CN117170228A - Adaptive sliding mode control method for spacing control of virtual marshalling high-speed trains - Google Patents

Abstract

The invention discloses an adaptive sliding mode control method for spacing control of virtual marshalling high-speed trains, which includes: considering changes in air resistance coefficients, unknown precise train loads and other modeling errors and parameter uncertainties, as well as untimely input feedback, etc. Under unfavorable conditions, a high-speed train longitudinal dynamics model is constructed; taking into account the difference in train braking performance, speed measurement positioning error and information transmission delay, a minimum safe interval model and a reference interval model for virtual grouping of high-speed trains are established, using the reference interval and the speed of the preceding vehicle as controls Objective: Use nonlinear control design method to design sliding mode control method; design adaptive law to feedback and adjust control parameters, and combine adaptive law with sliding mode control method. The advantages of this method are: good control robustness, strong anti-interference ability, and high control accuracy.

Description

Adaptive sliding mode control method for spacing control of virtual marshalling high-speed trains

The invention relates to the technical field of train operation control, and in particular to an adaptive sliding mode control method for spacing control of virtual grouping high-speed trains.

Background technique

In order to further improve the rail transit capacity level, shorten the train tracking interval, and improve the flexibility of train marshalling and demarshalling, based on train-to-train communication and collaborative control technology, virtual marshalling is used to replace physical couplings between trains, and train groups are controlled to converge at a convergent speed. Efficient and coordinated operation at smaller intervals. Among them, the design of the control method is the key to safe and efficient control of the intervals of virtual marshalling high-speed trains. The motion process of high-speed trains has the characteristics of nonlinear, complex, time-varying and multiple constraints. During the operation of the train, there are unfavorable factors such as changes in air resistance coefficient, unknown precise train load, untimely train input feedback, and train traction braking such as the maximum output power of the motor. Performance constraints. At present, although traditional controllers represented by PID control are simple in design, they have poor robustness and weak anti-disturbance capabilities. The control method represented by model predictive control has good robustness, but this method has complex design process, large amount of calculation, long calculation time, and poor real-time performance. In order to achieve safe, efficient and stable control of virtual marshalling high-speed train spacing, it is necessary to design a control method that can not only ensure control performance and robustness, but also design simple and high real-time performance to solve the above problems.

Contents of the invention

In view of the shortcomings of the existing technology, the present invention provides an adaptive sliding mode control method for spacing control of virtual grouping high-speed trains. The adaptive sliding mode control method of the present invention is suitable for use as a method for realizing train control in an automatic train driving system (ATO).

In order to achieve the above object of the invention, the technical solutions adopted by the present invention are as follows:

An adaptive sliding mode control method for spacing control of virtual grouping high-speed trains, including the following steps:

A1. Establish a high-speed train longitudinal dynamics model, and consider modeling errors and parameter uncertainties such as changes in air resistance coefficients, unknown precise train loads, and unfavorable conditions such as untimely input feedback.

A2. Considering the difference in train braking performance, speed measurement and positioning error and information transmission delay, establish the minimum safe separation model and reference separation model of virtual marshalling high-speed trains.

A3. Identify the high-speed train longitudinal dynamics model, divide the model into estimable parts and non-estimateable parts, define the system total uncertainty, use nonlinear control design methods, and design sliding mode control methods.

A4. For the designed sliding mode control method, design an adaptive law, and combine the adaptive law with sliding mode control to construct an adaptive sliding mode control method. The designed adaptive sliding mode control method can adaptively adjust control gain parameters based on input and output feedback to compensate for high-speed train longitudinal dynamics model parameter uncertainty and external disturbances.

Furthermore, the electronic map function of the high-speed train is considered in step A1. High-speed trains running on main lines will store the route information of the current line in the on-board computer, including: ramp gradient, tunnel length, curve radius and other parameters. Therefore, the present invention believes that the additional resistance currently experienced by the train can be calculated by the on-board computer.

