Train traction multi-agent cooperative control method considering axle load transfer

Abstract

The invention discloses a train traction multi-agent cooperative control method considering axle load transfer, and the method comprises the steps: firstly constructing a multi-motor train traction system model which comprises a vehicle dynamics model, an axle dynamics model and a wheel-rail adhesion coefficient calculation model, and comprehensively considering axle load transfer caused by factors such as traction force; and establishing a dynamic axle load calculation model. And then, designing a multi-axis maximum adhesion tracking collaborative optimization controller based on model predictive control, dynamically updating an axis weight, an adhesion coefficient and a system state through each predictive step, realizing accurate tracking of a reference creep speed, and carrying out optimal torque distribution on the premise of meeting motor torque constraint and total traction constraint. Therefore, multi-shaft idling and sliding are avoided, the adhesive force utilization efficiency is improved, and the device adapts to complex working conditions such as wet and slippery rail surfaces and ramp changes. According to the method, the traction safety and the operation efficiency of the multi-axle electric locomotive can be effectively improved.

Description

Technical Field

[0001] This invention relates to the field of rail transit control technology, and is a multi-agent cooperative control method for train traction that considers axle load transfer. It is particularly suitable for adhesion optimization and anti-slip control of multi-motor electric locomotives under complex track conditions. Background Technology

[0002] Wheel-rail adhesion control is a core technology of rail transit traction systems, directly affecting train traction capacity, operating efficiency, and safety. As trains develop towards higher speeds and heavier loads, higher demands are placed on adhesion control. In actual operation, the wheel-rail adhesion coefficient is comprehensively affected by track surface conditions (dry, wet, oily, icy, etc.), environmental conditions, wheel-rail interface characteristics, and axle load transfer factors, exhibiting highly nonlinear, time-varying, and difficult-to-measure characteristics. If traction or braking torque control is inadequate when adhesion conditions deteriorate, wheel slippage or wheel coasting can easily occur, leading to accelerated wheel-rail wear, decreased traction efficiency, and potentially endangering train safety.

[0003] For multi-axle train systems, axle load transfer becomes a key factor affecting adhesion performance. During traction, braking, and gradient operation, the vertical load on each axle is redistributed, causing changes in axle load. This axle load transfer significantly alters the available adhesion force of each axle, and without targeted control, it can lead to problems such as slippage on lightly loaded axles and insufficient traction on heavily loaded axles. Therefore, researching multi-axle adhesion synergy optimization considering axle load transfer is essential.

[0004] A review of existing literature reveals that Kawamura et al. proposed a control strategy based on adhesive derivative adjustment. While this strategy has made significant progress in improving uniaxial adhesion performance, it requires accurate estimation of the adhesion state and lacks robustness.

[0005] Abouzeid et al. developed a control strategy that integrates fuzzy logic and particle swarm optimization. Although it can adaptively track the changing peak values, it faces problems such as sensitivity to noise and computational complexity.

[0006] Wen et al. proposed an anti-slip and re-adhesion control system based on model predictive control. Although the adhesion control was further optimized and it can effectively handle multivariable and constrained control problems, it did not consider the multi-axis collaborative optimization of stability by axle load transfer.

[0007] It is particularly important to note that existing literature has significant shortcomings in multi-axle cooperative optimization. In actual train operation, the adhesion conditions of each axle may differ significantly, requiring consideration of dynamic load changes caused by axle load transfer. However, there is currently a lack of integrated control methods capable of simultaneously handling multiple factors such as axle load transfer, multi-axle cooperation, and changes in rail surface conditions. Most existing control strategies are either based on a fixed axle load assumption or only consider a single influencing factor, making it difficult to achieve optimal adhesion utilization under complex actual conditions.

