CN117170228A - Self-adaptive sliding mode control method for virtual marshalling high-speed train interval control - Google Patents
Self-adaptive sliding mode control method for virtual marshalling high-speed train interval control Download PDFInfo
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Abstract
The invention discloses a self-adaptive sliding mode control method for virtual marshalling high-speed train interval control, which comprises the following steps: modeling errors such as air resistance coefficient change and accurate load unknown of a train and uncertainty of parameters are considered, and adverse conditions such as untimely input feedback are considered to construct a longitudinal dynamics model of the high-speed train; taking the train braking performance difference, speed measurement positioning error and information transmission delay into consideration, establishing a virtual marshalling high-speed train minimum safety interval model and a reference interval model, and taking the reference interval and the front train speed as control targets; designing a sliding mode control method by using a nonlinear control design method; and designing an adaptive law, feeding back and adjusting control parameters, and combining the adaptive law with a sliding mode control method. The method has the advantages that: the control robustness is good, the anti-interference capability is strong, and the control precision is high.
Description
The invention relates to the technical field of train operation control, in particular to a self-adaptive sliding mode control method for virtual marshalling high-speed train interval control.
Background
In order to further improve the track traffic energy level, reduce the train tracking interval and improve the train grouping and de-grouping flexibility, based on the train-to-train communication and cooperative control technology, the physical connection is replaced by the virtual grouping among trains, and the train groups are controlled to efficiently and cooperatively operate at a converging speed and at smaller intervals. The design of the control method is a key of safe and efficient control of the virtual grouping high-speed train interval. The high-speed train motion process has the characteristics of nonlinear complex time-varying multiple constraints and the like, and adverse factors such as air resistance coefficient change, unknown accurate load of the train, untimely train input feedback and the like and constraints on train traction braking performance such as maximum output power of a motor exist in the running process of the train. At present, although the traditional controller represented by PID control is simple in design, robustness is poor and disturbance rejection capability is weak. The control method represented by model predictive control has better robustness, but the method has the advantages of complex design process, large operand, long operation time and poor instantaneity. In order to realize safe, efficient and stable control of virtual marshalling high-speed train intervals, a control method which can ensure control performance and robustness and is simple in design and high in instantaneity needs to be designed to solve the problems.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a self-adaptive sliding mode control method for virtual marshalling high-speed train interval control. The self-adaptive sliding mode control method is suitable for being used as a method for realizing train control in an Automatic Train Operation (ATO) system.
In order to achieve the above object, the present invention adopts the following technical scheme:
a self-adaptive sliding mode control method for virtual marshalling high-speed train interval control comprises the following steps:
a1, establishing a longitudinal dynamics model of the high-speed train, and taking modeling errors such as air resistance coefficient change, unknown accurate load of the train and uncertainty of parameters, and unfavorable conditions such as untimely input feedback into consideration in the model.
And A2, establishing a virtual marshalling high-speed train minimum safety interval model and a reference interval model by taking train braking performance difference, speed measurement positioning error and information transmission delay into consideration.
A3, identifying a longitudinal dynamics model of the high-speed train, dividing the model into an estimated part and an unestimable part, defining the total uncertainty of the system, and designing a sliding mode control method by using a nonlinear control design method.
And A4, designing a self-adaptive law aiming at the designed sliding mode control method, and constructing the self-adaptive law and sliding mode control combination into the self-adaptive sliding mode control method. The designed self-adaptive sliding mode control method can adaptively adjust and control gain parameters according to input and output feedback, and compensate the uncertainty of longitudinal dynamics model parameters and external disturbance of the high-speed train.
Further, the step A1 considers the electronic map function of the high-speed train. A high speed train operating on a trunk line stores line information of a current line in a vehicle-mounted computer, comprising: ramp gradient, tunnel length, curve radius, etc. Thus, the present invention contemplates that the additional resistance currently experienced by the train may be calculated by the on-board computer.
Further, the longitudinal dynamics model of the train established in A1 is specifically as follows:
the high-speed train is abstracted into a point mass system, has traction and braking capabilities and is subjected to basic resistance and additional resistance. By x 1 Indicating the position of the train, using x 2 Representing the train speed, the train longitudinal dynamics model can be written as:
wherein F is traction/braking force output by the train, the traction time is positive, the braking time is negative, and the idle time is zero. M is the mass of the train, R b 、R a The functions are calculated for the basic resistance of the train and the additional resistance of the train, respectively. u is the train input and τ is the time constant.