Furthermore, the train longitudinal dynamics model established in A1 is as follows:

The high-speed train is abstracted as a point mass system with traction and braking capabilities, and is subject to basic resistance and additional resistance. Using x ₁ to represent the train position and x ₂ to represent the train speed, the train longitudinal dynamics model can be written as:

In the formula, F is the traction/braking force output by the train. It is a positive value during traction, a negative value during braking, and zero when coasting. M is the train mass, R _b and R _a are the train basic resistance and train additional resistance calculation functions respectively. u is the train input and τ is the time constant.

The basic resistance is expressed by the Davis equation:

During high-speed train operation, c ₂ is not a fixed value due to changes in surrounding wind speed. In addition, due to changes in train load, the train mass M is a fixed but unknown value during operation. make Among them/> and/> is the estimate of c ₂ and M,/> and Me _are uncertain errors.

Further, the relative braking method is referred to in step A2. The driving permission position of the train behind is at the safety rear of the train in front. Different from the absolute braking method, the driving permission speed of the train behind is not zero, but Current speed of the train ahead. The information exchange and on-board equipment processing process of the train in the emergency braking scenario were analyzed. Various time delays in the process and the difference in braking performance of the front and rear trains were taken into account, and a minimum safety interval model was established. The established minimum safe interval model expresses the safe interval as:

In the formula, Indicates the maximum speed measurement error,/> Respectively represent the most unfavorable minimum emergency braking rate of the vehicle behind and the most unfavorable maximum emergency braking rate of the vehicle in front, v _i (t),/> Represents the speed of the following vehicle and the speed of the leading vehicle received by the following vehicle respectively, ΔV _EB represents the maximum speed change of the leading vehicle during the communication delay process, Δ/> Indicates the maximum positioning error.

Based on the minimum safe separation model, considering the maximum common braking applied by the vehicle behind, the expression of the reference separation model is given:

In the formula, l _SB (v) represents the distance traveled by the vehicle behind from applying maximum normal braking to stopping at speed v.

Further, in the step A3, the modeling error of the train longitudinal dynamics model, the uncertainty of the model parameters and the external disturbance that cannot be modeled are taken into account, and the modeling error, the uncertainty of the model parameters and the external disturbance are combined. is the total uncertainty. The train longitudinal dynamics model consists of an estimation part and a summation uncertainty part. Separately designing the control outputs for the model estimation part and the total uncertainty part is beneficial to improving the accuracy and robustness of the control.

Further, the sliding mode control method designed in A3 is as follows:

Based on the high-speed train longitudinal dynamics model in A1, the model is expressed in vector form:

X is a vector representing the train status, X=[x ₁ x ₂ ] ^T . The tracking target vector is written as The tracking error vector is defined as e=XX _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 determined part and an uncertain part.

f(X)＝[x ₂ -R _b -R _a ] ^T

For sliding mode control, the sliding mode surface function is designed as σ = C ^T e, where C = [C ₁ C ₂ ] and C ₁ and C ₂ are both positive constants. Considering other unconsidered errors and external disturbances ω of the train dynamics model, the total uncertainty of the system is defined as:

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 as follows:

F _s =-(C ^T b _o (X)) ^-1 βsgn(σ)

F＝F _s +F _o

In the formula, β represents the control output gain, f _o (X) and _bo (X) represent the determined part of the system, and Δf (X) and Δb (X) represent the uncertain part of the system.

Furthermore, the adaptive law designed in step A4 is used to dynamically adjust the control output gain to achieve online parameter adjustment and adaptation. The value of the control gain specified in the adaptive law depends on the value of the current sliding function. The introduction of adaptive gain eliminates the need to provide upper bounds for disturbances and errors when designing control methods, reducing the difficulty of design and eliminating the adverse effects of unknown parameters and time-varying disturbances on train control.

The adaptive law is designed as:

Among them, α is the gain of the adaptive amount, which is a design parameter used to adjust the change rate of the adaptive gain.

Compared with the prior art, the advantages of the present invention are:

1. The train longitudinal dynamics model established by the present invention fully considers the complex operating conditions of high-speed train operation, takes into account the changes in the Davis equation air resistance coefficient caused by changes in wind speed and direction, and takes into account the empirical calculation formulas of basic resistance and additional resistance. The existing unknown deviation takes into account the train input limitations and delays caused by the train's traction and braking performance limitations, and is consistent with the actual operating conditions of high-speed trains.

