A full-stage trajectory iterative learning control method for multi-particle high-speed trains

Abstract

The present invention relates to the field of train control technology, and particularly relates to a full-stage trajectory iterative learning control method for a multi-particle high-speed train; the method comprises the following steps: describing the dynamic behavior of the high-speed train based on a multi-particle model of the high-speed train, and establishing a dynamic model of the train; introducing an iterative learning control strategy based on the dynamic model and the control target; defining the tracking error of the train speed during the iterative process; analyzing the dynamic behavior of the tracking error to obtain dynamic behavior data, and completing the precise trajectory tracking control of the high-speed train in different operation stages. By the above method, the trajectory tracking accuracy and control stability of the high-speed train in a complex operation environment are improved.

Description

Technical Field

[0001] The present invention relates to the technical field of train control, and particularly to a full-stage trajectory iterative learning control method for a multi-particle high-speed train. Background Art

[0002] In recent years, high-speed trains have become an important means of transportation due to their environmental friendliness and high-speed performance. During the running process, high-speed trains involve complex dynamic systems, and their automatic control is particularly crucial for ensuring the safety and efficiency of trains. As the core technology of high-speed trains, the automatic train control system can achieve stable trajectory tracking control during high-speed running, but there are certain challenges in dealing with nonlinear and uncertain disturbances.

[0003] Traditional high-speed train control methods are mostly based on simplified single-particle models, which simplify the entire train system into a dynamic model of a single mass point. Although this model is relatively simple in design and analysis, its accuracy and adaptability are low, and it is difficult to capture complex interactions between train carriages and nonlinear factors such as resistance changes during actual operation. Therefore, in practical applications, control strategies based on multi-particle models have gradually received attention to better simulate the actual dynamic behavior of trains. In addition, the operating environment of high-speed trains is complex and changeable, and is significantly affected by wind resistance, track gradient, curves, and coupling effects between carriages. In response to these uncertainties and disturbances, many control methods such as adaptive control, robust control, and model predictive control have been applied to train speed control. However, these methods perform limitedly when dealing with complex and periodically changing environmental factors, and are prone to unstable system performance or slow regulation.

[0004] Iterative learning control is a control method that improves system performance through continuous learning and optimization during periodic operation, and has good adaptability and convergence. Iterative learning control gradually reduces the control error through multiple iterations, and is suitable for the operating scenario where high-speed trains repeatedly travel back and forth on a fixed track. However, traditional iterative learning control methods usually require resetting the initial conditions after each iteration, which is difficult to achieve during the continuous operation of trains. Therefore, introducing alignment conditions as an alternative method is not only more practical, but also helps to further improve the adaptability and control accuracy of the system.

[0005] In summary, it is highly necessary to propose a full-stage trajectory iterative learning control method for a multi-particle high-speed train based on alignment conditions to improve the trajectory tracking accuracy and control stability of high-speed trains in complex operating environments. Summary of the Invention

[0006] The purpose of the present invention is to provide a full-stage trajectory iterative learning control method for a multi-particle high-speed train, aiming to improve the trajectory tracking accuracy and control stability of high-speed trains in complex operating environments.

[0007] To achieve the above object, a multi-particle high-speed train full-stage trajectory iterative learning control method adopted by the present invention includes the following steps:

[0008] Describe the dynamic behavior of the high-speed train based on the multi-particle model of the high-speed train, and establish the dynamic model of the train;

[0009] Based on the dynamic model and the control objective, introduce the iterative learning control strategy;

[0010] Define the tracking error of the train speed during the iteration process;

[0011] Analyze the dynamic behavior of the tracking error, obtain the dynamic behavior data, and complete the precise trajectory tracking control of the high-speed train in different operation stages.

[0012] Among them, in the step of describing the dynamic behavior of the high-speed train based on the multi-particle model of the high-speed train and establishing the dynamic model of the train:

[0013] The dynamic model is:

[0014]

[0015] In the formula, is the order of the high-speed train, p j (t) is the displacement of the j-th carriage, with the unit of m, v j (t) represents the speed of the j-th carriage, with the unit of m / s, m j >0 represents the mass of the j-th carriage, with the unit of kg, is the traction / braking force of the j-th carriage, c0, c1, c2 and c3 represent unknown resistance coefficients, k j (t) is the other resistance of the j-th carriage.