The basic resistance is represented by the davis equation:
in the operation of the high-speed train, c due to the variation of the surrounding wind speed 2 And not a fixed value. In addition, due to the columnsThe change in the load of the train, the mass M, is a fixed but unknown value during operation. Order the Wherein->And->To pair c 2 And an estimated value of M->And M e Is an uncertainty error.
Further, in the step A2, the relative braking method is referred to, and the allowable driving speed of the rear train is different from the absolute braking method in that the allowable driving position of the rear train is at the safety tail of the front train, and the allowable driving speed of the rear train is not zero but the current speed of the front train. The information exchange and vehicle-mounted equipment processing process of the train in the emergency braking scene is analyzed, and the minimum safety interval model is established by considering various time delays in the process and the difference of front and rear vehicle braking performances. The minimum safety interval model established represents the safety interval as:
in the method, in the process of the invention,representing maximum speed error, +_>Representing the least unfavorable minimum emergency braking rate of the rear vehicle and the least unfavorable maximum emergency braking rate of the front vehicle respectively, v i (t)、/>Respectively representing the speed of the rear vehicle and the speed of the front vehicle received by the rear vehicle, deltaV EB Indicating the maximum speed change of the front vehicle in the communication time delay process, delta +.>Indicating the maximum positioning error.
Based on the minimum safety interval model, taking the maximum service brake applied by the rear vehicle into consideration, an expression of the reference interval model is given:
middle l SB (v) Indicating the distance traveled by the rear vehicle at speed v to apply the maximum service brake.
Further, in the step A3, modeling errors of the longitudinal dynamics model of the train, uncertainty of model parameters, and external disturbance that cannot be modeled are considered, and the modeling errors, uncertainty of the model parameters, and the external disturbance are combined into a total uncertainty. The longitudinal dynamics model of the train consists of an estimation part and a sum uncertainty part. The control outputs for the model estimation part and the sum uncertainty part are respectively designed, so that the accuracy and the robustness of control are improved.
Further, the sliding mode control method designed in A3 specifically comprises the following steps:
based on the longitudinal dynamics model of the high-speed train in A1, the model is expressed as a vector form:
x is a vector representing a train state, x= [ X ] 1 x 2 ] T . Tracking target vector write asTracking errorThe vector is defined as e=x-X d . The train dynamics model vector is further divided into a state transition matrix f (X) and a coefficient matrix b (X), and f (X) and b (X) may be further divided into a determination portion and an uncertainty portion.
f(X)＝[x 2 -R b -R a ] T
For sliding mode control, the sliding mode surface function is designed to be sigma=c T e, wherein c= [ C 1 C 2 ]And is C 1 、C 2 Are positive constants. Taking other unaccounted errors and external disturbance omega of the train dynamics model into consideration, defining the total uncertainty of the system as follows:
E(X,F)＝C T the traction/braking force output F ultimately required by the control method designed for (Δf (X) +Δb (X) f+ω) (10) is shown by the following formula:
F s ＝-(C T b o (X)) -1 βsgn(σ)
F＝F s +F o
where β represents the control output gain, f o (X) and b o (X) represents a deterministic portion of the system, and Δf (X) and Δb (X) represent an uncertain portion of the system.
Further, the adaptive law designed in step A4 is used for dynamically adjusting and controlling the output gain, so as to realize online parameter adjustment and adaptation. The value of the prescribed control gain in the adaptive law depends on the value of the current sliding function. The introduction of the self-adaptive gain ensures that the upper bound of disturbance and error is not required to be given when the control method is designed, reduces the design difficulty, and can eliminate the adverse effect of unknown parameters and time-varying disturbance on train control.
The adaptive law is designed as follows:
where α is the adaptive gain, which is a design parameter used to adjust the rate of change of the adaptive gain.
Compared with the prior art, the invention has the advantages that:
1. the longitudinal dynamics model of the train, which is built by the invention, fully considers the complex working condition of the high-speed train operation, considers the change of the air resistance coefficient of the davis equation caused by the change of the wind speed and the wind direction, considers the unknown deviation of the empirical calculation formula of the basic resistance and the additional resistance, considers the input limit and delay of the train caused by the limitation of the traction braking performance of the train, and accords with the actual condition of the high-speed train operation.
