Train driving curve dynamic tracking method and device based on model predictive control

Abstract

The present disclosure relates to the technical field of automatic control, and comprises a train driving curve dynamic tracking method and device based on model predictive control. By inputting expected driving parameters corresponding to the k+1th driving moment to the k+Pth driving moment in the target driving curve, and the actual train state at the kth driving moment into an MPC model, a train control quantity at the kth driving moment is obtained; by inputting the train control quantity and the observation value of the total disturbance of the extended state observer at the kth driving moment into a dynamic compensation model, a compensated control quantity at the kth driving moment is obtained to control the train operation; then by inputting the actual displacement at the k+1th driving moment and the observation value of the total disturbance at the kth driving moment into the extended state observer, the observation value of the total disturbance of the extended state observer at the k+1th driving moment is updated to control the train subsequently; various uncertainties can be considered, and the control method is simple and the calculation difficulty is low.

Description

Technical Field

[0001] This disclosure relates to the field of automatic control technology, and in particular to a method and apparatus for dynamic tracking of train driving curves based on model predictive control. Background Technology

[0002] Rail transit is a major mode of public transportation. High-speed rail is a fundamental component of rail transit systems. The high-speed rail train control system mainly consists of two parts: Automatic Train Protection (ATP) and Automatic Train Operation (ATO). The ATP system is primarily responsible for ensuring safe train operation, monitoring train speed in real time to ensure it operates within safe speed limits, preventing speeding, and avoiding collision risks. The ATO system is mainly responsible for controlling train operation, including starting, running, and stopping. It automatically adjusts train speed and controls stopping distance based on real-time track conditions and train timetables. The reliability of the ATO system is far superior to manual operation. It optimizes the acceleration and deceleration process, keeping the train running along the optimal speed curve throughout its journey. This not only reduces energy consumption and improves train operation efficiency but also maximizes passenger comfort. In summary, automatic train operation technology plays a crucial role in improving the efficiency of train control systems and railway transportation systems. However, there are still many problems with the automatic train operation system. For example, how to ensure that the ATO system operates stably and effectively in various uncertain environments. At the same time, the ATO system also needs to process a large amount of data in real time and make decisions in a very short time. This requires data processing and algorithms to be efficient and have online computing capabilities.

[0003] In an ATO (Automatic Train Operation) system, the optimal driving curve (such as the optimal speed curve or optimal displacement curve) is generally obtained by optimizing the train's route timetable and solving optimization problems related to comprehensive indicators such as energy consumption, passenger comfort, and network efficiency. The performance of the ATO system is determined by whether it can control the train to run according to the given optimal driving curve. However, because precise control of train speed or displacement involves complex dynamics problems, the acceleration and deceleration of the train are not only affected by the performance of the engine or braking system, but also by vehicle mass, track conditions, extreme weather, and different environments. Furthermore, the train itself is a multi-parameter, strongly coupled, large-inertia, and uncertain system. Therefore, controlling the train to track the target driving curve is challenging.

[0004] Traditional methods for controlling a train to track a target driving curve include the following:

[0005] The first method involves using Proportional-Integral-Derivative (PID) control to track the target driving curve. Because PID controllers are simple to design, have few parameters, and are not heavily dependent on models, they can be applied to train driving curve tracking. For example, classic PID algorithms can be used to control train operation, or a neural network PID controller can be designed to control train speed and displacement. Alternatively, multiple methods can be used to establish a process model for high-speed rail cruise control, and an adaptive fuzzy PID method can be used to control the train's speed cruise process.

[0006] While PID-based controllers are relatively simple, they cannot guarantee accurate trajectory tracking under conditions of significant train disturbances and uncertainties. Furthermore, these controllers are prone to introducing oscillations during operation, which can significantly impact passenger comfort.

[0007] The second approach involves using intelligent control methods such as neural networks, fuzzy control, and expert systems to control the train's tracking of the target driving curve. For example, fuzzy predictive control can be used to track the train's speed curve. However, the design of the membership function and fuzzy rules in fuzzy predictive control relies heavily on prior knowledge and expert experience, and there are no universally accepted conclusions regarding the stability of fuzzy control. It is overly dependent on specific system configurations, making the design and analysis of fuzzy controllers more complex than traditional controllers. Another example is the use of reinforcement learning combined with expert systems to implement intelligent train operation algorithms. However, reinforcement learning involves high computational costs, making it impossible for the train to run the algorithm online in real time. Yet another example is the design of adaptive control strategies for a multi-mass model of the train to track the target speed curve, primarily considering the multi-mass model to address parameter uncertainties. However, this method does not consider the stepped adjustment of the train system, and the tracked curve exhibits high-frequency vibrations, affecting passenger comfort.

[0008] The third approach is based on Model Predictive Control (MPC) to control train tracking of a target driving curve. MPC has been widely used in train tracking due to its advantages, including the ability to handle complex constraints and multivariable systems, robustness, ease of integration with other advanced algorithms, and the ability to freely set optimization indices. For example, speed threshold-based cruise control algorithms can control train tracking speed curves while ensuring infrequent mode switching. However, this algorithm does not consider the impact of uncertainties. Another example is Robust MPC (RMPC), which introduces uncertainties into the dynamic model and considers worst-case stability, ensuring the normal operation of the virtual coupled train in environments with uncertainties such as modeling errors, communication delays, and adhesion losses. However, Robust MPC design is overly conservative, and the upper and lower bounds of uncertainty are difficult to obtain precisely. Yet another example is using MPC for trajectory tracking control of trams with regenerative braking. While the algorithm has a fast solution speed, it does not fully consider the impact of uncertainties. For example, nonlinear model predictive control algorithms incorporate the effects of factors such as friction, track gradient, and strong winds on trains into the model, and the effectiveness of this method is verified under actual train operating conditions in a simulation scenario. However, nonlinear model predictive control can only adapt to relatively weak uncertainties and cannot handle situations with strong uncertainties.

[0009] The fourth approach involves introducing an observer during the control model design process to observe the true system state under disturbances. While methods that tolerate some uncertainty, such as fuzzy control and adaptive control, can be used directly to address uncertainties, or the impact of uncertainty can be considered directly in the model, such as with robust MPC, this approach is overly conservative and may lead to unnecessary performance losses. Therefore, this fourth method introduces an observer during model design to observe the true system state under disturbances. For example, a neural network can be used to design an observer to monitor parameters in the train's dynamic model, and a sliding diaphragm control can be used to design a train trajectory tracking control law. Under external disturbances, the algorithm successfully tracks the train's target speed curve in simulations. However, the performance improvement compared to sliding diaphragm control is only slight, and the model and parameter uncertainties are not considered in the simulation. Furthermore, the neural network observer's observations of system parameters also exhibit some bias under disturbances.

[0010] In addition, the above-mentioned design of the observer only considers the impact of external disturbances and noise on the system, but does not consider the "internal disturbances" existing in the system, namely the impact of model parameter perturbations, model mismatches and unmodeled features on system dynamics. Based on this, the following fifth method for tracking the target driving curve is provided in the related technology.

[0011] The fifth approach involves incorporating a design similar to an extended state observer during the control model design process. This type of observer can observe and compensate for disturbances as extended states. For example, a neural network observer can be used to address issues such as the unmeasurable speed of high-speed trains and the presence of external disturbances. Two neural networks are used to observe speed and approximate model uncertainties, and a robust controller ensures stable train operation under uncertain conditions. However, the uncertainty bound function required for the robust controller is difficult to obtain. Another example is the development of a train trajectory tracking control algorithm based on an extended state observer, combining genetic algorithms. This algorithm extends the system's internal resistance and external disturbances into a new state variable for estimation. Comparison with traditional PID control on a hardware-in-the-loop simulation platform demonstrates better robustness. However, this algorithm does not consider constraints on train gear positions, and the established model is too simplistic, only considering resistance and not model parameter perturbations. Yet another example is the proposal of an extended state observer combined with a Koopman operator-based model predictive control method to address the speed control problem of high-speed trains under external disturbances. This method can accurately track train speed curves in environments with disturbances and white noise. However, the data-based model has poor generalization performance for unknown situations, and the method does not consider the case of discrete gears.

[0012] In summary, some traditional methods for controlling trains to follow driving curves fail to adequately consider external disturbances, parameter uncertainties, and model mismatches in the train system. Fuzzy controllers rely too heavily on prior knowledge, resulting in poor generalization ability. Reinforcement learning combined with expert control involves high computational costs, making online implementation on train systems difficult. Adaptive control methods exhibit poor performance, speed judder, and do not consider stepped gear adjustments, making it difficult to obtain the bounding function for the introduced uncertainties. Furthermore, this method is overly robust, leading to unnecessary performance losses. Techniques combining MPC and state observers use data-driven models with poor generalization performance and do not consider stepped train control adjustments. Summary of the Invention

[0013] In view of this, this disclosure proposes a dynamic tracking method for train driving curves based on model predictive control. Based on a model of stepped train regulation, it not only takes into account various uncertainties of the train system, but also has a very simple design in terms of control method, reducing computational difficulty.