[0016] Among them, in the step of introducing the iterative learning control strategy based on the dynamic model and the control objective:

[0017] Define:

[0018]

[0019] In the formula, p i,j (t) and v i,j (t) respectively represent the displacement and speed of the j-th carriage in the i-th iteration, u i,j (t) represents the control input signal;

[0020] The dynamic model of the high-speed train can be expressed in the iterative framework as:

[0021]

[0022] Among them, in the step of defining the tracking error of the train speed in the iterative process:

[0023] Obtain the total resistance F during the train operation i (P i (t), V i (t), t) range:

[0024] 0 < ||F i (P i (t), V i (t), t)||2 ≤ δ i (t);

[0025] In the formula, δ i (t) is a known locally Lipschitz continuous function used to limit the upper bound of the total resistance;

[0026] Define the tracking error of the train speed in the i-th iteration process:

[0027]

[0028] In the formula, e i,j (t) represents the speed tracking error of the j-th carriage in the i-th iteration, is the reference speed.

[0029] Among them, in the step of analyzing the dynamic behavior of the tracking error to obtain dynamic behavior data:

[0030] In each iteration process, the initial state of the high-speed train needs to meet the following alignment conditions:

[0031] The speed at the end of each iteration should be equal to the initial speed of the next iteration:

[0032] V i-1 (T) = V i (0);

[0033] The initial and final states of the reference speed should be the same:

[0034] V r (T) = V r (0);

[0035] The initial and final states of the tracking error need to be the same:

[0036] e i-1 (T) = e i (0);

[0037] By taking the derivative of the tracking error e i (t) and combining it with the system dynamics model, we can obtain:

[0038]

[0039] Among them, in the step of analyzing the dynamic behavior of the tracking error and obtaining the dynamic behavior data:

[0040] Define the iterative learning control strategy:

[0041]

[0042] In the formula, Β -1 is the inverse of matrix Β, is a symmetric positive definite matrix, representing the control gain, is the estimated parameter in the i-th iteration, and α(t) represents a non-linear function based on the error and speed.

[0043] A multi-particle high-speed train full-stage trajectory iterative learning control method of the present invention describes its dynamic behavior based on a multi-particle model of a high-speed train, establishes a dynamic model of the train; introduces an iterative learning control strategy based on the dynamic model and control objectives; defines the tracking error of the train speed during the iteration process; analyzes the dynamic behavior of the tracking error to obtain dynamic behavior data, completes the precise trajectory tracking control of the high-speed train in different operating stages, and realizes improving the trajectory tracking accuracy and control stability of the high-speed train in a complex operating environment. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for use in the description of the embodiments or the prior art. Obviously, the following drawings are only some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0045] Figure 1 is the flow chart of the steps of the multi-particle high-speed train full-stage trajectory iterative learning control method of the present invention.

[0046] Figure 2 is the control effect diagram of the train motion state in the first iteration of the present invention.

[0047] Figure 3 is the control effect diagram of the train motion state in the 30th iteration of the present invention.

[0048] Figure 4 is the displacement and speed tracking error curve of the high-speed train iterative learning control of the present invention.

[0049] Figure 5 is the maximum absolute displacement and speed tracking error along the iteration axis of the present invention.

[0050] Figure 6 are the input curves of the 1st and 30th iterations of the present invention. Detailed implementation manners

[0051] Here, the exemplary embodiments will be described in detail, and the examples are shown in the drawings. When the following description refers to the drawings, unless otherwise indicated, the same numbers in different drawings represent the same or similar elements. The implementation manners described in the following exemplary embodiments do not represent all the implementation manners consistent with the present application.

[0052] The terms used in the present application are only for the purpose of describing specific embodiments and are not intended to limit the present application. The singular forms of "a", "the", and "said" used in the present application and the appended claims are also intended to include the plural forms unless the context clearly indicates otherwise. It should also be understood that the term "and / or" used herein refers to and includes any or all possible combinations of one or more of the associated listed items.