2. The minimum safety interval model based on relative braking, which is established by the invention, analyzes the influence of adverse factors such as communication delay, speed measurement positioning error and the like on the safety interval, considers the virtual grouping condition of trains with different braking performances, and has wider application range.
3. The self-adaptive sliding mode control method designed by the invention can effectively reduce the influence of air resistance change disturbance and train parameter uncertainty on the control effect in the running process of the train, adjusts the control output gain by a self-adaptive law, reduces the output shake of the system by a saturation function, has high control stability and smooth output, does not need to give an uncertainty upper limit during the design, and reduces the design difficulty.
Drawings
FIG. 1 is a control structure block diagram and a train information interaction schematic diagram adopted by an embodiment of the invention;
FIG. 2 is a graph showing the results of simulation experiments for verifying the effectiveness of the embodiment of the present invention.
Detailed Description
The invention will be described in further detail below with reference to the accompanying drawings and by way of examples in order to make the objects, technical solutions and advantages of the invention more apparent.
The virtual marshalling train operation control system is a train control system which uses virtual connection to replace physical connection among trains to realize that the trains run at the same speed and minimum spacing, and can allow trains of different types to cooperatively run on a line, thereby improving the line transportation efficiency and the marshalling flexibility.
High speed trains are limited in operation by the interference and constraints of a variety of disturbances. Disturbances experienced by trains during operation include changes in line conditions, changes in wind resistance, etc., which can cause inaccuracy in the established train dynamics model. The train operation is also constrained by various conditions, including maximum power constraint of the traction braking system, upper limit of the train impact rate, line speed limit and the like. The introduction of virtual consist places higher demands on train control, so the designed control method must be robust.
The sliding mode control (Sliding Mode Control, SMC) is also called variable structure control, and is a special nonlinear control method. The sliding mode control can enable the structure of the system to be switched according to the control rule, so that the system is forced to run in a sliding state. The sliding mode control is simple to realize, has complete robustness to interference and modeling errors meeting the matching conditions, and has strong anti-interference capability. Taking train operation control as an example, the robustness of sliding mode control can enable the train to still keep running stably when running is disturbed (such as a ramp, a curve and upwind), and to follow an ideal running state in real time.
The invention provides a self-adaptive sliding mode control method for virtual marshalling high-speed train control, which comprises the following basic ideas: the method comprises the steps of establishing a longitudinal dynamics model of a high-speed train, taking the relative braking characteristics of virtual marshalling into consideration, establishing a minimum safety interval model and a reference interval model, taking the reference interval as a train control target after virtual marshalling, designing a sliding mode control method, designing a self-adaptive law, combining the two, proving the effectiveness of the control method by using a Lyapunov second method, and finally completing the design.
The invention provides a self-adaptive sliding mode control method for virtual marshalling high-speed train control, which specifically comprises the following steps:
a1, establishing a longitudinal kinematic model of the high-speed train.
The high-speed train is abstracted into a point mass system, has traction and braking capabilities and is subjected to basic resistance and additional resistance. By x 1 Indicating the position of the train, using x 2 Representing the train speed, the train longitudinal dynamics model can be written as:
wherein F is traction/braking force output by the train, the traction time is positive, the braking time is negative, and the idle time is zero. M is the mass of the train, R b 、R a The functions are calculated for the basic resistance of the train and the additional resistance of the train, respectively. u is the train input and τ is the time constant. The basic resistance is represented by the davis equation:
in the operation of the high-speed train, c due to the variation of the surrounding wind speed 2 And not a fixed value. Furthermore, the train mass M is a fixed but unknown value during operation due to variations in the train load. Order the Wherein->And->To pair c 2 And an estimated value of M->And M e Is an uncertainty error.
And the values of all symbol parameters in A1 refer to the data of the CRH380B train.
