive sliding mode control model based on an extended state observer provided by an embodiment of the present invention; Figure 2 It is a schematic diagram of the design principle of an adaptive non-singular terminal sliding mode train controller based on an extended state observer provided in an embodiment of the present invention; Figure 3is a schematic diagram of a multi-train tracking model for urban rail provided by an embodiment of the present invention; Figure 4 is a speed tracking result diagram of three trains provided by an embodiment of the present invention; Figure 5 It is a three-dimensional diagram of the coordinated tracking of three trains provided by an embodiment of the present invention; Figure 6 It is a comparison diagram of different external interference observation states provided by an embodiment of the present invention; Figure 7 is a speed error comparison diagram of three different control methods provided by an embodiment of the present invention; Figure 8 is a displacement error comparison diagram of three different control methods provided by an embodiment of the present invention; Fig. 9 It is a control force output comparison diagram of three different control methods provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0011] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with specific embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0012] 1. Basic analysis of train dynamics modeling In the study of multi-train coordinated control of urban rail transit, based on Newton's second law, the train is simplified as a mass point, and the track slope and bending resistance are assumed to be ignored, and the train longitudinal dynamics model is established: (1) Where: for The displacement of the train at time instant, the first-order derivative of the displacement is the train speed, for The speed of the train at that moment, the first derivative of the speed is the acceleration of the train; is the mass of the train, for Train Schedule of traction / braking force, is the basic resistance of the unit train, ,in, , , All are Davis coefficients; Due to external uncertain interference and ,in is the upper bound of the external uncertain interference.

[0013] In order to facilitate the derivation of the formula, the time is omitted below. The control force is Taylor expanded at the equilibrium point (x0, v0), and the state space equation is obtained according to the longitudinal dynamic equation of the train control system: (2) Where: For trains The displacement of , the first-order derivative of the displacement is the speed of the train; For trains The speed is , the first-order derivative of velocity is the acceleration of the train; For trains Traction / braking force; basic resistance of unit train , The train displacement Output.

[0014] Under the virtual marshaling strategy, the urban rail multi-train cooperative tracking operation control system has multi-variable, nonlinear and strong coupling characteristics. In actual operation, the system parameters may deviate from the design values ​​and are susceptible to uncertain interference in complex environments, making it difficult to establish an accurate mathematical model, resulting in a decrease in controller performance. To solve this problem, the present invention constructs a virtual marshaling multi-train cooperative adaptive sliding mode control model based on an extended state observer to improve the multi-train cooperative tracking accuracy and enhance operation stability.

[0015] 2. Establishment and stability analysis of the collaborative adaptive sliding mode control model of virtual marshaling multi-trains based on extended state observer The construction process of the control model of the present invention is as follows Figure 1 As shown in the figure, for the problem of coordinated operation of multiple trains in virtual marshaling, an adaptive non-singular terminal sliding mode controller based on extended state observer is designed. The design principle of the controller is as follows: Figure 2 As shown, the following is described in detail.

[0016] 2.1 Design and stability analysis of adaptive non-singular terminal sliding mode controller Figure 3 This is a schematic diagram of the multi-train tracking model of urban rail. In the multi-train coordinated tracking operation control, the first train tracks the expected speed curve, and the subsequent trains obtain the speed and position information of the preceding train through train-to-train communication to track the preceding train. Figure 3 Establishment of the tracking error dynamics model of multiple trains in urban rail: (3) Where: is the displacement tracking error, is the speed tracking error; For trains displacement; For trains Displacement of the preceding vehicle; For trains speed; For trains The speed of the vehicle ahead; is a fixed safety distance between trains. is the number of trains; when =1, is the expected displacement, is the expected speed, =0; The dynamic balance of multiple trains with consistent speed is defined as the convergence state of the system. In order to make the multi-train control system reach the convergence state in a short time, a non-singular terminal sliding surface is designed: (4) Where: is the sliding surface, and is a positive odd number and satisfies , is the sliding surface weight coefficient and >0. Calculate the first-order derivative of the sliding surface of equation (4): (5) make , we can get: (6) In order to make the control system maintain stability on the sliding surface, Equation (3) is substituted into Equation (6) and the equivalent control law of the virtual marshaling multi-train cooperative control system is derived by solving the system dynamic equations: : (7) Where: , is the expected acceleration.

[0017] In order to prevent the control system from deviating from the sliding surface, a fast response mechanism is used to ensure that the system can quickly return to the desired state when it deviates from the sliding surface. Therefore, the switching control law is designed. : (8) Where: And they are all switching gains.