[0008] In summary, existing technologies for multi-axle train adhesion coordination control fail to fully consider the dynamic impact of axle load transfer on adhesion performance. They lack integrated control methods capable of simultaneously handling multi-axle coordination, dynamic load distribution, and changes in rail surface conditions. Furthermore, their adaptability and robustness under complex real-world operating conditions need improvement. Therefore, there is an urgent need to develop a new control method that can optimize multi-axle adhesion coordination while considering axle load transfer, thereby improving train traction performance and operational safety under various operating conditions. Summary of the Invention

[0009] The purpose of this invention is to provide a multi-axle train traction cooperative control method and system that considers axle load transfer. This method employs a model predictive control (MPC) framework, explicitly constructing an optimization control problem that incorporates axle load transfer dynamics, wheel-rail adhesion nonlinearity, and multi-axle coupling. By dynamically updating axle load parameters and adhesion prediction models online, it achieves cooperative and optimized allocation of torque across multiple axles. This method can effectively improve the overall vehicle adhesion utilization rate, suppress wheel slip and coasting, and ensure train traction performance and operational safety under complex operating conditions, especially in scenarios involving gradient operation, non-uniform changes in rail surface conditions, and dynamic axle load transfer.

[0010] To achieve the above objectives, the present invention provides the following technical solution:

[0011] 1. A multi-agent cooperative control method for train traction considering axle load transfer, comprising the following steps:

[0012] Step 1: Establish a multi-agent model of the multi-motor train traction system that considers axle load transfer.

[0013] Step 2: Describe the multi-axis adhesion collaborative optimization problem.

[0014] Step 3: Provide relevant parameter designs to reflect the actual train parameter designs.

[0015] Step 4: Based on the above steps, add relevant constraints to the optimization problem and design the MPC algorithm to control the train.

[0016] Step 1, establishing a multi-agent model of the multi-motor train traction system considering axle load transfer, includes the following specific steps:

[0017] Step 1.1: Establish the vehicle dynamics model. For a four-axle electric locomotive, its dynamic equations are as follows:

[0018]

[0019]

[0020]

[0021] in The train's operating speed; Indicates the total mass of the train; For the first Adhesion between the axle and the rail; The basic resistance for train operation is specifically expressed as about The function is shown in formula (3). , , The coefficients related to the calculation of basic resistance; For the first The adhesion coefficient of the shaft; For the first The creep speed of the shaft; For the first Axle load, .

[0022] Step 1.2: Establish the shaft dynamics model. This invention adopts a simplified shaft dynamics model, whose rotational dynamics equations are:

[0023]

[0024] in, For the first The output angular velocity of the shaft motor, For the first The output torque of the shaft motor For the first Moment of inertia of the shaft motor For adhesive force equivalent to the first The load torque at the motor end of the shaft.

[0025] No. The rotational dynamics equation of the shaft is:

[0026]

[0027]

[0028]

[0029] in, For the first Angular velocity of the axle-wheel pair The gearbox transmission ratio of the vehicle. For the first Moment of inertia of the gear pair Let be the radius of the wheel. The equation for the moment of inertia can then be obtained as follows:

[0030]

[0031]

[0032] in, Indicates equivalence up to the first Moment of inertia at the shaft motor end.

[0033] Based on the locomotive traction balance, we have , The axle load transfer calculation model established by this invention is as follows:

[0034]

[0035] in, Indicates the first Axle load, This refers to the total axle load of the train. For the total locomotive resistance, The height of the coupler from the ground. The height of the bogie, The distance between the centers of the two bogies. The wheelbase between the two axes. For the first Resistance on each wheel pair.

[0036] Step 1.3: Establish a model for calculating the wheel-rail adhesion coefficient. The empirical formula for the adhesion characteristic curve is as follows:

[0037]

[0038] Among them, creep speed It is the circumferential speed of the wheel. With train speed The difference between them:

[0039]

[0040] , , , These are parameters related to the rail surface condition. The parameter values ​​for the two rail surfaces are shown in Table 1:

[0041] Table 1. Parameter values ​​of empirical formulas under different orbital planes

[0042]

[0043] Step 1.4: Based on the above formulas, establish a multi-agent model of the multi-motor train traction system and discretize it. By combining equations (1)-(3) and (8)-(11), the multi-agent model describing the entire multi-motor train traction system can be derived:

[0044]

[0045] Let the state variable be... Control input quantity The output is The state-space equations of the system can be constructed based on formulas (10) and (13), and their expressions are as follows:

[0046]

[0047]

[0048] in , Therefore, it can be seen that this system has... One input, A dynamically coupled nonlinear multi-agent system with multiple outputs.