2. The minimum safe interval model based on relative braking established by the present invention analyzes the impact of communication delay, speed measurement and positioning error and other unfavorable factors on the safe interval, and takes into account the situation of virtual marshalling of trains with different braking performance. The proposed The safety margin model has wider application.

3. The adaptive sliding mode control method designed by the present invention can effectively reduce the impact of air resistance change disturbance and train parameter uncertainty on the control effect during train operation. The control output gain is adjusted with an adaptive law and reduced with a saturation function. The system output is jitter-free, with high control stability and smooth output. There is no need to give an upper limit of uncertainty during design, which reduces the design difficulty.

Description of drawings

Figure 1 is a control structure block diagram and a schematic diagram of train information interaction adopted in the embodiment of the present invention;

Figure 2 is a diagram of simulation experiment results to verify the effectiveness of the embodiment of the present invention.

Detailed ways

In order to make the purpose, technical solutions and advantages of the present invention more clear, the present invention will be further described in detail below based on the accompanying drawings and examples.

The virtual marshalling train operation control system is a train control system that uses virtual connections instead of physical connections between trains to realize trains running at the same speed and at very small intervals. It can allow different types of trains to operate cooperatively on the line, thereby improving line transportation efficiency and marshalling. flexibility.

High-speed trains are subject to various disturbances and constraints during operation. Disturbances encountered by trains during operation include changes in line conditions, changes in wind resistance, etc. These disturbances will cause the established train dynamics model to be inaccurate. Train operation will also be subject to various conditions, including the maximum power constraints of the traction braking system, the upper limit of train impact rate, line speed limit, etc. The introduction of virtual marshalling places higher requirements on train control, so the designed control method must have strong robustness.

Sliding Mode Control (SMC), also called variable structure control, is a special nonlinear control method. Sliding mode control can make the structure of the system switch according to the control rules, forcing the system to run in a "sliding state". Sliding mode control is simple to implement, fully robust to interference and modeling errors that meet matching conditions, and has strong anti-disturbance capabilities. Taking train operation control as an example, the robustness of sliding mode control can enable the train to maintain smooth operation and follow the ideal operating state in real time when the operation is disturbed (such as ramps, curves, headwinds).

The present invention provides an adaptive sliding mode control method for virtual marshalling high-speed train control. The basic idea of the method is to establish a high-speed train longitudinal dynamics model, consider the relative braking characteristics of virtual marshalling, and establish a minimum safe interval model and a reference interval. model, and use the reference interval as the virtual grouping train control target, design the sliding mode control method, design the adaptive law and combine the two, use Lyapunov's second method to prove the effectiveness of the control method, and finally complete the design .

The invention provides an adaptive sliding mode control method for virtual grouping high-speed train control, which specifically includes the following steps:

A1. Establish a longitudinal kinematics model of a high-speed train.

The high-speed train is abstracted as a point mass system with traction and braking capabilities, and is subject to basic resistance and additional resistance. Using x ₁ to represent the train position and x ₂ to represent the train speed, the train longitudinal dynamics model can be written as:

In the formula, F is the traction/braking force output by the train. It is a positive value during traction, a negative value during braking, and zero when coasting. M is the train mass, R _b and R _a are the train basic resistance and train additional resistance calculation functions respectively. u is the train input and τ is the time constant. The basic resistance is expressed by the Davis equation:

During high-speed train operation, c ₂ is not a fixed value due to changes in surrounding wind speed. In addition, due to changes in train load, the train mass M is a fixed but unknown value during operation. make Among them/> and/> is the estimate of c ₂ and M,/> and Me _are uncertain errors.

The values of all symbol parameters in A1 refer to the data of CRH380B train.