[0014] According to one aspect of this disclosure, a method for dynamic tracking of train driving curves based on model predictive control is provided, the method comprising:

[0015] Obtain the target driving curve of the train, which is used to indicate the desired driving parameters of the train at each driving moment;

[0016] For the current k-th driving moment and the subsequent F-1 driving moments during the train's operation, the expected driving parameters corresponding to the (k+1)-th to (k+P)-th driving moments in the target driving curve, and the actual train state at the k-th driving moment, are input into a preset Model Predictive Control (MPC) model to obtain the train control quantities corresponding to the k-th to (k+F-1)-th driving moments respectively; wherein, the train control quantities are used to control the actual train state; k is an integer starting from 1, F and P are integers greater than or equal to 1, and P is greater than or equal to F;

[0017] The train control quantity at the k-th driving moment and the observed value of the total disturbance of the preset extended state observer at the k-th driving moment are input into the preset dynamic compensation model to compensate the train control quantity and the observed value of the total disturbance at the k-th driving moment, respectively, to obtain the compensated control quantity at the k-th driving moment; the total disturbance is used to represent all disturbance factors that the MPC model did not simulate during the train's operation, and the observed value of the total disturbance is initialized to a preset value;

[0018] The train operation is controlled based on the compensated control quantity;

[0019] If the runtime reaches the (k+1)th driving moment, obtain the actual displacement at the (k+1)th driving moment;

[0020] The actual displacement at the (k+1)th driving moment, the compensated control quantity at the kth driving moment, and the extended state observer are input to update the observed value of the total disturbance at the (k+1)th driving moment. This updated value is then used to determine the compensated control quantity at the (k+1)th driving moment based on the observed value of the total disturbance at the (k+1)th driving moment when determining the train control quantity in the next test. The extended state observer is established based on the dynamic model of the train and the total disturbance.

[0021] In one possible implementation, the train's dynamic model includes a constant torque stage model corresponding to a first speed range and a constant power stage model corresponding to a second speed range, wherein the first speed range is smaller than the second speed range; accordingly,

[0022] The extended state observer includes a first observer based on the constant torque stage model and a second observer based on the constant power stage model.

[0023] The dynamic compensation model includes a first compensation model for compensating for the total disturbance of the first observer's output and a second compensation model for compensating for the total disturbance of the second observer's output.

[0024] In one possible implementation, the step of inputting the train control quantity at the k-th driving moment and the observed value of the total disturbance of the preset extended state observer at the k-th driving moment into a preset dynamic compensation model includes:

[0025] If the actual speed at the k-th driving moment is within the first speed range, the train control quantity at the k-th driving moment and the observed value of the total disturbance at the k-th driving moment are input into the first compensation model.

[0026] If the actual speed at the k-th driving moment falls within the second speed range, the train control quantity at the k-th driving moment and the observed value of the total disturbance at the k-th driving moment are input into the second compensation model.

[0027] In one possible implementation, inputting the actual displacement at the (k+1)th driving moment and the compensated control quantity at the kth driving moment into the extended state observer includes:

[0028] If the actual speed at the (k+1)th driving moment is within the first speed range, the actual displacement at the (k+1)th driving moment and the compensated control quantity at the kth driving moment are input into the first observer.

[0029] If the actual speed at the (k+1)th driving moment falls within the second speed range, the actual displacement at the (k+1)th driving moment and the compensated control quantity at the kth driving moment are input into the second observer.

[0030] In one possible implementation, the extended state observer is a linear state observer determined based on the state-space model of the dynamic model;

[0031] The first observer is represented by the following formula:

[0032] ;

[0033] The second observer is represented by the following formula:

[0034] ;

[0035] in, This represents the gain of the extended state observer. The value is a preset value; I represents the identity matrix, T S The input vector represents the time step between two adjacent driving moments. u1 and u2 represent the compensated control values ​​at the k-th driving moment, and y1 represents the actual displacement at the (k+1)-th driving moment. This is a three-dimensional vector. The first two dimensions represent the observed values ​​of train displacement and velocity, respectively, and the third component is the observed value of the total disturbance at the k-th driving moment. The third component represents the observed value of the total disturbance at the (k+1)th driving moment. M represents the actual speed of the train at the k-th driving moment; M represents the total mass of the train. This indicates the maximum traction gear of the train. This indicates the maximum braking gear of the train, and N represents the total number of carriages in the train. M Indicates the number of carriages in the train. This indicates the maximum value of the train's traction force. This indicates the maximum value of the train's braking force. This indicates the maximum value of the train's traction power.

[0036] In one possible implementation, the gain of the extended state observer is such that the poles of the extended state observer are located inside the unit circle.

[0037] In one possible implementation, the first compensation model is expressed by the following equation:

[0038] ;

[0039] The second compensation model is expressed by the following formula:

[0040] ;

[0041] Where u1 and u2 represent the control quantities at the k-th driving moment, and This represents the compensated control quantity at the k-th driving moment; Let M represent the observed value of the total disturbance at the k-th driving moment, and M represent the total mass of the train. This indicates the maximum traction gear of the train. This indicates the maximum braking gear of the train, and N represents the total number of carriages in the train. M Indicates the number of carriages in the train. This indicates the maximum value of the train's traction force. This indicates the maximum value of the train's braking force. represents the maximum value of the train's traction power, and v represents the actual speed of the train at the k-th driving moment.

[0042] In one possible implementation, the constraints of the MPC model are expressed by the following equation:

[0043]

[0044]

[0045] in, H(k) represents the expected driving parameters from the (k+1)th driving time to the (k+P)th driving time; h(k+1) represents the expected driving parameters at the (k+1)th driving time, ..., h(k+P) represents the expected driving parameters at the (k+P)th driving time.

[0046] Y(k) represents the predicted driving parameters corresponding to the (k+1)th driving time to the (k+P)th driving time; x(k) represents the actual train state at the kth driving time.

[0047] ;

[0048] y(k+1) represents the predicted driving parameters at the (k+1)th driving time, ..., y(k+P) represents the predicted driving parameters at the (k+P)th driving time; L represents the constant term of the disturbance factor simulated by the MPC model; T S F represents the time step between two adjacent driving moments. r This represents the drag value of the disturbance factor simulated by the MPC model;

[0049] , When the desired driving parameter is the desired speed, When the desired driving parameter is the desired displacement, ;

[0050] U(k) represents the train control quantity corresponding to the k-th driving time to the (k+F-1)-th driving time respectively; u(k) represents the train control quantity at the k-th driving time, ..., u(k+F-1) represents the train control quantity at the (k+F-1)-th driving time;

[0051] R and Q represent the preset weight matrices; U(k) 2i This represents the train control quantity at even-numbered positions, where the even-numbered train control quantity is the train braking gear; U(k) 2i-1 This indicates the train control quantity at odd-numbered positions, where the train control quantity at odd-numbered positions is the train traction gear.

[0052] According to another aspect of this disclosure, a train driving curve dynamic tracking device based on model predictive control is provided, the device comprising:

[0053] The curve acquisition module is used to acquire the target driving curve of the train, which is used to indicate the expected driving parameters of the train at each driving moment.

[0054] The control quantity prediction module is used to, for the current k-th driving moment and the subsequent F-1 driving moments during the train's operation, input the expected driving parameters corresponding to the (k+1)th to (k+P)th driving moments in the target driving curve and the actual train state at the k-th driving moment into a preset model predictive control (MPC) model to obtain the train control quantities corresponding to the k-th to (k+F-1)th driving moments respectively; wherein, the train control quantities are used to control the actual train state; k is an integer starting from 1, F and P are integers greater than or equal to 1, and P is greater than or equal to F;

[0055] The control quantity compensation module is used to input the train control quantity at the k-th driving moment and the observed value of the total disturbance of the preset extended state observer at the k-th driving moment into the preset dynamic compensation model, so as to compensate the train control quantity and the observed value of the total disturbance at the k-th driving moment respectively, to obtain the compensated control quantity at the k-th driving moment; the total disturbance is used to represent all disturbance factors that the MPC model did not simulate during the train driving process, and the observed value of the total disturbance is initialized to a preset value;

[0056] The train control module is used to control the train operation based on the compensated control quantity;

[0057] The displacement acquisition module is used to acquire the actual displacement at the (k+1)th driving moment when the running time reaches the (k+1)th driving moment.

[0058] The total disturbance observation module is used to input the actual displacement at the (k+1)th driving moment and the compensated control quantity at the kth driving moment into the extended state observer, and update the observed value of the total disturbance at the (k+1)th driving moment of the extended state observer. In the next determination of the train control quantity, the compensated control quantity at the (k+1)th driving moment is determined based on the observed value of the total disturbance at the (k+1)th driving moment to control the train. The extended state observer is established based on the dynamic model of the train and the total disturbance.

[0059] According to another aspect of this disclosure, a train driving curve dynamic tracking device based on model predictive control is provided, comprising: a processor; a memory for storing processor-executable instructions; wherein the processor is configured to implement the above method when executing the instructions stored in the memory.

[0060] According to another aspect of this disclosure, a non-volatile computer-readable storage medium is provided that stores computer program instructions thereon, wherein the computer program instructions, when executed by a processor, implement the above-described method.

[0061] According to another aspect of this disclosure, a computer program product is provided, including computer-readable code, or a non-volatile computer-readable storage medium carrying computer-readable code, wherein when the computer-readable code is run in a processor of an electronic device, the processor in the electronic device performs the above-described method.

[0062] By acquiring the target driving curve of the train; for the current k-th driving moment and the subsequent F-1 driving moments during the train's operation, the expected driving parameters corresponding to driving moments k+1 to k+P of the target driving curve, and the actual train state at the k-th driving moment, are input into a preset Model Predictive Control (MPC) model to obtain the train control quantities corresponding to driving moments k to k+F-1 respectively; the train control quantity at the k-th driving moment, and the observed value of the total disturbance at the k-th driving moment from the preset extended state observer, are input into a preset dynamic compensation model to compensate for the observed value of the train control quantity and the total disturbance at the k-th driving moment, respectively, to obtain the compensated control quantity at the k-th driving moment; based on the compensated control... The system controls train operation by controlling the flow of the train. When the running time reaches the (k+1)th driving moment, the actual displacement at the (k+1)th driving moment is obtained. The actual displacement at the (k+1)th driving moment and the compensated control quantity at the (k)th driving moment are input into the extended state observer to update the observed value of the total disturbance at the (k+1)th driving moment. This allows the system to determine the compensated control quantity at the (k+1)th driving moment based on the observed value of the total disturbance in the next train control operation, thus controlling the train. This method solves the problem of poor tracking accuracy caused by traditional driving curve tracking methods that do not consider all disturbance factors during train operation. Since the extended state observer can observe the total disturbance, it can improve the tracking accuracy of the driving curve.