[0049] To facilitate controller design, the state-space equation (13) is discretized, resulting in the following discrete-time model:

[0050]

[0051] in This is the sampling interval.

[0052] Step 2, the multi-axis adhesion collaborative optimization problem, includes the following specific steps:

[0053] Step 2.1: Define the objective function.

[0054] Considering the significant impact of axle load transfer on system dynamics, the MPC controller of this invention integrates dynamic axle load calculation into the predictive model. At each step, it recalculates the load on each axle based on the control input, thereby more accurately describing viscosity changes and improving the adaptability of multi-axis cooperative control. Its primary control objective is to accurately track the reference slip velocity trajectory.

[0055] Let the reference slip velocity trajectory be... To achieve arbitrary Shaft reference slip velocity The tracking and predictive controller at time steps The objective function can be expressed in the following form:

[0056]

[0057] in and Given a weight matrix, it is required that... It is a positive semi-definite matrix. It is a positive definite matrix. Indicates the prediction time domain, This indicates the control time domain.

[0058] Step 2.2: Design constraints.

[0059] To ensure the physical realizability and safety of the control system and to fully utilize adhesion, the optimization problem must satisfy the following constraints:

[0060] Due to the limitations of the traction motor in the traction system, the torque output by the predictive control must not exceed the effective torque command value provided by the traction control unit (TCU). To achieve the tracking target of the sum of the output torque of multiple motors. The equation must be satisfied. To ensure that the reference slip speed does not exceed the maximum jamming point, a relaxation coefficient is introduced to guarantee the safe operation of the traction system. Based on the axle load transfer effect, it is also necessary to ensure that the axle load of each axle varies within a reasonable range to prevent the risk of idling caused by excessive unloading.

[0061] Based on these constraints, the constraint design of the controller can be expressed as follows:

[0062]

[0063] Step 2.3: Establish the MPC optimization problem.

[0064] At any moment The optimization problem for MPC is as follows:

[0065]

[0066]

[0067] In solving the above optimization problem, the MPC controller recalculates the axle load transfer based on the current control input at each prediction step, dynamically updating the axle load of each axle. This ensures that the prediction model matches the actual physical process. The specific implementation is as follows:

[0068] 1) Based on control input Calculate total traction force .

[0069] 2) Calculate the dynamic axle load of each axle according to the axle load transfer calculation formula (10). .

[0070] 3) Update the axle load parameters in the prediction model and update the adhesion.

[0071] 4) Use the updated model to perform state prediction and cost calculation to solve the optimization problem with dynamic axle load constraints.

[0072] At time k, by solving the above-mentioned constrained nonlinear optimization problem, the optimal output torque of all motors can be obtained. Then at the time With the initial value Repeat the solution process for this optimization problem.

[0073] Step 3: Design of relevant parameters.

[0074] To ensure the feasibility of the control method described in this invention, the following key parameters need to be designed and selected.

[0075] Step 3.1: Selection of System Model Parameters. This invention takes a certain type of four-axle B0-B0 electric locomotive as the research object, involving the following train physical parameter coefficients and simulation parameters: total train weight. Gravitational acceleration Wheel radius Gearbox transmission ratio , No. Moment of inertia of the shaft equivalent to that at the motor end Geometric parameters used for axle load transfer calculations: Coupler height to ground Bogie height Center distance between the two bogies Wheelbase .

[0076] The specific values ​​are shown in Table 2.

[0077] Table 2 Simulation Parameters

[0078]

[0079] Step 3.2: Parameter Selection for the Model Predictive Controller. The parameter design of the Model Predictive Controller (MPC) directly affects control performance and computational complexity. Key parameters include:

[0080] 1) Sampling time: This determines the update frequency of the control system.

[0081] 2) Prediction Time Domain and Control Time Domain: Prediction Time Domain Control time domain .