A2. Construct the virtual marshalling minimum safe separation model and reference separation model. During the operation of the virtual marshalling train, the interval between trains is the relative braking distance. When an emergency occurs, the leading train starts emergency braking, and the following train also implements emergency braking immediately after receiving relevant information from the leading train. Therefore, there is a safe interval. is mainly composed of the emergency braking distance of the vehicle behind minus the emergency braking distance of the vehicle in front. Furthermore, the impact of errors and delays on the security model needs to be considered in this process. Due to the error of the speed measurement sensor, when the actual speed of the vehicle behind is higher than the measured speed and the speed of the vehicle in front is lower than the measured speed, the actual allowable safe interval will further increase. It is necessary to consider the maximum speed of the vehicle behind and the maximum speed of the vehicle behind within the speed measurement error range. The minimum speed of the vehicle in front. In addition, there are certain errors in the virtual marshalling train positioning system, which should be considered in the safety interval. Virtual marshalling uses vehicle-to-vehicle communication to exchange speed, location and other information, and communication delay is inevitable. Therefore, it is necessary to consider that the vehicle in front may brake during the communication delay process, resulting in a reduction in speed. Based on the above analysis of the tracking operation of virtual marshalling trains, the minimum safe interval model of virtual marshalling is given as follows:

The minimum safe interval is the minimum guarantee to ensure that no rear-end collisions occur in virtual marshalling trains. However, in train operation control, the tracking target of the actual interval cannot be set to the minimum safe interval. Otherwise, changes in line conditions will cause train speed fluctuations and thus reduce the actual operating interval. If the distance is less than the safe interval, it may trigger train braking and even endanger driving safety. Based on the above considerations, it is necessary to set the virtual grouping reference train interval on the basis of the minimum safe interval, leaving a certain margin to deal with changes in line conditions, deceleration of the leading train, or control overshoot of the following train. Considering that the train behind the train applies maximum normal braking instead of emergency braking when braking, the reference interval model is obtained as follows:

Table 1 The meaning of each symbol in the model

When the virtual marshalling train set is running on the main line, the ideal running state of the following train is: the speed is consistent with the speed of the preceding train, and the interval with the preceding train is equal to the reference interval.

A3. Use nonlinear control design theory to design a sliding mode control method.

Based on the train dynamics model in A1, the model is expressed in vector form using the representation method in modern control theory:

X is a vector representing the train status, X=[x ₁ x ₂ ] ^T . The tracking target vector is written as The tracking error vector is defined as e=XX _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 determined part and an uncertain part.

f(X)＝[x ₂ -R _b -R _a ] ^T (7)

For sliding mode control, the sliding mode surface function is designed as σ = C ^T e, where C = [C ₁ C ₂ ] and C ₁ and C ₂ are both positive constants. Considering other unconsidered errors and external disturbances ω of the train dynamics model, the total uncertainty of the system is defined as:

E(X,F)＝C ^T (Δf(X)+Δb(X)F+ω) (9)

The final required traction/braking force control output F is as follows:

F _s =-(C ^T b _o (X)) ^-1 βsgn(σ) (11)

F＝F _s +F _o (12)

In the formula, β represents the control output gain, f _o (X) and _bo (X) represent the determined part of the system, and Δf (X) and Δb (X) represent the uncertain part of the system.

A4. Design an adaptive law and combine it with the sliding mode control method to compensate for the inaccuracies in train modeling.

In the general sliding mode control method, the control gain β is determined by the upper bound calculation of various disturbances. In the adaptive sliding mode control method designed by the present invention, it is not necessary to provide an upper bound for each disturbance, but to automatically adjust the control gain with an adaptive value Γ, so that The adaptive law is designed as:

Among them, α is the gain of the adaptive amount, which is a design parameter used to adjust the change rate of the adaptive gain.

A5. Prove the stability of the designed control method.

Lyapunov's second property principle is a method used to prove system stability in modern control theory. The control method in the present invention uses this principle to prove its stability, which is proved as follows:

Assumption: There is an ideal adaptive gain value Γ _d , which can make F meet the requirements of adaptation and robustness and become the final solution, and Γ _d >|E(X,F)|. Define adaptive bias

Design the Lyapunov function as:

Derivative of V with respect to time:

Various factors brought into the control method design process include:

Through the above process, it is proved that the Lyapunov function stably tends to 0, which means that the system will gradually tend to the sliding mode surface, control error e and adaptive value deviation All will tend to 0 within a limited time, and the system stability is proved.