A2, constructing a virtual marshalling minimum safety interval model and a reference interval model. In the running process of the virtual marshalling trains, the intervals of the trains are relative braking distances, when an emergency occurs, the front vehicles start to perform emergency braking, and the rear vehicles immediately implement emergency braking after receiving the related information of the front vehicles, so that the safety interval mainly consists of the emergency braking distance of the rear vehicles minus the emergency braking distance of the front vehicles. Further, the influence of errors and time delays on the security model needs to be considered in the process. Due to the existence of errors of the speed measuring sensor, when the actual speed of the rear vehicle is higher than the measured speed and the speed of the front vehicle is lower than the measured speed, the allowable safety interval is actually further increased, and the maximum speed of the rear vehicle and the minimum speed of the front vehicle in the speed measuring error range need to be considered. In addition, the virtual marshalling train positioning system has certain errors and should be considered in the safety interval. The virtual marshalling adopts vehicle-to-vehicle communication to exchange information such as speed, position and the like, and communication delay is unavoidable, so that the fact that a front vehicle possibly brakes in the communication delay process is considered to cause speed reduction is needed. In summary, the analysis of the tracking operation of the virtual marshalling train is given as follows:
the minimum safety interval is the minimum guarantee for ensuring that the virtual marshalling train does not have a rear-end collision accident, but in train operation control, the tracking target of the actual interval cannot be set to be the minimum safety interval, otherwise, the change of line conditions can cause the fluctuation of the speed of the train, so that the actual operation interval is smaller than the safety interval, and the train braking is triggered and even the driving safety is endangered. Based on the above consideration, it is necessary to set a virtual consist reference train interval on the basis of the minimum safety interval, leaving a margin to cope with the lineRoad condition change, front vehicle deceleration or rear vehicle control overshoot, etc. Taking into consideration that the rear train applies maximum service braking rather than emergency braking when braking, obtaining a reference interval modelThe following are provided:
TABLE 1 meanings of symbols in the model
When the virtual marshalling train set runs on a trunk line, the ideal running state of the back running train is as follows: the speed is consistent with the speed of the front vehicle, and the interval with the front vehicle is equal to the reference interval.
A3, designing a sliding mode control method by applying a nonlinear control design theory.
Based on the train dynamics model in A1, the model is expressed as a vector form by using a representation method in modern control theory:
x is a vector representing a train state, x= [ X ] 1 x 2 ] T . Tracking target vector write asThe tracking error vector is defined as e=x-X d . The train dynamics model vector is further divided into a state transition matrix f (X) and a coefficient matrix b (X), and f (X) and b (X) can be further divided into a determination part and an uncertaintyPart(s).
f(X)＝[x 2 -R b -R a ] T (7)
For sliding mode control, the sliding mode surface function is designed to be sigma=c T e, wherein c= [ C 1 C 2 ]And is C 1 、C 2 Are positive constants. Taking other unaccounted errors and external disturbance omega of the train dynamics model into consideration, defining the total uncertainty of the system as follows:
E(X,F)＝C T (Δf(X)+Δb(X)F+ω) (9)
the final required traction/braking force control output F is shown as follows:
F s ＝-(C T b o (X)) -1 βsgn(σ) (11)
F＝F s +F o (12)
where β represents the control output gain, f o (X) and b o (X) represents a deterministic portion of the system, and Δf (X) and Δb (X) represent an uncertain portion of the system.
And A4, designing a self-adaptive law, and compensating inaccurate parts of train modeling by combining the self-adaptive law with a sliding mode control method.
In a general sliding mode control method, the control gain β is determined by calculation of the upper bounds of various disturbances. In the self-adaptive sliding mode control method designed by the invention, each disturbance upper bound is not required to be given, but the control gain is automatically adjusted by an adaptive value gamma, so thatThe adaptive law is designed as follows:
where α is the adaptive gain, which is a design parameter used to adjust the rate of change of the adaptive gain.
A5, proving the stability of the designed control method.
The second principle of Lyapunov is a method for proving system stability in modern control theory. The control method in the invention adopts the principle to prove the stability, and the method is proved as follows:
assume that: there is an ideal adaptive gain value Γ d Can make F meet the requirements of self-adaption and robustness and become a final solution, and Γ d >I E (X, F) |. Defining adaptive bias
The lyapunov function was designed as:
v deriving time:
various kinds of control method design process are carried in:
it is demonstrated by the above procedure that the lyapunov function steadily tends to 0, which means that the system will gradually tend to the slip plane, the control error e and the adaptive value biasWill tend to 0 in a limited time and system stability will be demonstrated.