[0082] 3) Weighting matrix: Output error weighting matrix With control weight matrix It is used to adjust the balance between tracking accuracy and energy consumption. Take a positive semi-definite matrix, Take a positive definite matrix.

[0083] 4) Constraint parameters: Maximum torque limit for single-axis motor: Total traction torque command: Its value is determined by the train's operating conditions (for example, the value taken in the simulation). ); creep speed safety relaxation coefficient ε.

[0084] Step 4 of the Model Predictive Control (MPC) algorithm specifically includes the following steps:

[0085] Step 4.1: Initialization. At time t=0, assume the train starts moving from a stationary state. Set the initial parameters as follows:

[0086]

[0087] The predicted output can be derived from formulas (13) and (14).

[0088] Step 4.2: Online rolling optimization of the main loop. At that time, the following loop is executed:

[0089] 1) Estimate the total traction force based on the current control input, calculate the axle load transfer, and update the axle load parameters in the prediction model.

[0090] 2) The MPC controller solves the optimal control problem. Thus, the optimal predictive control input is obtained. .

[0091] 3) Optimal control input obtained through application Determine the optimal state within the prediction range.

[0092]

[0093]

[0094] 4) Input the optimal predictive control... The first term extracted is used as the actual system control input.

[0095]

[0096] 5) Calculate the actual state and output using the train dynamics equations.

[0097] 6) Order Then repeat the above steps until the loop ends.

[0098] Beneficial Effects: This invention is applied to the field of rail transit traction control. It primarily employs a Model Predictive Control (MPC) framework and a multi-agent cooperative optimization approach. By constructing a predictive model incorporating a dynamic axle load update mechanism and integrating axle load transfer constraints, wheel-rail adhesion nonlinearity, and multi-axle coupling effects into the optimization problem, a novel multi-axle train traction cooperative control method is proposed. This method can achieve adaptive optimization allocation of motor torque for each axle under complex operating conditions such as track surface condition switching and dynamic axle load redistribution, thereby significantly improving the overall vehicle adhesion utilization rate and effectively suppressing the risks of slippage and coasting. Using this method, the traction robustness and operational safety of trains in non-uniform adhesion environments can be enhanced without relying on precise adhesion force measurements. Simultaneously, it helps reduce wheel-rail wear, improve energy efficiency, and provide passengers with a smoother and more comfortable riding experience. Attached Figure Description

[0099] Figure 1 This is a flowchart illustrating the entire method of the present invention.

[0100] Figure 2 This is a simplified diagram of the i-th axis dynamics model in this invention;

[0101] Figure 3 This is a simplified model and force analysis diagram of the four-axle locomotive of the present invention;

[0102] Figure 4 This is a graph showing the adhesion characteristics between the wheels and rails of a subway vehicle under different road surface conditions according to the present invention.

[0103] Figure 5 This is a simulation result diagram of the four-axis track surface switching of the present invention.

[0104] Figure 6 This is a simulation result diagram of the single-axis track surface switching of the present invention.

[0105] Figure 7 The figure shows the simulation results of the dual-axis track surface switching of the present invention. Detailed Implementation

[0106] The present invention will now be further described in conjunction with the embodiments and accompanying drawings:

[0107] A multi-agent cooperative control method for train traction considering axle load transfer, specifically including:

[0108] Step 1: Establish a multi-agent model of the multi-motor train traction system considering axle load transfer.

[0109] This invention is based on the establishment and discretization of vehicle dynamics model, axle dynamics model, axle load transfer calculation model, and wheel-rail adhesion coefficient calculation model, and derives a multi-agent model describing the entire multi-motor train traction system:

[0110] .

[0111] This invention employs a model predictive control method for the control input. To facilitate controller design, the state-space equation (24) is first discretized, resulting in the following offline model:

[0112]

[0113] Step 2: Design of Multi-Axis Adhesion Co-optimization Problem Based on MPC

[0114] The optimization problem design in this step is shown in the objective function (17) and constraint conditions (18), and the MPC optimization is established as shown in (19).