When proving the stability of the system in step A5, it is not necessary to give the boundaries of various disturbances and uncertainties. The Lyapunov function is designed through the error between the current adaptive gain and the ideal control gain, which proves that the sliding mode function and the adaptive error will both As time tends to zero, the designed control method can make the system reach a stable state within a limited time. In order to verify the effectiveness of the adaptive sliding mode control method designed in this invention, a simulation experiment was designed. The control structure block diagram and train information interaction schematic diagram of the designed simulation experiment embodiment are shown in Figure 1. During the control process, the train status information (position, speed, acceleration, etc.) During the planned train operation, the rear train uses the adaptive sliding mode control method to calculate the control output based on the status of the train in front and its own status and applies it to the current train to achieve tracking control of the rear train.

The experimental line scenario is set between Huashan North and Lintong stations on the Zhengxi Line high-speed passenger line. Using real line data, a tracking operation simulation scenario between stations is designed for verification. In this scenario, the leading car 0 and the following car 1 have just completed the virtual grouping The communication link is established, and when there is a certain speed difference, the vehicle behind gradually reaches the same speed as the vehicle in front. The simulation step size is 0.1s, the total simulation time is 200s, and the simulation results are shown in Figure 2.

Figure 2(a) is a diagram of changes in train running intervals. The legend shows the actual distance between the front and rear trains, the ideal distance and the minimum safe distance from top to bottom. It can be seen from the figure that, except for the braking time of 180s-200s, the car behind can track the ideal interval and maintain stability most of the time. Figure 2(b) is a diagram of the speed changes of the leading vehicle 0 and the following vehicle 1 during operation. The legend indicates the speed of the leading vehicle and the following vehicle in turn. There is a certain speed difference between the front and rear vehicles at the beginning of the simulation. The adaptive sliding mode control method controls the acceleration of the rear vehicle in a short period of time and maintains the same speed as the front vehicle in a long period of time. Under smooth operation, the front and rear vehicle speeds are The difference is no more than 0.5m/s. Figure 2(c) is the change diagram of the sliding mode function (σ) during the simulation process. Under the action of the adaptive sliding mode control method, the system reaches the sliding state (σ=0) in a short time, with low overshoot. And it can maintain the sliding state in the subsequent process, which proves the effectiveness of the present invention. Based on the content shown in Figure 2, the embodiment of the present invention makes the distance between virtual grouping trains approach the reference distance and keeps the speed consistent, achieving the ideal effect of virtual grouping.

Those of ordinary skill in the art will realize that the embodiments described here are to help readers understand the implementation methods of the present invention, and it should be understood that the protection scope of the present 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 based on the technical teachings disclosed in the present invention without departing from the essence of the present invention, and these modifications and combinations are still within the protection scope of the present invention.

Claims (7)