[0063] Other features and aspects of this disclosure will become clear from the following detailed description of exemplary embodiments with reference to the accompanying drawings. Attached Figure Description

[0064] The accompanying drawings, which are included in and form part of this specification, illustrate exemplary embodiments, features, and aspects of this disclosure together with the specification and serve to explain the principles of this disclosure.

[0065] Figure 1 A flowchart illustrating a train driving curve dynamic tracking method based on model predictive control according to an embodiment of the present disclosure is shown.

[0066] Figure 2 A schematic diagram of a single-mass model of a train according to an embodiment of the present disclosure is shown;

[0067] Figure 3 A schematic diagram showing the traction force of a single-section motor car as a function of speed according to an embodiment of the present disclosure;

[0068] Figure 4 A schematic diagram showing the variation curve of electric braking force versus speed of a single carriage according to an embodiment of the present disclosure;

[0069] Figure 5 A schematic diagram illustrating a dynamic tracking process for train driving curves according to an embodiment of the present disclosure is shown.

[0070] Figure 6 A schematic diagram illustrating a train driving curve dynamic tracking process without using an extended state observer according to an embodiment of the present disclosure is shown.

[0071] Figure 7 A schematic diagram showing a target velocity curve according to an embodiment of the present disclosure;

[0072] Figure 8 A schematic diagram showing the tracking results of two curve tracking methods according to an embodiment of the present disclosure is provided.

[0073] Figure 9 An embodiment according to the present disclosure is shown. Figure 8 A magnified schematic diagram of the tracking results shown;

[0074] Figure 10 A schematic diagram showing the tracking results of two curve tracking methods according to another embodiment of the present disclosure;

[0075] Figure 11 An embodiment according to the present disclosure is shown. Figure 10 A magnified schematic diagram of the tracking results shown;

[0076] Figure 12 A schematic diagram showing the observed results of the total disturbance according to an embodiment of the present disclosure;

[0077] Figure 13 A schematic diagram showing a target velocity curve according to another embodiment of an embodiment of the present disclosure;

[0078] Figure 14 A schematic diagram showing the tracking results of two curve tracking methods according to yet another embodiment of the present disclosure;

[0079] Figure 15 A block diagram of a train driving curve dynamic tracking device based on model predictive control according to an embodiment of the present disclosure is shown.

[0080] Figure 16 A block diagram of a train driving curve dynamic tracking device based on model predictive control according to another embodiment of the present disclosure is shown. Detailed Implementation

[0081] Various exemplary embodiments, features, and aspects of this disclosure will now be described in detail with reference to the accompanying drawings. The same reference numerals in the drawings denote elements that have the same or similar functions. Although various aspects of the embodiments are shown in the drawings, they are not necessarily drawn to scale unless specifically indicated otherwise.

[0082] The term “exemplary” as used herein means “serving as an example, embodiment, or illustration.” Any embodiment illustrated herein as “exemplary” is not necessarily to be construed as superior to or better than other embodiments.

[0083] Furthermore, to better illustrate this disclosure, numerous specific details are set forth in the following detailed description. Those skilled in the art will understand that this disclosure can be practiced without certain specific details. In some instances, methods, means, components, and circuits well known to those skilled in the art have not been described in detail in order to highlight the main points of this disclosure.

[0084] First, let me introduce some of the terms used in this application.

[0085] 1. Model Predictive Control (MPC) is a control strategy that uses a dynamic model to predict the future behavior of the system and then determines the current control action based on these predictions. Generally, MPC defines an objective function, such as making the output as close as possible to the desired value while minimizing the variation in control actions. MPC attempts to find a set of control actions that minimizes the value of the objective function within the predicted future timeframe. Then, MPC executes the first action in this set and repeats the process. In this way, MPC can continuously adjust and optimize the control strategy to adapt to changes in system behavior and the environment.

[0086] 2. State-space model: A mathematical model that describes the behavior of a dynamic system. A state-space model consists of a set of first-order differential equations or difference equations, which describe the changes of the system's state variables over time.

[0087] 3. State Observer: A state observer is a dynamic system whose purpose is to estimate the values ​​of system states that cannot be directly measured. In control systems, not all state variables can be directly measured; in such cases, a state observer is needed to estimate these unmeasurable states. The working principle of a state observer is based on the system's inputs and outputs, using a dynamic model to estimate the system's state. The design of a state observer is typically based on the system's mathematical model, such as a state-space model.

[0088] 4. Extended State Observer (ESO): This is a core component of Active Disturbance Rejection Control (ADRC). Unlike a typical state observer, the extended state observer treats the parts of the system whose actual characteristics do not conform to expected characteristics (internal disturbances) and parameter uncertainties and model errors (external disturbances) as the total disturbance. It expands this total disturbance into a new state variable and then reconstructs all states containing the original system state and the disturbance using the system's inputs and outputs. In other words, the working principle of the extended state observer involves treating the total disturbance of the system (including unmodeled internal dynamics and external disturbances) as an additional state and adding it to the system's state-space model. Thus, the original n-order system is expanded into an n+1-order system.

[0089] Figure 1 A flowchart illustrating a model predictive control-based dynamic tracking method for train driving curves according to an embodiment of this disclosure is shown. This embodiment uses the method in a train control device as an example for explanation. This train control device is used to automatically control train operation, that is, to control train operation without manual intervention, such as controlling train start-up, braking, acceleration, and deceleration. This embodiment does not limit the control content of the control device. The train refers to a railway train equipped with an ATO (Automatic Train Operation) system and an ATP (Automatic Train Protection) system, which operate in the control device, such as a road train, subway train, or elevated train. This embodiment does not limit the type of train. Figure 1 As shown, the method includes:

[0090] Step 101: Obtain the target driving curve of the train. The target driving curve is used to indicate the expected driving parameters of the train at each driving moment.

[0091] Optionally, the target driving curve is generated by the control device or sent by other devices. This embodiment does not limit the method of obtaining the target driving curve.

[0092] In one example, the target driving curve is generated by the ATO system operating in the control unit. The generation method includes solving an optimization problem based on the timetable, addressing comprehensive indicators such as energy consumption, passenger comfort, and network efficiency, to generate the target driving curve. The objective function of the optimization problem is determined based on the optimization requirements. For example, if the optimization requirement is to reduce train operating energy consumption, the objective function is used to minimize energy consumption; or if the optimization requirement is to improve passenger comfort, the objective function is used to minimize passenger waiting time and / or minimize carriage crowding, etc. This embodiment does not limit the method of generating the target driving curve.

[0093] Optionally, the target driving curve can be a target speed curve, in which case the target driving curve indicates the desired speed of the train at each driving moment, and the desired driving parameters include the desired speed. Alternatively, the target driving curve can also be a target displacement curve, in which case the target driving curve indicates the desired displacement of the train at each driving moment, and the desired driving parameters include the desired displacement.

[0094] Step 102: For the current k-th driving moment and the subsequent F-1 driving moments during the train's operation, input the expected driving parameters corresponding to the (k+1)-th to (k+P)-th driving moments in the target driving curve and the actual train state at the k-th driving moment into the preset Model Predictive Control (MPC) model to obtain the train control quantities corresponding to the k-th to (k+F-1)-th driving moments respectively.

[0095] Among them, the train control quantity is used to control the actual train state; k is an integer starting from 1, F and P are integers greater than or equal to 1, and P is greater than or equal to F.

[0096] The actual train state includes the train's actual speed and / or actual displacement. Specifically, the types of parameters included in the actual train state are determined based on the types of state variables in the MPC model. For example, if the types of state variables in the MPC model are the train's actual speed and actual displacement, then the actual train state includes the train's actual speed and actual displacement. The actual train state is determined through actual data collected by sensors on board the train. For example, the actual speed and actual displacement of the train can be obtained by integrating the acceleration collected by the train's Inertial Measurement Unit (IMU); or, the actual speed can be obtained through the train's speed sensor, and the actual displacement can be obtained through the train's positioning system.

[0097] Within each control cycle, the MPC model optimizes the objective function based on the system model under the corresponding control window and prediction window of that control cycle to obtain an optimal control sequence, so as to adopt the first time value of the optimal control sequence (i.e. u(k) below) in the next control cycle to achieve rolling optimization.

[0098] In this embodiment, the control window has a duration of F driving moments, and the prediction window has a duration of P driving moments. Therefore, for the current control window, from the k-th driving moment to the (k+F-1)-th driving moment (i.e., the current k-th driving moment and the subsequent F-1 driving moments), the MPC model is used to predict the train control quantities corresponding to each driving moment in the current control window based on the actual train state corresponding to the k-th driving moment. Under the influence of [the system / mechanism], the predicted driving parameters for the next P driving moments.

[0099] Specifically, the displacement prediction formula for the next P times in the MPC model can be expressed by the following equation:

[0100] ;

[0101] Where Y(k) represents the predicted driving parameters from the (k+1)th driving time to the (k+P)th driving time (i.e., the future P driving times corresponding to the prediction window); that is, referring to the matrix of Y(k) below, Y(k) includes the predicted driving parameters y(k+1) of the (k+1)th driving time, the predicted driving parameters y(k+2) of the (k+2)th driving time, ..., and so on, until the predicted driving parameters y(k+P) of the (k+P)th driving time.

[0102] x(k) represents the actual train state at the k-th driving moment.