[0115] Step 3: Design of relevant parameters

[0116] Step 3.1: Selection of system model parameters. The specific data is shown in Table 2.

[0117] Step 3.2: Parameter selection for the model predictive controller, setting the sampling time... Predicting the time domain Control time domain Maximum torque of a single-axis motor: .

[0118] Step 4: Implement the MPC algorithm

[0119] At each sampling moment, the current state of each axis is obtained, and the dynamic axle load of each axis is calculated in real time based on the axle load transfer model (8), and the prediction model is updated. By solving the optimal control problem, the optimal predictive control input is obtained. Then, the optimal control input obtained through application is used. Determine the optimal state within the prediction range. , input the optimal predictive control The first term is extracted as the actual system control input, and the actual state and output are calculated using the train dynamics equations. The above steps are repeated until the loop ends.

Claims

1. A multi-agent cooperative control method for train traction considering axle load transfer, characterized in that, Includes the following steps: Step 1: Establish a multi-agent system model for multi-motor train traction considering axle load transfer, specifically including: Step 1.1: Establish a vehicle dynamics model to describe the relationship between train speed and the adhesion and basic resistance of each axle; Step 1.2: Establish a shaft dynamics model, considering the motor output torque, wheelset rotational inertia and axle load transfer effect, and derive the axle load transfer calculation formula; Step 1.3: Establish a wheel-rail adhesion coefficient calculation model, and describe the adhesion characteristics based on creep speed and rail surface state parameters; Step 1.4: Based on the above model, construct a multi-agent state space model of the multi-motor train traction system and discretize it; Step 2: Construct a multi-axis adhesion collaborative optimization problem, specifically including: Step 2.1: Define the objective function to track the reference slip velocity trajectory, and introduce a weight matrix to balance tracking accuracy and energy consumption; Step 2.2: Design constraints, including motor output torque limit, total traction force constraint, slip speed safety margin, and axle load variation range; Step 2.3: Establish the model predictive control (MPC) optimization problem, update the model parameters based on the dynamic axle load in each control cycle, and solve for the optimal torque distribution; Step 3: Set the key parameters required for the control method, including train physical parameters and MPC controller parameters; Step 4: Implement train traction control based on the MPC algorithm, specifically including: Step 4.1: Initialize system state and predict output; Step 4.2: Within each control cycle, based on the current state and control input, dynamically calculate the axle load transfer, update the prediction model, solve the optimization problem, apply the optimal control input, and iterate until the end of control.

2. The multi-agent cooperative control method for train traction considering axle load transfer according to claim 1, characterized in that, The state-space model described in step 1.4 is a dynamically coupled nonlinear multi-agent system with multiple inputs and outputs, which can reflect the influence of axle load transfer on the adhesive force distribution.

3. The multi-agent cooperative control method for train traction considering axle load transfer according to claim 1, characterized in that, The objective function described in step 2.1 includes two terms: the first term measures the system's ability to track the reference creep velocity, and the second term characterizes the system's energy consumption level. The two terms are balanced by a weight matrix.

4. The multi-agent cooperative control method for train traction considering axle load transfer according to claim 1, characterized in that, The constraints mentioned in step 2.2 include: the output torque of each axle motor does not exceed the command value of the traction control unit; the sum of the output torques of each axle meets the total traction force target; the slip speed does not exceed the maximum jamming point to introduce a safety margin; and the axle load of each axle varies within a reasonable range to prevent idling.

5. The multi-agent cooperative control method for train traction considering axle load transfer according to claim 1, characterized in that, In step 2.3, the MPC optimization problem is to recalculate the axle load transfer based on the current control input in each control cycle, dynamically update the axle load parameters, and update the prediction model accordingly to achieve accurate modeling and coordinated control of adhesion.

6. The multi-agent cooperative control method for train traction considering axle load transfer according to claim 1, characterized in that, In step 4.2, rolling optimization is used to accurately track the reference creep speed and optimize the torque distribution of each axle to adapt to the changes caused by axle load transfer, prevent wheel slippage, and meet the total torque constraint and the torque limit of each axle.

Images