[0018] For model (3), a non-singular terminal sliding surface is selected and the equivalent control law is and switching control law The summation gives the non-singular terminal sliding mode control law : (9) In the non-singular terminal sliding mode control law Under this condition, the system will reach the sliding surface in a finite time, and the system on the sliding surface will converge to zero in a finite time: Combining equations (7), (8) and (9), the non-singular terminal sliding mode control law can be further It is expressed as: (10) Since equation (10) contains external uncertain interference , its control law cannot be realized. Therefore, without considering the external interference, the non-singular terminal sliding mode control law of equation (10) is written as: (11) The stability of the designed non-singular terminal sliding mode control law is proved. First, define The Lyapunov function: (12) By taking the derivative of formula (12), we can get: (13) Substituting formula (5) into formula (13) yields: (14) In the formula, let , substituting formula (11) into formula (14) yields: (15) because , is a positive odd number and satisfies , then there is , , from formula (15) we can get: (16) Lyapunov function is positive definite, and is a negative definite function, and according to Barbalat's theorem, It is a continuously decreasing function, so it converges to the equilibrium state in a finite time. Therefore, the designed non-singular terminal sliding mode control law is stable.

[0019] However, due to the external uncertain interference when multiple vehicles cooperate, and The value of will cause poor accuracy. In order to reduce and The control complexity is reduced, and the dynamic response of the system is improved without losing the steady-state performance and disturbance suppression. The gain in the controller is designed and The adaptive law of: (17) Where: and All are adaptive variable gains. , , , are all positive real numbers, is the gain boundary of the adaptive law.

[0020] Introducing the adaptive law into the non-singular terminal sliding mode control law, we get: (18).

[0021] Apply control law (18) to model (3) for stability analysis and construct the Lyapunov function as , where , , and is a positive real number, and , and is the gain factor of the adaptive law, we can get: (19) in, and They are and The derivative of , assuming that in formula (17) Sometimes, there is ; when When , it can be known from formula (17) that , , so that , then you need to choose the appropriate and , so according to formula (19) we can get: , ; when hour, , It is obvious from formula (19) that Therefore, the designed adaptive non-singular terminal sliding mode control law improves the controller performance while maintaining stability.

[0022] In the sliding mode controller, the existence of the sign function can easily cause high-frequency chattering of the control output. In order to further weaken the chattering, the saturation function is introduced: (20) Where: The boundary layer is used; outside the boundary layer, switching control is used to make the system state quickly tend to the sliding mode. Inside the boundary layer, feedback control is used to reduce the chattering generated when the sliding mode switches quickly and ensure Always within the boundary layer.

[0023] Further introducing the saturation function into the non-singular terminal sliding mode control law, we get: (twenty one).

[0024] 2.2 Extended State Observer Design and Stability Analysis When multiple urban rail trains under virtual marshaling are running in a complex environment, they are subject to external interferences such as different track sections and uneven tracks, which will affect the stable output and accuracy of the multi-train tracking model. The present invention designs an Extended State Observer (ESO) to estimate unknown interference online to improve the system's anti-interference and tracking accuracy.

[0025] The extended state observer expands the external disturbance into a new state variable for observation, so the external uncertain disturbance in the train dynamics model is Expand to a new variable , combined with formula (2) to design the extended state observer: (twenty two) Where: , , are the extended state observer pairs , , Observed value of , , are all positive real numbers, is the observer parameter; is the observation error; the extended state observer can be used to achieve hour, , , .

[0026] The stability of the designed extended state observer is analyzed and the error matrix is ​​defined: (twenty three) Where: ; ; , we can get the observation error matrix equation: (twenty four) Where: ; ; is the weight coefficient; Assume the characteristic equation of matrix A is: (25) Where: is the identity matrix, For the matrix The characteristic root of , in order to make To satisfy Hurwaitz's theorem, we need to choose a suitable , so the characteristic root of the extended state observer characteristic equation is designed as ,but , , , then we only need to design the parameters so that the matrix Stable, this design not only simplifies the selection of characteristic root parameters, but also ensures the stability of the extended state observer. For any given symmetric positive definite matrix , there exists a symmetric positive definite matrix Satisfies the following Lyapunov equation: (26) Assume that the Lyapunov function of the extended state observer is: but: (27) and , in order to make the extended state observer converge ,but: (28) In the formula, for The minimum eigenvalue of , L is the gain parameter.