[0103] U(k) represents the train control quantities corresponding to the k-th driving time to the (k+F-1)-th driving time, respectively. That is, referring to the vector of U(k), U(k) includes the train control quantity u(k) at the k-th driving time, the train control quantity u(k+1) at the (k+1)-th driving time, the train control quantity u(k+2) at the (k+2)-th driving time, ..., and so on, until the train control quantity u(k+F-1) at the (k+F-1)-th driving time. In this embodiment, U(k) is the optimal control sequence to be determined by the MPC model.

[0104] ;

[0105] , ;

[0106] L represents the constant term of the disturbance factor simulated by the MPC model. Optionally, L can be 0, or it can be non-zero. For example, L is used to simulate air resistance during train operation, in which case L is not 0. S F represents the time step between two adjacent driving moments. r This represents the drag value of the disturbance factor simulated by the MPC model.

[0107] Optionally, when the desired driving parameter is the desired speed, Accordingly, the MPC model is used to predict the train's speed at the next P driving moments; the desired speed is then compared with the predicted speed to obtain the optimal control sequence. Alternatively, when the desired driving parameter is the desired displacement, Accordingly, the MPC model is used to predict the train's displacement at the next P driving moments; the expected displacement is then compared with the predicted displacement to obtain the optimal control sequence.

[0108] In one example, the constraints of the MPC model are expressed by the following formula:

[0109]

[0110]

[0111] in, H(k) represents the expected driving parameters from the (k+1)th driving time to the (k+P)th driving time. According to the matrix of H(k), H(k) includes the expected driving parameter h(k+1) at the (k+1)th driving time, the expected driving parameter h(k+2) at the (k+2)th driving time, ..., and so on, until the expected driving parameter h(k+P) at the (k+P)th driving time.

[0112] R and Q represent the preset weight matrices; U(k) 2i U(k) represents the train control quantity at even-numbered positions, which is the train braking gear; 2i-1 This represents the train control quantity at odd-numbered positions, where the train control quantity at odd-numbered positions is the train traction gear. In this embodiment, each group of train control quantities includes two control parameters: the train traction gear and the train braking gear. For example, u(k) includes two control parameters, u1(k) and u2(k), where u1(k) represents the train traction gear at the k-th driving moment, and u2(k) represents the train braking gear at the k-th driving moment.

[0113] Under the above constraints, the objective function The first term minimizes the expected and predicted driving parameters for each driving moment, while the second term prevents the train control quantity from exceeding a preset threshold, which is less than or equal to the maximum value of the train control quantity. U(k) 2i-1 ≥0 is used to limit the train traction gear. ;U(k) 2i ≤0 is used to limit the train's braking gear. Since the feedback coefficient for the train's braking gear is negative, it is represented in the constraint conditions using the less than or equal to sign. U(k) 2i ·U(k) 2i-1 =0 is used to restrict the train to be in either traction or braking mode at the same driving time.

[0114] The above MPC model is affected by the constraint "U(k)". 2i·U(k) 2i+1 The existence of "=0" indicates that the MPC model is a mixed-integer quadratic programming (MIQP) problem. After inputting the expected driving parameters corresponding to the (k+1)th to (k+P)th driving times in the target driving curve and the actual train state at the kth driving time into the MPC model, the control device can solve the problem based on the solver Gurobi to obtain the train control quantities U(k) corresponding to the kth to (k+F-1)th driving times.

[0115] In other embodiments, the control device may also use other solvers for solving MIQP problems, such as CPLEX, mathematical optimization software for solving constrained integer programming problems (SCIP), etc. This embodiment does not limit the way the output results of solving the MPC model are obtained.

[0116] Step 103: Input the train control quantity at the k-th driving moment and the observation value of the total disturbance of the preset extended state observer at the k-th driving moment into the preset dynamic compensation model to compensate the train control quantity and the observation value of the total disturbance at the k-th driving moment respectively, so as to obtain the compensated control quantity at the k-th driving moment.

[0117] In this context, the total disturbance represents all disturbance factors not simulated by the MPC model during train operation. For example, if L is 0 in the MPC model, then the total disturbance represents all disturbance factors during train operation, including external and internal disturbances. Alternatively, if L in the MPC model is used to simulate air resistance during train operation, then the total disturbance represents all disturbances other than that air resistance. In other words, in this embodiment, all disturbance factors not simulated by the MPC model are represented by observed values.

[0118] The initial observation value for the total disturbance is a preset value. In this embodiment, the preset value can be any value set by the developers. It should be noted that even if the initial observation value for the total disturbance is inaccurate, it can be adjusted to be accurate through subsequent dynamic feedback and compensation processes. Therefore, in this embodiment, the accuracy of the initial preset value for the total disturbance is not required.

[0119] In this embodiment, the dynamic compensation model is used to compensate for the error between the actual complex control system of the train and the simple simulation system corresponding to the MPC model. Therefore, the MPC model only needs to be designed for the simple model system (refer to Y(k) above), while the dynamic compensation model is responsible for mapping the output U(k) of the MPC model to the input of the actual complex control system of the train.

[0120] In this embodiment, the dynamic compensation model makes the observed total disturbance obtained by the extended state observer infinitely close to the actual total disturbance. The extended state observer is established based on the train's dynamic model and the total disturbance.

[0121] In this embodiment, the train's dynamic model is determined based on the resultant forces acting on the train during operation. Depending on the perspective of train dynamics modeling, train dynamic models can be divided into single-mass models and multi-mass models. Multi-mass models treat each carriage as a single mass, possessing its own independent dynamic model, while the carriages interact with each other. Multi-mass models can more accurately approximate the actual train model, but they involve more parameters and are more complex. In contrast, single-mass models treat the entire train as a single mass, resulting in a clearer and simpler model. Generally, single-mass models are sufficiently accurate for train tracking curve algorithms; therefore, this embodiment uses a single-mass model to establish the train's dynamic model as an example for explanation.

[0122] In one example, a schematic diagram of a single-mass model of a train is shown below. Figure 2 As shown, Figure 2 In the middle, F N F represents the total support capacity of the train. T F represents the traction force of the train. g F represents the component of gravity of the train. r F represents the air resistance of the train. B G represents the train's braking force (or, as mentioned below, the electric braking force), and G represents the train's total weight. According to Figure 2 As shown in the single-mass model, the train travels at a speed of v and a traction gear of... The traction force at high speed is shown in Equation 3-1, and the electric braking force is shown in Equation 3-2. Since the electric braking force is much greater than the mechanical braking force when the train is at a high speed, the mechanical braking force can be ignored.

[0123] ;

[0124] ;

[0125] Among them, F T (v, This indicates that at a speed of v and a traction gear of The traction force of the train at that time

[0126] F B (v, This indicates that at a speed of v and a traction gear of The train braking force at that time Indicates the train's traction gear. This indicates the train's maximum traction gear. Indicates the train's braking gear. N indicates the train's maximum braking gear. M This indicates the number of motor cars in the train, and N represents the total number of carriages in the train. This represents the traction force of each motor car when the train is using its maximum traction gear and traveling at a speed of v. This indicates the braking force of each car when the train is in its maximum traction gear and traveling at a speed of v.

[0127] The air resistance experienced by the train during operation is determined using the Davis formula, as shown in Equation 3-3 below.

[0128] ;

[0129] Among them, F r (v) represents the air resistance experienced at a speed of v, M represents the total mass of the train, and a1, a2 and a3 represent the preset air resistance coefficients of the train.

[0130] The formula for the gradient resistance experienced by the train during its journey is shown in Equation 3-4 below.

[0131] ;

[0132] Among them, F g (θ) represents the component of the train's gravity at an angle of θ.

[0133] Combining equations 3-1 to 3-4 above, we can see that the resultant force on the train is as shown in equation 3-5 below.

[0134]

[0135] Where, F(v, , θ) represents the train's traction gear at a speed of v. The train's braking gear is The resultant force on the train when the gradient is θ.

[0136] Based on Equation 3-5, the train's acceleration a(t) is obtained (refer to Equation 3-6), velocity v(t) is obtained (refer to Equation 3-7), and displacement s(t) is obtained (refer to Equation 3-8).

[0137] ;

[0138] ;

[0139] .

[0140] Traction force of a single-car train as a function of speed like Figure 3 As shown, according to Figure 3 It can be seen that the change in traction force is mainly divided into two stages. When the train speed is low, the train traction mode is constant torque mode, at which time the maximum traction force of the train is constant. When the train speed is high, the train traction mode switches to constant power mode, at which time the maximum traction power of the train remains unchanged.

[0141] Therefore, the simplified train's traction force F T Formula (t) is a piecewise function, as shown in Equation 3-9 below.

[0142] ;

[0143] in, This indicates the train's maximum traction power. Let v(t) represent the maximum traction force of the train, and v(t) represent the speed of the train.

[0144] The curves showing the change in electric braking force versus speed for a single carriage are as follows: Figure 4 As shown, according to Figure 4 It is known that the maximum electric braking force of the train remains almost constant, only gradually decreasing to 0 at higher speeds. However, in reality, the train rarely operates within this speed range during normal operation. Therefore, we assume the maximum electric braking force is a constant value. Based on this, the simplified braking force F... B The formula (t) is shown in Equation 3-10 below.

[0145] .

[0146] in, This indicates the train's maximum braking force.

[0147] Since the gravitational components caused by air resistance and gradient are generally small, the gravitational components caused by air resistance and gradient during the journey are ignored. The simplified resultant force F(t) and acceleration a(t) of the train are shown in Equations 3-11 and 3-12 below.

[0148] ;

[0149] .