When the stability of the system is proved in the step A5, various disturbance and uncertainty boundaries are not required to be given, and the lyapunov function is designed through the error between the current adaptive gain and the ideal control gain, so that the sliding mode function and the adaptive error tend to be zero along with time, and the designed control method can enable the system to reach a stable state within a limited time. In order to verify the effectiveness of the self-adaptive sliding mode control method, a simulation experiment is designed. The control structure block diagram and the train information interaction diagram of the designed simulation experiment embodiment are shown in fig. 1, in the control process, the train state information (position, speed, acceleration and the like) is interacted between the front train and the rear train, the front train runs according to the train running plan, and the rear train calculates and controls output according to the front train state and the self state by using the self-adaptive sliding mode control method and applies the control output to the train, so that the tracking control of the rear train is realized.
The experimental line scene is set as Zheng Xixian between the North China and the on-the-fly stations of the high-speed passenger line, real line data are used, a station tracking operation simulation scene is designed for verification, under the scene, the front vehicle 0 and the rear vehicle 1 just complete virtual marshalling communication link establishment, and under the condition of a certain speed difference, the rear vehicle gradually reaches the same speed as the front vehicle. The simulation step length is 0.1s, the total simulation time length is 200s, and the simulation result is shown in fig. 2.
Fig. 2 (a) is a diagram showing the change of the train operation interval, and the actual interval, the ideal interval and the minimum safety interval of the front and rear vehicles are sequentially shown from top to bottom in the illustration. It is clear from the figure that the following vehicle can track and keep stable for the ideal interval most of the time except for the accident of 180s-200s braking time. Fig. 2 (b) is a graph of the speed change of the front vehicle 0 and the rear vehicle 1 during operation, and the legend sequentially shows the front vehicle speed and the rear vehicle speed. The self-adaptive sliding mode control method controls the acceleration of the rear vehicle in a short time, keeps the same speed with the front vehicle in a long time after the acceleration, and ensures that the speed difference between the front and rear vehicles is not more than 0.5m/s under the condition of stable running. Fig. 2 (c) is a graph of the sliding mode function (σ) in the simulation process, and under the action of the adaptive sliding mode control method, the system reaches a sliding state (σ=0) in a short time, the overshoot is low, and the sliding state can be maintained in the subsequent process, so that the effectiveness of the invention is proved. By combining the contents shown in fig. 2, the embodiment of the invention enables the distance between the virtual marshalling trains to approach to the reference distance, the speed is kept consistent, and the ideal effect of virtual marshalling is achieved.
Those of ordinary skill in the art will appreciate that the embodiments described herein are intended to aid the reader in understanding the practice of the invention and that the scope of the invention is not limited to such specific statements and embodiments. Those of ordinary skill in the art can make various other specific modifications and combinations from the teachings of the present disclosure without departing from the spirit thereof, and such modifications and combinations remain within the scope of the present disclosure.
Claims (7)
1. The self-adaptive sliding mode control method for virtual marshalling high-speed train interval control is characterized by comprising the following steps:
a1, establishing a longitudinal dynamics model of the high-speed train, and considering modeling errors and parameter uncertainties including air resistance coefficient changes and unknown accurate load of the train and unfavorable conditions of untimely input feedback in the model.
And A2, establishing a virtual marshalling high-speed train minimum safety interval model and a reference interval model by taking train braking performance difference, speed measurement positioning error and information transmission delay into consideration.
A3, identifying a longitudinal dynamics model of the high-speed train, dividing the model into an estimated part and an unestimable part, defining the total uncertainty of the system, and designing a sliding mode control method by using a nonlinear control design method.
And A4, designing a self-adaptive law aiming at the designed sliding mode control method, and combining the self-adaptive law and the sliding mode control method to construct the self-adaptive sliding mode control method. The self-adaptive sliding mode control method can adaptively adjust and control gain parameters according to input and output feedback, and compensate uncertainty of longitudinal dynamics model parameters and external disturbance of the high-speed train.
2. The adaptive sliding mode control method for virtual marshalling high-speed train interval control according to claim 1, wherein the method comprises the following steps: the longitudinal dynamics model of the train, which is established in the step A1, considers parameter uncertainty and time-varying disturbance, including unknown train load and air resistance coefficient change.