[0027] 2.3 Design and stability analysis of adaptive non-singular terminal sliding mode controller based on extended state observer In order to improve the ability of multi-train coordination to cope with external interference during operation, according to the designed multi-train coordination control model, the observation value of the ESO observed interference is introduced into the model control law, and the Lyapunov function is designed to prove the stability. Based on the actual interference value in the control law formula (10) replaced by the observed interference value, a non-singular terminal sliding mode control law with interference compensation is constructed: (29) Where: is the observed value of the disturbance. Combined with the adaptive non-singular terminal sliding mode control law designed previously, an adaptive non-singular terminal sliding mode control law based on the extended state observer is constructed: (30).

[0028] The stability analysis of the designed adaptive non-singular terminal sliding mode control law based on the extended state observer is carried out, and the Lyaunov function is constructed. , taking the derivative and combining equation (15) with equation (30), we can get: (31) In the formula, It can be seen that the stability of the controller with disturbance compensation depends on the observed disturbance error of the extended state observer. ,and is the upper bound of the interference observation error, then:

[0029] Lemma 1: For , the inequality equation , The solution is in, is an arbitrary constant, is the change time, For Follow Varying interference function.

[0030] According to Lemma 1, we take , , the inequality equation The solution is: Pick ,but when , so When, due to and is the adaptive gain, and is based on So The convergence speed depends on and observer parameters .

[0031] Considering the closed-loop system composed of the observer and the controller, the Lyapunov function is ,but: Big enough and Make , that is, the controller is stable, so hour, , , The convergence speed depends on the adaptive gain , and observer parameters The stability of the adaptive non-singular terminal sliding mode control based on the extended state observer was proved by Lyapunov, and the coordinated tracking operation control of urban rail multi-trains under virtual marshaling was achieved in a short time, which improved the dynamic response and robustness of the control system.

[0032] 3. Simulation experiment and result analysis

[0033] In order to verify the effectiveness of the adaptive non-singular terminal sliding mode control model (ESO-ANTSMC) based on the extended state observer of the present invention, the extended state observer non-singular terminal sliding mode control (ESO-NTSMC) and the extended state observer sliding mode control (ESO-SMC) are used as comparisons. At the same time, considering the influence of platform length and interval, three urban rail unit B-type trains are taken as examples to verify the coordinated tracking operation control. The basic parameters of the train are shown in Table 1: Table 1 Basic parameters of urban rail trains

[0034] 3.1 Multi-train coordinated control The simulated platoon operation process is an interval with a duration of 720 seconds, which is divided into five stages: The first stage is 0-100s. Speed ​​up to ; The second stage is 100s-400s. The speed is constant; The third stage is 400s-500s. Slow down to ; The fourth stage is 500s-600s. The speed is constant; The fifth stage is 600s-720s. Slow down to ; Set the initial speeds and positions of the three vehicles to be , , recorded as train 1; , , recorded as train 2; , , recorded as train 3. Figure 4 The speed tracking results of three trains are displayed, and the superior performance of the ESO-ANTSMC controller in the coordinated operation of multiple trains in urban rail can be clearly seen. In the face of sinusoidal interference and random interference, the control system can stably maintain the speed tracking of the train, ensuring that the coordination between trains is not affected under interference conditions, and avoiding the instability that may occur in the operation of multiple trains. Although there are certain fluctuations in the process of train speed changes, the system can quickly recover to a coordinated state, indicating that the controller performs well in dynamic response. The designed controller significantly improves the dynamic response speed of the coordinated train, and can quickly adjust in the face of external interference, ensuring the stability and safety of the train system. Through these characteristics, the controller effectively improves the reliability of train operation and provides a strong guarantee for the safe operation of the urban rail system.

[0035] In order to more clearly describe the superiority of ESO-ANTSMC in multi-train coordinated tracking operation control, Figure 5 The multi-train collaborative three-dimensional tracking diagram shows that the three trains can closely follow the expected curve at different stages in terms of displacement, speed and time.

[0036] 3.2 Verification of the validity of the extended state observer In order to verify the performance of the extended state observer in multi-train coordinated control, interference is added in the process of simulating the coordinated operation of multiple trains in urban rail. , respectively, interference 1 is and random interference 2 that obeys Gaussian distribution and has an average amplitude of 3. The observation time is set to 100s. The observation states of interference 1 and interference 2 are as follows: Figure 6 As shown. Figure 6 It can be seen from the observation results in (a) and (b) that the extended state observer can stably and quickly estimate external interference, ensuring that multiple urban rail trains can maintain stable operation in the face of external interference during actual operation, significantly enhancing the robustness of the multi-train cooperative operation system.