[0150] In this embodiment, the low-speed phase is referred to as the constant torque phase, and the high-speed phase is referred to as the constant power phase. Since curve tracking typically involves tracking either the speed curve or the displacement curve, the train's speed and displacement can be used as state variables to construct a state-space model. Based on this, by selecting state variables... Input vector We can obtain two state-space models for the two stages. The dynamic models of the train corresponding to the two stages are shown in Equations 3-13 and 3-14, respectively. Equation 3-13 is the dynamic model corresponding to the constant torque stage, and Equation 3-14 is the dynamic model corresponding to the constant power stage.

[0151] ;

[0152] ;

[0153] Where x1 represents the train's displacement, x2 represents the train's speed v, and u1 represents the train's traction gear. u2 indicates the train's braking gear. y = [y1, y2] represents the output vector of the state-space model.

[0154] As can be seen from the above dynamic model, on the one hand, the model ignores air resistance, gravity components, and changes in braking force at higher speeds, all of which affect the dynamic characteristics of the system. On the other hand, the train control system contains various disturbances and uncertainties, such as the large error of the Davis approximation at lower speeds and the additional resistance generated when the train passes through tunnels. Therefore, this application proposes an extended state observer to handle the uncertainties present in the system.

[0155] Generally, extended state observers are nonlinear. In this case, parameter tuning and analysis of the extended state observer are relatively complicated. Therefore, optionally, in this embodiment, the extended state observer is a linear extended state observer. In other embodiments, a traditional nonlinear extended state observer can also be constructed to observe the total disturbance. In this case, referring to the existing construction methods of nonlinear extended state observers, this embodiment will not elaborate further.

[0156] Since the train's dynamics model includes a constant torque stage model corresponding to the first speed range (i.e., the dynamics model corresponding to the constant torque stage shown in Equation 3-13) and a constant power stage model corresponding to the second speed range (i.e., the dynamics model corresponding to the constant power stage shown in Equation 3-14), the first speed range is smaller than the second speed range. The extended state observer is established based on the train's dynamics model; therefore, the extended state observer includes a first observer based on the constant torque stage model and a second observer based on the constant power stage model. The extended state observers for each stage are described below. The first and second speed ranges are determined based on the actual traction force of a single motorized vehicle as a function of speed, for example: according to... Figure 3The curve shown has a first speed range of [0, 32 km / h] and a second speed range of speeds greater than 32 km / h. In other embodiments, the first and second speed ranges may be implemented in other ways depending on the actual operation of the train. This embodiment does not limit the values ​​of the first and second speed ranges.

[0157] First, for the constant torque stage, a total disturbance W is introduced into the system's state-space model (i.e., the constant torque stage model). This term includes disturbance factors not considered in the MPC model, such as air resistance, gravity components, acceleration changes caused by parameter variations, external disturbances, and noise. In other words, the existence of W leads to a difference between the constant torque stage model and the actual state-space model of the train. Therefore, the actual state-space model is shown in Equation 3-15 below.

[0158] .

[0159] Based on the implementation principle of the extended state observer, W is regarded as a state component x3, resulting in Equation 3-16.

[0160] .

[0161] The linear state observer corresponding to the constant torque stage is determined based on the state-space model after the expansion of the dimension, as shown in Equation 3-17 below.

[0162] ;

[0163] in, Indicates the gain of the first observer. The observed values ​​represent the displacement. The observed value represents the total disturbance. The observed value represents the velocity.

[0164] At this point, let the input vector after the dimension expansion be... u1 indicates the train traction gear. u2 represents the train braking gear, and the matrix expression of the state-space model in Equation 3-17 can be converted into Equation 3-18 below.

[0165] ;

[0166] in, This represents the observed values ​​of state variables, specifically including observed values ​​of displacement. Observations of velocity Observations of total disturbance .

[0167] After discretizing Equation 3-18 above, and taking the output of the linear observer as equivalent to the state variable at the current moment, the linear state observer (i.e., the first observer) corresponding to the constant torque stage yields Equation 3-19:

[0168] ;

[0169] in, Indicates the gain of the first observer. The value is a preset value; I represents the identity matrix, T S The input vector represents the time step between two adjacent driving moments. u1 and u2 represent the control quantities actually acting on the train control system at the k-th driving moment (i.e., the compensated control quantities in the following text), and y1 represents the actual displacement at the (k+1)-th driving moment. This is a three-dimensional vector. The first two dimensions represent the observed values ​​of train displacement and velocity, respectively, and the third component is the observed value of the total disturbance at the k-th driving moment. The third component represents the observed value of the total disturbance at the (k+1)th driving moment.

[0170] The discretization methods for Equation 3-18 include, but are not limited to, forward Euler method, bilinear transformation (Bilinear or Tustin's Method), Runge-Kutta method, etc. This embodiment uses forward Euler method as an example for discretization. In other embodiments, other discretization methods can also be used. This embodiment does not limit the discretization method.

[0171] The characteristic equation of the first-state observer in Equation 3-19 above is shown in Equation 3-20 below:

[0172] ;

[0173] in, This represents the pole of the first observer. According to Equation 3-20, the gain of the first observer is selected... Placing the poles within the unit circle ensures the stability of the first-state observer. Therefore, in this embodiment, the gain of the first observer is such that its poles are placed within the unit circle.

[0174] Second, for the constant power stage, according to the dynamic model corresponding to the constant power stage shown in Equation 3-14 (i.e., the constant power model), it can be seen that the constant power model has... This term causes the constant power model to be nonlinear. Based on this, in one example, to implement the design of a linearly extended state observer (i.e., a second observer), the small-bias linearization result of the nonlinear term in the constant power model is determined.

[0175] Optionally, the method for determining the small-deviation linearization result of the nonlinear term includes: performing a Taylor expansion on the nonlinear term, retaining the linear first-order term obtained after the Taylor expansion, and obtaining the linear extended state observer corresponding to the constant power stage. Since the linear extended state observer can observe not only external disturbances (external disturbances, such as noise, disturbance torque, etc.) but also internal disturbances (model mismatch, parameter mismatch), based on this, in order to transform the original nonlinear state-space expression into a linear state-space expression, in this embodiment, the other terms after the Taylor expansion can be regarded as disturbances.

[0176] Schematic, the Taylor expansion of the nonlinear term can be expressed by the following equation 3-21:

[0177] ;

[0178] in, This represents the actual speed of the train at the current operating point (i.e., the k-th driving moment), and this actual speed is a constant, i.e., It will not cause nonlinearity in the term in question. x1 represents the actual traction gear at the current working point, x2 represents the actual speed within the neighborhood of the current working point, and u1 represents the actual traction gear within the neighborhood of the current working point. The neighborhood of the current working point refers to a time region surrounding that point, which is small enough that within this time region, the properties of the working point can be considered the same as or similar to those within the time region.

[0179] Accordingly, the linear terms obtained after Taylor expansion are retained, including: retaining the linearized linear terms. .

[0180] Based on the above linearization process, the linear extended state observer corresponding to the constant power stage is obtained, as shown in Equation 3-22 below. According to Equation 3-22, compared with the linear extended state observer Equation 3-15 corresponding to the constant torque stage, there is only a difference in parameters.

[0181] .

[0182] Based on the derivation of the linear extended state observer corresponding to the constant torque stage, the linear state observer (i.e., the second observer) corresponding to the constant power stage can be obtained similarly as shown in Equation 3-23:

[0183] ;

[0184] in, This represents the gain of the second observer. The value is a preset value; I represents the identity matrix, T S The input vector represents the time step between two adjacent driving moments. u1 and u2 represent the compensated control values ​​at the k-th driving moment, and y1 represents the actual displacement at the (k+1)-th driving moment. This is a three-dimensional vector. The first two dimensions represent the observed values ​​of train displacement and velocity, respectively, and the third component is the observed value of the total disturbance at the k-th driving moment. The third component is the observed value of the total disturbance at the (k+1)th driving moment. This represents the actual speed of the train at the k-th driving moment. That is, if the stage corresponding to the actual speed at the current driving moment is the constant power stage, then the parameters input to the second observer also include the actual speed of the train at the k-th driving moment.

[0185] In this embodiment, the gain of the first observer and the gain of the second observer are the same or different. The gain is such that the poles of the corresponding extended state observer are configured within the unit circle.

[0186] Based on the linearly extended state observer, the observed value of the total disturbance can be obtained. In this embodiment, a dynamic compensation model is introduced to compensate for the disturbance value at the input. As mentioned above, the dynamic compensation model is used to make the observed value of the total disturbance infinitely close to the actual total disturbance. That is, the compensation objective of the dynamic compensation model is the target state-space model expressed by the following formula, which, after discretization, yields the expression of the MPC model. In other words, the compensation objective of the dynamic compensation model is the continuous state-space model corresponding to the expression of the MPC model.

[0187] ;

[0188] Where x1 represents the actual displacement at the (k+1)th driving moment, x2 represents the actual speed at the (k+1)th driving moment, u1 represents the traction gear at the kth driving moment, and u2 represents the braking gear at the kth driving moment.

[0189] In this embodiment, the observed values ​​of the state variables For the internal parameters of the extended state observer, that is, the observed values ​​of the state variables. It changes according to the changes in the external input of the extended state observer.

[0190] Based on the above target state-space model, a dynamic compensation model is constructed, including a first compensation model corresponding to the constant torque stage and a second compensation model corresponding to the constant power stage:

[0191] The first compensation model is expressed by the following equation 3-24:

[0192] ;

[0193] The second compensation model is expressed by the following equation 3-25:

[0194] ;

[0195] Where u1 and u2 represent the control quantities at the k-th driving moment (i.e., the output of the MPC model), specifically, u1 represents the traction gear at the k-th driving moment; u2 represents the braking gear at the k-th driving moment. and This represents the compensated control quantity at the k-th driving moment, specifically, This indicates the traction gear after compensation at the k-th driving moment; This indicates the post-compensation braking gear at the k-th driving moment; Let M represent the observed value of the total disturbance at the k-th driving moment, and M represent the total mass of the train. This indicates the train's maximum traction gear. This indicates the train's maximum braking gear, and N represents the total number of train cars. M Indicates the number of carriages in the train. This indicates the maximum traction force of the train. This indicates the maximum braking force of the train. This indicates the maximum traction power of the train. This represents the maximum value of the train's braking power, and v represents the actual speed of the train at the k-th driving moment.