3. The self-adaptive sliding mode control method for virtual marshalling high-speed train interval control according to claim 2, wherein the train longitudinal dynamics model established in A1 is specifically as follows:
the high-speed train is abstracted into a point mass system, has traction and braking capabilities and is subjected to basic resistance and additional resistance. By x 1 Indicating the position of the train, using x 2 Representing the train speed, the train longitudinal dynamics model can be written as:
wherein F is traction/braking force output by the train, the traction time is positive, the braking time is negative, and the idle time is zero. M is the mass of the train, R b 、R a The functions are calculated for the basic resistance of the train and the additional resistance of the train, respectively. u is the train input and τ is the time constant.
The basic resistance is represented by the davis equation:
in the operation of the high-speed train, c due to the variation of the surrounding wind speed 2 And not a fixed value. Furthermore, the train mass M is a fixed but unknown value during operation due to variations in the train load. Order the Wherein->And->To pair c 2 And an estimated value of M->And M e Is an uncertainty error.
4. The adaptive sliding mode control method for virtual marshalling high-speed train interval control according to claim 1, wherein the method comprises the following steps:
the minimum safety interval model established in the step A2 analyzes the movement process from normal marshalling operation to unexpected emergency braking in the virtual marshalling, and considers various time delays and equipment processing time in the process, and train speed change and train speed measurement positioning errors in the information transmission process. The expression of the minimum safe interval model is:
in the method, in the process of the invention,representing maximum speed error, +_>Indicating the minimum emergency brake rate of the rear vehicle in the worst case,indicating the maximum emergency brake rate, v, of the preceding vehicle in the worst case i (t) represents the speed of the rear vehicleDegree (f)>Representing the speed of the transmission of the front vehicle i-1 received by the rear vehicle i, deltaV EB Indicating the maximum speed change of the front vehicle during the communication time delay, < > of the front vehicle>Indicating the maximum positioning error.
Based on the minimum safety interval model, taking the maximum service brake applied by the rear vehicle into consideration, an expression of the reference interval model is given:
middle l SB (v) Indicating the distance traveled by the rear vehicle at speed v to apply the maximum service brake.
5. The adaptive sliding mode control method for virtual marshalling high-speed train interval control according to claim 1, wherein the method comprises the following steps: in the step A3, the longitudinal dynamics model of the train is further identified, the longitudinal dynamics model of the train is divided into an estimated system determining part and an unknown system error, the unknown part and external disturbance are combined into the system total uncertainty, and a sliding mode control method is designed to respectively control and output the system determining part and the system total uncertainty.
6. The self-adaptive sliding mode control method for virtual marshalling high-speed train interval control according to claim 3, wherein the sliding mode control method designed in A3 is specifically as follows:
based on the longitudinal dynamics model of the high-speed train in A1, the model is expressed as a vector form:
x is a vector representing a train state, x= [ X ] 1 x 2 ] T . Tracking target vector write asThe tracking error vector is defined as e=x-X d . The train dynamics model vector is further divided into a state transition matrix f (X) and a coefficient matrix b (X), and f (X) and b (X) may be further divided into a determination portion and an uncertainty portion.
f(X)＝[x 2 -R b -R a ] T
For sliding mode control, the sliding mode surface function is designed to be sigma=c T e, wherein c= [ C 1 C 2 ]And is C 1 、C 2 Are positive constants. Taking other unaccounted errors and external disturbance omega of the train dynamics model into consideration, defining the total uncertainty of the system as follows:
E(X,F)＝C T (Δf(X)+Δb(X)F+ω) (10)
the traction/braking force output F ultimately required by the designed control method is shown as follows:
F s ＝-(C T b o (X)) -1 βsgn(σ)
F＝F s +F o
where β represents the control output gain, f o (X) and b o (X) represents a deterministic portion of the system, and Δf (X) and Δb (X) represent an uncertain portion of the system.
7. The adaptive sliding mode control method for virtual marshalling high-speed train interval control according to claim 1, wherein the method comprises the following steps: the self-adaptive law designed in the step A4 is used for dynamically adjusting and controlling the output gain, so that the self-adaptive sliding mode control method does not need to give an upper bound of disturbance and error when in design, the difficulty of design is reduced, and adverse effects of unknown parameters and time-varying disturbance on train control can be eliminated.
The adaptive law is designed as follows:
where α is the adaptive gain, which is a design parameter used to adjust the rate of change of the adaptive gain.
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| CN117389157B (en) * | 2023-12-11 | 2024-02-27 | 华东交通大学 | Virtual marshalling high-speed train operation sliding mode control method, system, equipment and medium |
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