[0037] 3.3 Controller Verification Take the first unit train in multi-train coordination as an example. Figure 2 The controller schematic diagram is used to build a controller in Matlab / Simulink. Three control methods are used to compare and verify the speed error, displacement error, and control force. The parameters of each method are set as follows: (1) ESO-ANTSMC proposed by the present invention: , , , , , , , , , , , the control law is formula (30); (2) ESO-NTSMC: , , , , the control law is formula (11); (3)ESO-SMC: , , , the control law is .

[0038] Comparison of speed errors of three control methods Figure 7 As shown in the figure, in the initial stage of operation, the speed errors of the three control methods gradually converged. After a period of time, the speed errors all converged to the vicinity of the origin, and all achieved good control effects. It can be observed from the local enlarged figure that the error of the ESO-ANTSMC method proposed in the present invention is more superior than that of the other two methods.

[0039] Comparison of displacement errors of the three control methods Figure 8 As shown in the figure, it can be seen from the trend of the curve that all three methods have large displacement errors in the initial stage, but the errors gradually decrease over time. Compared with the ESO-NTSMC and ESO-SMC methods, the error of ESO-ANTSMC decreases faster and can stabilize in a shorter time. The final displacement error is close to zero, showing good convergence and robustness.

[0040] Comparison of control force output of three control methods Fig. 9 As shown in the figure, the ESO-ANTSMC method is smoother in the regulation of control force, the control force fluctuation is significantly smaller, and the control force chattering is effectively suppressed. This smooth control characteristic improves the comfort during the actual operation of the train, avoids the impact caused by severe acceleration or braking, and at the same time improves the robustness of the train under external interference operating conditions.

[0041] In summary, ESO-ANTSMC shows obvious advantages over other control methods in terms of speed error, displacement error, and control force output, and has the best dynamic performance, tracking accuracy, and stability. It is suitable for the needs of high precision and fast response in the process control of coordinated tracking of multiple trains in urban rail.

[0042] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. 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 present invention.

Claims

1. A virtual marshaling multi-train cooperative adaptive sliding mode control method based on an extended state observer, characterized in that: The steps include: S1. Construct a multi-train tracking error dynamics model for urban rail based on the unit train dynamics equation; S2. Based on the multi-train tracking error dynamics model of urban rail, a non-singular terminal sliding surface is established to obtain the equivalent control law of the virtual marshaling multi-train cooperative control system : Where: , and is a positive odd number and satisfies , is the speed error, is the sliding surface weight coefficient and >0, is the mass of the train, is the basic resistance of the unit train, ,in, , , are Davis coefficients, for Train Schedule speed, is the expected acceleration, Due to external uncertain interference and ,in is the upper bound of the external uncertain interference; S3. Design of switching control law : Where: And they are all switching gains, is the sliding surface; S4. The equivalent control law and the switching control law are summed to obtain a non-singular terminal sliding mode control law: S5. Design the adaptive law of switching gain in the virtual marshaling multi-train cooperative control system: Where: and All are adaptive variable gains. , , , are all positive real numbers, is the gain boundary of the adaptive law; S6. Establish saturation function: Where: The boundary layer is used; outside the boundary layer, switching control is used to make the system state quickly tend to the sliding mode. Inside the boundary layer, feedback control is used to reduce the chattering generated when the sliding mode switches quickly and ensure Always within the boundary layer; S7. Uncertain interference from the outside world Expand to a new variable , design the extended state observer: Where: , , are the extended state observer pairs , , The observed value of For trains The displacement of For trains speed; , , are all positive real numbers, are observer parameters, is the observation error; The extended state observer is used to estimate the external uncertain interference and obtain the observed value of the interference; S8, introducing the adaptive law and saturation function into the non-singular terminal sliding mode control law, and adding the observed value of the disturbance instead of the actual disturbance value to the output of the adaptive non-singular terminal sliding mode controller as feedforward compensation, to construct an adaptive non-singular terminal sliding mode control law based on an extended state observer: Where: is the observed value of the interference.

2. The method for cooperative adaptive sliding mode control of multiple trains in virtual marshaling based on extended state observer according to claim 1, characterized in that: In S1, the urban rail multi-train tracking error dynamics model is: Where: is the displacement tracking error; is the speed tracking error; For trains displacement; For trains Displacement of the preceding vehicle; For trains speed; For trains The speed of the vehicle ahead; is a fixed safety distance between trains. is the number of trains; when =1, is the expected displacement, is the expected speed, =0.

3. The method for cooperative adaptive sliding mode control of multiple trains in virtual marshaling based on extended state observer according to claim 1, characterized in that: In S3, the calculation formula of the sliding surface is: 。

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