[0196] In other words, (include and The control quantity (i.e., the compensated control quantity) refers to the actual control quantity acting on the train dynamics system after dynamic compensation, where u is the output of the MPC model. The control quantity u, which is the output of the model predicts the control output, is then dynamically compensated to obtain the input to the actual train dynamics system. ,here, These are the compensated traction gear and compensated braking gear of the train, i.e. , The value can be any value between the minimum and maximum gears. For example, the minimum gear is 0 and the maximum gear is 100. This embodiment does not limit the values ​​of the minimum and maximum gears.

[0197] Based on the above dynamic compensation model, for the constant torque stage and the constant power stage, the compensated control quantity will be... Applying this to the train's control system, we can obtain the following equations 3-26 and 3-27:

[0198] ;

[0199] ;

[0200] According to equations 3-26 and 3-27, under the condition that the extended state observer's observation is accurate (i.e.) The state equation of a control system with dynamic compensation can be simplified to the form of the target state-space model mentioned above, that is, to achieve the above dynamic compensation target.

[0201] After obtaining the above dynamic compensation model, the train control quantity at the k-th driving moment and the observed value of the total disturbance at the k-th driving moment are input into the preset dynamic compensation model to compensate for the observed value of the train control quantity and the total disturbance at the k-th driving moment, respectively, and obtain the compensated control quantity at the k-th driving moment.

[0202] Since the dynamic compensation model includes a first compensation model and a second compensation model, the train control quantity at the k-th driving moment and the observed value of the total disturbance at the k-th driving moment from the preset extended state observer are input into the preset dynamic compensation model. This includes: if the actual speed at the k-th driving moment is within a first speed range, the train control quantity at the k-th driving moment and the observed value of the total disturbance at the k-th driving moment are input into the first compensation model; if the actual speed at the k-th driving moment is within a second speed range, the train control quantity at the k-th driving moment and the observed value of the total disturbance at the k-th driving moment are input into the second compensation model.

[0203] Schematic, the actual train state at the k-th driving moment includes the actual speed at the k-th driving moment. At this time, after obtaining the actual train state at the k-th driving moment in step 102, the actual speed at the k-th driving moment is obtained.

[0204] The first speed range and the second speed range are preset in the control device. For specific settings, please refer to the description above. This embodiment will not repeat them here.

[0205] The train control quantity at the k-th driving time is obtained from the output U(k) of the MPC model. That is, U(k) includes the train control quantities corresponding to the k-th to k+F-1-th driving times respectively. The train control quantity corresponding to the k-th driving time is extracted as u1 and u2 of the first compensation model shown in Equation 3-24 or the second compensation model shown in Equation 3-25. The observed value of the total disturbance at the k-th driving time is used as the first compensation model shown in Equation 3-24 or the second compensation model shown in Equation 3-25. We obtain the compensated control quantity at the k-th driving moment.

[0206] In addition, according to Equation 3-25, if the actual speed at the k-th driving moment falls within the second speed range, the actual speed at the k-th driving moment needs to be input into the second compensation model to obtain the compensated control quantity at the k-th driving moment.

[0207] Since the train control quantity U(k) is obtained without considering the total disturbance, its accuracy is not high. In this embodiment, the train control quantity U(k) is compensated by a dynamic compensation model with reference to the observed value of the total disturbance, resulting in a compensated control quantity, which can improve the accuracy of the final control quantity acting on the train.

[0208] In addition, in this embodiment, by inputting the observed value of the total disturbance at the k-th driving moment into the dynamic compensation model for compensation, the dynamic changes of the total disturbance are taken into account, which can ensure that the observed value of the total disturbance is corrected in real time, thereby ensuring the accuracy of the observed value of the total disturbance.

[0209] Step 104: Control train operation based on the compensated control quantity.

[0210] In this embodiment, the compensated control quantity at the k-th driving moment, after being applied to the train's control system, will change the actual state of the train after the k-th driving moment. In other words, the effect of the compensated control quantity at the k-th driving moment will be manifested in the train after the k-th driving moment.

[0211] The compensated control quantity at the k-th driving moment includes the compensated traction gear and the compensated braking gear. At the k-th driving moment, the train is in either the traction gear or the braking gear. Accordingly, controlling the train operation based on the compensated control quantity includes controlling the train to run in the compensated traction gear or in the compensated braking gear.

[0212] Step 105: If the running time reaches the (k+1)th driving moment, obtain the actual displacement at the (k+1)th driving moment.

[0213] In this embodiment, the (k+1)th driving moment refers to the next control moment of the train, and the distance between the (k+1)th driving moment and the kth driving moment is T. S The length of time.

[0214] The method for obtaining the actual displacement at the (k+1)th driving moment is described in the relevant description of obtaining the actual train state above, and will not be repeated here in this embodiment.

[0215] Step 106: Input the actual displacement at the (k+1)th driving moment and the compensated control quantity at the kth driving moment into the extended state observer to update the observed value of the total disturbance at the (k+1)th driving moment. In the next determination of the train control quantity, the compensated control quantity at the (k+1)th driving moment is determined based on the observed value of the total disturbance at the (k+1)th driving moment to control the train.

[0216] As described above, the extended state observer includes a first observer corresponding to the constant torque stage and a second observer corresponding to the constant power stage. Accordingly, the actual displacement at the (k+1)th driving moment and the compensated control quantity at the kth driving moment are input into the extended state observer, including:

[0217] If the actual speed at the (k+1)th driving moment is within the first speed range, the actual displacement at the (k+1)th driving moment and the compensated control quantity at the kth driving moment are input into the first observer (as shown in Equation 3-19 above).

[0218] If the actual speed at the (k+1)th driving moment falls within the second speed range, the actual displacement at the (k+1)th driving moment and the compensated control quantity at the kth driving moment are input into the second observer (as shown in Equation 3-23 above).

[0219] The method for obtaining the actual speed at the (k+1)th driving moment is described in the relevant description of obtaining the actual train status above, and will not be repeated here in this embodiment.

[0220] After the first or second observer obtains the compensated control value at the (k+1)th driving moment, the control window slides backward by one step, that is, the (k+1)th driving moment is set to the kth driving moment, and steps 102 to 106 are executed again to track the target driving curve until the (k+1)th driving moment indicates the last driving moment of the target driving curve, at which point the current curve tracking is completed, or when a stop tracking command is received, the current curve tracking is completed.

[0221] It should be noted that in this embodiment, the train's dynamic model is a simplified model. In other embodiments, the dynamic model may not be simplified, or it may be simplified in other ways, such as not ignoring air resistance. However, since the extended state observer can observe the total disturbance including model error, it can handle certain model uncertainties. Therefore, the construction method of the extended state observer and dynamic compensation link proposed in this embodiment is still applicable to the new scenario. The specific establishment process is the same as the above embodiment, and will not be repeated here.

[0222] In summary, the model predictive control-based dynamic tracking method for train driving curves provided in this embodiment obtains the target driving curve of the train. For the current k-th driving moment and subsequent F-1 driving moments during the train's operation, the desired driving parameters corresponding to driving moments k+1 to k+P of the target driving curve, and the actual train state at the k-th driving moment, are input into a preset model predictive control (MPC) model to obtain the train control quantities corresponding to driving moments k to k+F-1. The train control quantity at the k-th driving moment, along with the observed total disturbance value from a preset extended state observer at the k-th driving moment, are input into a preset dynamic compensation model to compensate for the observed train control quantity and total disturbance value at the k-th driving moment, respectively, resulting in the compensated control quantity at the k-th driving moment. The method involves controlling train operation based on the compensated control quantity. When the running time reaches the (k+1)th driving moment, the actual displacement at the (k+1)th driving moment is obtained. The actual displacement at the (k+1)th driving moment, the compensated control quantity at the (k)th driving moment, and the observed total disturbance at the (k)th driving moment are input into the extended state observer. This updates the observed total disturbance at the (k+1)th driving moment, allowing the compensated control quantity at the (k+1)th driving moment to be determined based on the observed total disturbance in the next train control determination, thus controlling the train. This method solves the problem of poor tracking accuracy caused by traditional driving curve tracking methods that do not consider all disturbance factors during train operation. Since the extended state observer can observe the total disturbance, it can improve the tracking accuracy of the driving curve.

[0223] In addition, the curve tracking method in this embodiment does not require the use of a fuzzy controller and does not rely on prior knowledge, which can improve the generalization ability of the method.

[0224] In addition, the computational complexity of the dynamic compensation model, extended state observer, and MPC model in this embodiment is less than that of the traditional reinforcement learning combined with expert control, which can reduce the difficulty of online operation of the train control system.

[0225] In addition, in this embodiment, the curve tracking method is based on the dynamic model of the train. Therefore, it takes into account the stepped adjustment of the train gears and does not require the introduction of an uncertain boundary function, which can ensure the accuracy of curve tracking.

[0226] Furthermore, since the train control quantity is obtained without considering the total disturbance, its accuracy is not high. This embodiment, however, compensates for the train control quantity by referencing the observed values ​​of the total disturbance using a dynamic compensation model, resulting in a compensated control quantity that improves the accuracy of the final control quantity applied to the train.

[0227] In addition, by inputting the observed total disturbance at the k-th driving moment into the dynamic compensation model for compensation, the dynamic changes of the total disturbance are taken into account, which can ensure that the observed total disturbance can be corrected in real time, thereby ensuring the accuracy of the observed total disturbance.