1. An adaptive sliding mode control method for spacing control of virtual grouping high-speed trains, which is characterized by including the following steps: A1. Establish a high-speed train longitudinal dynamics model, and consider in the model changes in air resistance coefficients, modeling errors and parameter uncertainties due to unknown precise train loads, as well as unfavorable conditions such as untimely input feedback. A2. Considering the difference in train braking performance, speed measurement and positioning error and information transmission delay, establish the minimum safe separation model and reference separation model of virtual marshalling high-speed trains. A3. Identify the high-speed train longitudinal dynamics model, divide the model into estimable parts and non-estimateable parts, define the system total uncertainty, use nonlinear control design methods, and design sliding mode control methods. A4. For the designed sliding mode control method, design an adaptive law, and combine the adaptive law with the sliding mode control method to construct an adaptive sliding mode control method. This adaptive sliding mode control method can adaptively adjust control gain parameters based on input and output feedback to compensate for high-speed train longitudinal dynamics model parameter uncertainty and external disturbances. 2. An adaptive sliding mode control method for spacing control of virtual grouping high-speed trains according to claim 1, characterized in that: the train longitudinal dynamics model established in step A1 takes into account parameter uncertainty and time variation. Disturbance includes unknown train load and changes in air resistance coefficient. 3. An adaptive sliding mode control method for spacing control of virtual grouping high-speed trains according to claim 2, characterized in that the train longitudinal dynamics model established in A1 is as follows: The high-speed train is abstracted as a point mass system with traction and braking capabilities, and is subject to basic resistance and additional resistance. Using x ₁ to represent the train position and x ₂ to represent the train speed, the train longitudinal dynamics model can be written as: In the formula, F is the traction/braking force output by the train. It is a positive value during traction, a negative value during braking, and zero when coasting. M is the train mass, R _b and R _a are the train basic resistance and train additional resistance calculation functions respectively. u is the train input and τ is the time constant. The basic resistance is expressed by the Davis equation: During high-speed train operation, c ₂ is not a fixed value due to changes in surrounding wind speed. In addition, due to changes in train load, the train mass M is a fixed but unknown value during operation. make Among them/> and/> is the estimate of c ₂ and M,/> and Me _are uncertain errors. 4. An adaptive sliding mode control method for spacing control of virtual grouping high-speed trains according to claim 1, characterized in that: The minimum safe interval model established in step A2 analyzes the movement process from normal marshalling operation to unexpected emergency braking in the virtual marshalling, taking into account various delays and equipment processing time in the process, as well as the train during the information transmission process. Speed changes and train speed measurement positioning errors. The expression of the minimum safe margin model is: In the formula, Indicates the maximum speed measurement error,/> Indicates the minimum emergency braking rate of the vehicle behind in the most unfavorable situation, represents the maximum emergency braking rate of the vehicle in front under the most unfavorable situation, v _i (t) represents the speed of the vehicle behind, /> Represents the speed of the transmission received by the following vehicle i from the preceding vehicle i-1, ΔV _EB represents the maximum speed change of the preceding vehicle during the communication delay process, /> Indicates the maximum positioning error. Based on the minimum safe separation model, considering the maximum common braking applied by the vehicle behind, the expression of the reference separation model is given: In the formula, l _SB (v) represents the distance traveled by the vehicle behind from applying maximum normal braking to stopping at speed v. 5. An adaptive sliding mode control method for spacing control of virtual grouping high-speed trains according to claim 1, characterized in that: in step A3, the train longitudinal dynamics model is further identified, and the train longitudinal dynamics model is It is divided into an estimable determined part of the system and an unknowable system error. The unknown part and external disturbances are combined into the system sum uncertainty, and a sliding mode control method is designed to control the output of the determined part of the system and the system sum uncertainty respectively. . 6. An adaptive sliding mode control method for virtual grouping high-speed train spacing control according to claim 3, characterized in that the sliding mode control method designed in A3 is as follows: Based on the high-speed train longitudinal dynamics model in A1, the model is expressed in vector form: X is a vector representing the train status, X=[x ₁ x ₂ ] ^T . The tracking target vector is written as The tracking error vector is defined as e=XX _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 determined part and an uncertain part. f(X)＝[x ₂ -R _b -R _a ] ^T For sliding mode control, the sliding mode surface function is designed as σ = C ^T e, where C = [C ₁ C ₂ ] and C ₁ and C ₂ are both positive constants. Considering other unconsidered errors and external disturbances ω of the train dynamics model, the total uncertainty of the system is defined as: 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 as follows: F _s =-(C ^T b _o (X)) ^-1 βsgn(σ) F＝F _s +F _o In the formula, β represents the control output gain, f _o (X) and _bo (X) represent the determined part of the system, and Δf (X) and Δb (X) represent the uncertain part of the system. 7. An adaptive sliding mode control method for virtual grouping high-speed train interval control according to claim 1, characterized in that: the adaptive law designed in step A4 is used to dynamically adjust the control output gain, so that the adaptive The sliding mode control method does not need to provide upper bounds for disturbances and errors during design, which reduces the difficulty of design and can eliminate the adverse effects of unknown parameters and time-varying disturbances on train control. The adaptive law is designed as: Among them, α is the gain of the adaptive amount, which is a design parameter used to adjust the change rate of the adaptive gain.