[0228] In addition, the extended state observer in this embodiment is a linear extended state observer, which can further reduce the model parameters and improve computational efficiency.

[0229] To better understand the model predictive control-based dynamic tracking method for train driving curves provided in this application, an example is given below for illustration. Figure 5 The diagram shown illustrates the dynamic tracking process of the train driving curve. This embodiment uses the target driving curve as the target speed curve as an example for explanation. Figure 5 It can be seen that the method includes the following steps:

[0230] Step 51: For driving time 1 (the kth driving time) to driving time F (the (k+F-1)th driving time) corresponding to the current control window, calculate the expected speed v from driving time 2 to driving time F in the speed tracking curve. ref The actual displacement s and actual velocity v at time 1 are input into the MPC model to obtain the control quantity σ output by the MPC. T and σ B ;

[0231] Step 52: Based on the stage corresponding to driving time 1 (constant power stage or constant torque stage), adjust the control quantity σ for driving time 1. T and σ B Input the dynamic compensation model corresponding to this stage (i.e., the first compensation model or the second compensation model) to obtain the compensated control quantity at driving time 1;

[0232] Step 53: Apply the compensated control quantity to the actual train control system through "rounding and limiting" to obtain the actual speed v and actual displacement s at driving time 2.

[0233] Rounding and limiting are used to convert the compensated control quantity into a value that the control system can process. Optionally, the rounding and limiting methods include, but are not limited to, the following processes: rounding and / or limiting. Rounding refers to the process of approximating a value to the nearest integer or a specific value; limiting refers to the process of restricting the value of a signal to a specific range.

[0234] Step 54: Input the actual displacement s of driving time 2, the compensated control quantity of driving time 1 after rounding and limiting, and the observed value of the total disturbance of driving time 1 into the extended state observer (i.e., the first observer or the second observer) of the actual speed indication of driving time 2 to obtain the observed value of the total disturbance corresponding to driving time 2. Let the control window slide backward by one step, update the driving time corresponding to the control window, and obtain the updated control window corresponding to driving time 1 to driving time F (actually driving time 2 to driving time F-1). Repeat steps 51-54 until the target driving curve tracking is completed.

[0235] To more clearly illustrate Figure 5 The tracking effect of the curve tracking method shown below is compared with the reference. Figure 6 The scheme shown is compared to one that does not use an extended state observer. According to... Figure 6 It can be seen that without using an extended state observer, the control device only uses a nonlinear dynamic compensation model to compensate for the control quantity, without considering the observation results of the total disturbance. The parameter values ​​in the formulas above are shown in Table 1 below as an example.

[0236] Table 1:

[0237]

[0238] Assume the target driving curve is the target speed curve H, and that target speed curve H is a start-cruise-deceleration curve. The desired speed starts from 0, accelerates uniformly to a maximum speed of 15 m / s over 30 seconds, then maintains cruise control for 30 seconds, followed by uniform deceleration to 0 m / s over 30 seconds, and then remains stationary. In one example, the target speed curve is as follows: Figure 7 As shown, when controlling the train based on the parameters shown in Representation 1, without introducing additional parameter uncertainties, the curve tracking method proposed in this application and the comparison method (i.e. Figure 6 The tracking results of the curve tracking method shown are as follows: Figure 8 As shown, its local magnified result is for reference. Figure 9 . Figure 8 and Figure 9 In the diagram, the red line represents the target velocity curve, the green line represents the tracking result of the curve tracking method provided in this application, and the blue line represents the tracking result of the curve tracking method without introducing an extended state observer. According to... Figure 8 and Figure 9 It is evident that the tracking method provided in this application performs better than the comparison method without using the extended state observer, especially at higher speeds. Since the extended state observer can observe and compensate for the error caused by model mismatch as a disturbance, the optimization effect is more significant.

[0239] The integral absolute error (IAE) of the two tracking methods was calculated. The IAE of the curve tracking method in this application was 0.9839, while the IAE of the comparison method was 2.0455. The integral absolute error of this application is smaller than that of the comparison method, indicating higher accuracy.

[0240] Furthermore, to verify the robustness of the tracking method provided in this application, a random disturbance of ±0.1 m / s² was introduced into the acceleration of the simulation model, and a train mass error of ±5% was introduced into both methods to simulate the effects of parameter uncertainty, disturbance, and unmodeled characteristics. The seed of the random number module used in both methods was set to 0 to ensure that the additional uncertainties introduced by the two methods were consistent. After introducing uncertainty, the tracking results provided in this application and the tracking results of the comparison method are as follows: Figure 10 As shown, Figure 10 The local magnification result is as follows Figure 11 As shown. Figure 10 and Figure 11 In the diagram, the red line represents the target velocity curve, the green line represents the tracking result of the curve tracking method provided in this application, and the blue line represents the tracking result of the curve tracking method without introducing an extended state observer. According to... Figure 10 and Figure 11 As can be seen, the tracking method provided in this application can eliminate tracking errors in a timely manner because the extended state observer observes and compensates for the total disturbance. In contrast, the tracking performance of the comparison method is significantly reduced when there is uncertainty, and it cannot eliminate errors in a timely manner.

[0241] Furthermore, in this case, the IAE of the tracking method provided in this application is 1.4521, while the IAE of the comparison method is 4.1792. It can be seen that introducing the extended state observer in this application can effectively improve the robustness of the system. At this time, the observed result of the total disturbance output by the extended state observer is as follows... Figure 12 As shown.

[0242] In another example, the target velocity curve is a sine wave with an amplitude of 16 m / s. Since the train speed cannot be lower than 0, only half a cycle of the image is taken. The target velocity curve is as follows: Figure 13 As shown.

[0243] A random disturbance of ±0.1 m / s² is introduced into the acceleration of the simulation model, and an error of ±5% is introduced into the train mass of both methods to simulate the effect of uncertainty. At this point, the tracking results of the tracking method provided in this application and the tracking results of the comparison method are as follows: Figure 14 As shown. Figure 14In the diagram, the red line represents the target velocity curve, the green line represents the tracking result of the curve tracking method provided in this application, and the blue line represents the tracking result of the curve tracking method without introducing an extended state observer. At this point, the IAE of the tracking method provided in this application is 1.0921, while the IAE of the comparative method is 1.9340. This shows that when tracking a sinusoidal velocity curve, the tracking method provided in this application has a significant improvement in tracking performance compared to the general method.

[0244] In summary, the tracking method provided in this application has at least the following advantages compared with traditional tracking methods:

[0245] (1) Does not depend on precise model parameters:

[0246] Since this application can observe the total disturbance of the system, the part of the nominal model that differs from the actual model during the model construction process can also be regarded as a disturbance. For example, even if the parameters we use in the observer do not match the actual parameters, the extended state observer can still observe the disturbance caused by this parameter mismatch. Subsequently, the dynamic characteristics of the system can be tuned to the characteristics of the nominal model using dynamic feedback.

[0247] (2) Strong robustness:

[0248] One major problem with MPC is the need for an accurate model of the controlled object. However, the extended state observer greatly reduces the difference between the controlled object and the nominal object used in MPC by observing and compensating for disturbances in the system in real time, thus improving robustness.

[0249] (3) Good control performance:

[0250] Robust MPC can also address uncertainty issues, but its design requires knowledge of the upper and lower bounds of uncertainty, which is often difficult to obtain in real-world scenarios. Furthermore, if the uncertainty boundaries are not sufficiently tight, robust MPC's performance will degrade because it optimizes based on the "worst-case" scenario. The proposed method, combining an extended state observer and MPC, does not require obtaining these upper and lower bounds, thus maintaining control performance.

[0251] (4) The design process is simple

[0252] The extended state observer and MPC provided in this application are actually designed separately. The design of the extended state observer only involves the selection of the observer gain, which can be determined by stability and pole placement. The MPC, on the other hand, is designed for the simplified model. The overall system structure is clear and concise, with low design difficulty and high computational efficiency.

[0253] Figure 15 A block diagram of a train driving curve dynamic tracking device based on model predictive control according to an embodiment of the present disclosure is shown, as follows: Figure 15 As shown, the device includes: a curve acquisition module 1510, a control quantity prediction module 1520, a control quantity compensation module 1530, a train control module 1540, a displacement acquisition module 1550, and a total disturbance observation module 1560.

[0254] The curve acquisition module 1510 is used to acquire the target driving curve of the train, which is used to indicate the expected driving parameters of the train at each driving moment.

[0255] The control quantity prediction module 1520 is used to, for the current k-th driving moment and the subsequent F-1 driving moments during the train's operation, input the expected driving parameters corresponding to the (k+1)-th to (k+P)-th driving moments in the target driving curve and the actual train state at the k-th driving moment into a preset model predictive control (MPC) model to obtain the train control quantities corresponding to the k-th to (k+F-1)-th driving moments respectively; wherein, the train control quantities are used to control the actual train state; k is an integer starting from 1, F and P are integers greater than or equal to 1, and P is greater than or equal to F;

[0256] The control quantity compensation module 1530 is used to input the train control quantity at the k-th driving moment and the observed value of the total disturbance of the preset extended state observer at the k-th driving moment into the preset dynamic compensation model, so as to compensate the train control quantity and the observed value of the total disturbance at the k-th driving moment respectively, to obtain the compensated control quantity at the k-th driving moment; the total disturbance is used to represent all disturbance factors that the MPC model did not simulate during the train driving process, and the observed value of the total disturbance is initialized to a preset value;

[0257] Train control module 1540 is used to control the train operation based on the compensated control quantity;

[0258] The displacement acquisition module 1550 is used to acquire the actual displacement at the (k+1)th driving moment when the running time reaches the (k+1)th driving moment.

[0259] The total disturbance observation module 1560 is used to input the actual displacement at the (k+1)th driving moment and the compensated control quantity at the kth driving moment into a preset extended state observer, and update the observed value of the total disturbance at the (k+1)th driving moment of the extended state observer. In the next determination of the train control quantity, the compensated control quantity at the (k+1)th driving moment is determined based on the observed value of the total disturbance at the (k+1)th driving moment to control the train. The extended state observer is established based on the dynamic model of the train and the total disturbance.

[0260] For details, please refer to the above method implementation examples.

[0261] In some embodiments, the functions or modules of the apparatus provided in this disclosure can be used to perform the methods described in the above method embodiments. The specific implementation can be referred to the description of the above method embodiments, and for the sake of brevity, it will not be repeated here.

[0262] This disclosure also proposes a computer-readable storage medium storing computer program instructions that, when executed by a processor, implement the above-described method. The computer-readable storage medium can be volatile or non-volatile.

[0263] This disclosure also proposes an electronic device, including: a processor; and a memory for storing processor-executable instructions; wherein the processor is configured to implement the above method when executing the instructions stored in the memory.

[0264] This disclosure also provides a computer program product, including computer-readable code, or a non-volatile computer-readable storage medium carrying computer-readable code, wherein when the computer-readable code is run in a processor of an electronic device, the processor in the electronic device performs the above-described method.

[0265] Figure 16 This is a block diagram illustrating a model predictive control-based train driving curve dynamic tracking device 1900 according to an exemplary embodiment. For example, the device 1900 can be provided as a server or terminal device. (Refer to...) Figure 16 The apparatus 1900 includes a processing component 1922, which further includes one or more processors, and memory resources represented by memory 1932 for storing instructions, such as application programs, that can be executed by the processing component 1922. The application programs stored in memory 1932 may include one or more modules, each corresponding to a set of instructions. Furthermore, the processing component 1922 is configured to execute instructions to perform the methods described above.

[0266] Device 1900 may also include a power supply component 1926 configured to perform power management of device 1900, a wired or wireless network interface 1950 configured to connect device 1900 to a network, and an input / output interface 1958 (I / O interface). Device 1900 can operate on an operating system, such as Windows Server, stored in memory 1932. TM macOS X TM Unix TM Linux TM FreeBSD TM Or similar.

[0267] In an exemplary embodiment, a non-volatile computer-readable storage medium is also provided, such as a memory 1932 including computer program instructions that can be executed by a processing component 1922 of the device 1900 to perform the above-described method.

[0268] The various embodiments of this disclosure have been described above. These descriptions are exemplary and not exhaustive, nor are they limited to the disclosed embodiments. Many modifications and variations will be apparent to those skilled in the art without departing from the scope and spirit of the described embodiments. The terminology used herein is chosen to best explain the principles, practical application, or technical improvements to the embodiments in the market, or to enable others skilled in the art to understand the embodiments disclosed herein.

Claims

1. A model predictive control-based train driving curve dynamic tracking method, characterized in that, The method includes: Obtain the target driving curve of the train, which is used to indicate the desired driving parameters of the train at each driving moment; For the current k-th driving moment and the subsequent F-1 driving moments during the train's operation, the expected driving parameters corresponding to the (k+1)-th to (k+P)-th driving moments in the target driving curve, and the actual train state at the k-th driving moment, are input into a preset Model Predictive Control (MPC) model to obtain the train control quantities corresponding to the k-th to (k+F-1)-th driving moments respectively; wherein, the train control quantities are used to control the actual train state; k is an integer starting from 1, F and P are integers greater than or equal to 1, and P is greater than or equal to F; The train control quantity at the k-th driving moment and the observed value of the total disturbance of the preset extended state observer at the k-th driving moment are input into the preset dynamic compensation model to compensate the train control quantity and the observed value of the total disturbance at the k-th driving moment, respectively, to obtain the compensated control quantity at the k-th driving moment; the total disturbance is used to represent all disturbance factors that the MPC model did not simulate during the train's operation, and the observed value of the total disturbance is initialized to a preset value; The train operation is controlled based on the compensated control quantity; If the runtime reaches the (k+1)th driving moment, obtain the actual displacement at the (k+1)th driving moment; The actual displacement at the (k+1)th driving moment and the compensated control quantity at the kth driving moment are input into the extended state observer to update the observed value of the total disturbance at the (k+1)th driving moment. This updated state observer is then used to determine the compensated control quantity at the (k+1)th driving moment based on the observed value of the total disturbance at the (k+1)th driving moment when determining the train control quantity in the next test. The extended state observer is established based on the dynamic model of the train and the total disturbance.

2. The method of claim 1, wherein, The train's dynamic model includes a constant torque stage model corresponding to a first speed range and a constant power stage model corresponding to a second speed range, where the first speed range is smaller than the second speed range; correspondingly, The extended state observer includes a first observer based on the constant torque stage model and a second observer based on the constant power stage model. The dynamic compensation model includes a first compensation model for compensating for the total disturbance of the first observer's output and a second compensation model for compensating for the total disturbance of the second observer's output.

3. The method of claim 2, wherein, The step of inputting the train control quantity at the k-th driving moment and the observed value of the total disturbance of the preset extended state observer at the k-th driving moment into the preset dynamic compensation model includes: If the actual speed at the k-th driving moment is within the first speed range, the train control quantity at the k-th driving moment and the observed value of the total disturbance at the k-th driving moment are input into the first compensation model. If the actual speed at the k-th driving moment falls within the second speed range, the train control quantity at the k-th driving moment and the observed value of the total disturbance at the k-th driving moment are input into the second compensation model.

4. The method of claim 2, wherein, The step of inputting the actual displacement at the (k+1)th driving moment and the compensated control quantity at the kth driving moment into the extended state observer includes: If the actual speed at the (k+1)th driving moment is within the first speed range, the actual displacement at the (k+1)th driving moment and the compensated control quantity at the kth driving moment are input into the first observer. If the actual speed at the (k+1)th driving moment falls within the second speed range, the actual displacement at the (k+1)th driving moment and the compensated control quantity at the kth driving moment are input into the second observer.

5. The method of claim 2, wherein, The extended state observer is a linear state observer determined based on the state-space model of the dynamic model; The first observer is represented by the following formula: ； The second observer is represented by the following formula: ； in, This represents the gain of the extended state observer. The value is a preset value; I represents the identity matrix, T S The input vector represents the time step between two adjacent driving moments. u1 and u2 represent the compensated control values ​​at the k-th driving moment, and y1 represents the actual displacement at the (k+1)-th driving moment. This is a three-dimensional vector. The first two dimensions represent the observed values ​​of train displacement and velocity, respectively, and the third component is the observed value of the total disturbance at the k-th driving moment. The third component represents the observed value of the total disturbance at the (k+1)th driving moment. M represents the actual speed of the train at the k-th driving moment; M represents the total mass of the train. This indicates the maximum traction gear of the train. This indicates the maximum braking gear of the train, and N represents the total number of carriages in the train. M Indicates the number of carriages in the train. This indicates the maximum value of the train's traction force. This indicates the maximum value of the train's braking force. This indicates the maximum value of the train's traction power.

6. The method according to claim 5, characterized in that, The gain of the extended state observer is such that the poles of the extended state observer are located inside the unit circle.

7. The method according to claim 2, characterized in that, The first compensation model is expressed by the following formula: ； The second compensation model is expressed by the following formula: ； Where u1 and u2 represent the control quantities at the k-th driving moment, and This represents the compensated control quantity at the k-th driving moment; Let M represent the observed value of the total disturbance at the k-th driving moment, and M represent the total mass of the train. This indicates the maximum traction gear of the train. This indicates the maximum braking gear of the train, and N represents the total number of carriages in the train. M Indicates the number of carriages in the train. This indicates the maximum value of the train's traction force. This indicates the maximum value of the train's braking force. This represents the maximum value of the train's traction power. This represents the actual speed of the train at the k-th driving moment.

8. The method according to any one of claims 1 to 7, characterized in that, The constraints of the MPC model are expressed by the following formula: in, H(k) represents the expected driving parameters from the (k+1)th driving time to the (k+P)th driving time; h(k+1) represents the expected driving parameters at the (k+1)th driving time, ..., h(k+P) represents the expected driving parameters at the (k+P)th driving time. Y(k) represents the predicted driving parameters corresponding to the (k+1)th driving time to the (k+P)th driving time; x(k) represents the actual train state at the kth driving time. ； y(k+1) represents the predicted driving parameters at the (k+1)th driving time, ..., y(k+P) represents the predicted driving parameters at the (k+P)th driving time; L represents the constant term of the disturbance factor simulated by the MPC model; T S F represents the time step between two adjacent driving moments. r This represents the drag value of the disturbance factor simulated by the MPC model; , When the desired driving parameter is the desired speed, When the desired driving parameter is the desired displacement, ; U(k) represents the train control quantity corresponding to the k-th driving time to the (k+F-1)-th driving time respectively; u(k) represents the train control quantity at the k-th driving time, ..., u(k+F-1) represents the train control quantity at the (k+F-1)-th driving time; R and Q represent preset weight matrices; U(k) 2i represents train control quantity on even bits, which is train braking gear; U(k) 2i-1 represents train control quantity on odd bits, which is train traction gear.

9. A dynamic tracking device for train driving curves based on model predictive control, characterized in that, include: processor; Memory used to store processor-executable instructions; The processor is configured to implement the method of any one of claims 1 to 8 when executing instructions stored in the memory.

10. A non-volatile computer-readable storage medium storing computer program instructions thereon, characterized in that, When the computer program instructions are executed by the processor, they implement the method described in any one of claims 1 to 8.

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