[0053] It should be understood that although the terms first, second, third, etc. may be used in the present application to describe various information, such information should not be limited to these terms. These terms are only used to distinguish the same type of information from each other. For example, without departing from the scope of the present application, the first information may also be referred to as the second information, and similarly, the second information may also be referred to as the first information. Depending on the context, the word "if" as used herein may be interpreted as "when" or "while" or "in response to determining".

[0054] Please refer to Figures 1 to 6 , the present invention provides a multi-particle high-speed train full-stage trajectory iterative learning control method, including the following steps:

[0055] S100: Describe the dynamic behavior of a high-speed train based on its multi-particle model, and establish a dynamic model of the train.

[0056] In this embodiment, in order to achieve the trajectory tracking control of a high-speed train, first, the dynamic behavior of the high-speed train is described based on its multi-particle model, and the comprehensive influence of traction force, braking force, and resistance, such as wind resistance, coupler force, and mechanical resistance, on the train movement is comprehensively considered to establish a dynamic model of the train; this model is the basis for realizing trajectory tracking control, and the dynamic model is:

[0057]

[0058] In the formula, is the order of the high-speed train, p j (t) is the displacement of the j-th carriage, in m, v j(t) represents the speed of the j-th carriage, with the unit of m / s, m j >0 represents the mass of the j-th carriage, with the unit of kg, is the traction / braking force of the j-th carriage, and c0, c1, c2, and c3 represent unknown resistance coefficients, k j (t) is the other resistance of the j-th carriage.

[0059] S200: Based on the dynamic model and control objectives, an iterative learning control strategy is introduced.

[0060] In this embodiment, based on the dynamic model and control objectives, an iterative learning control strategy is introduced. By running multiple iterations, control experience is extracted and control performance is optimized to address the complex non-linear disturbances and uncertainties existing in train operation;

[0061] Definition:

[0062]

[0063] In the formula, p i,j (t) and v i,j (t) respectively represent the displacement and speed of the j-th carriage in the i-th iteration, u i,j (t) represents the control input signal; as Figure 2 、 Figure 3 and Figure 6 shown, where Figure 2 is the control effect diagram of the train motion state in the 1st iteration, Figure 3 is the control effect diagram of the train motion state in the 30th iteration, Figure 6 is the input curves of the 1st and 30th iterations.

[0064] The dynamic model of the high-speed train can be expressed in the iterative framework as:

[0065]

[0066] S300: Define the tracking error of the train speed during the iterative process.

[0067] In this embodiment, the total resistance F during train operation is obtained i (P i (t), V i (t), t) range. To ensure the robustness of the control algorithm, the total resistance F during train operation i (P i (t), V i (t), t) is bounded, and its Euclidean norm satisfies the following relationship:

[0068] 0 < ||F i (P i(t), V i (t), t) || 2 ≤ δ i (t);

[0069] where δ i (t) is a known locally Lipschitz continuous function used to limit the upper bound of the total resistance.

[0070] To design the controller of the high-speed train, first define the tracking error of the train speed in the i-th iteration process:

[0071]

[0072] where e i,j (t) represents the speed tracking error of the j-th carriage in the i-th iteration, as Figure 4 shown, Figure 4 is the displacement and speed tracking error curve of the iterative learning control of the high-speed train, is the reference speed;

[0073] In the control objective, design a robust iterative learning controller U i (t) such that the train speed V i (t) can track the reference speed V r (t) within the interval t ∈ [0, T], and as the number of iterations i increases, the tracking error gradually converges.

[0074] S400: Analyze the dynamic behavior of the tracking error, obtain the dynamic behavior data, and complete the precise trajectory tracking control of the high-speed train at different operating stages.

[0075] In this embodiment, in order to find the control input signal suitable for the reference trajectory, it is necessary to analyze the dynamic behavior of the tracking error, obtain the dynamic behavior data, and complete the precise trajectory tracking control of the high-speed train at different operating stages;

[0076] To achieve smooth transition during the iterative update process, in each iteration process, the initial state of the high-speed train needs to meet the following alignment conditions:

[0077] The speed at the end of each iteration should be equal to the initial speed of the next iteration:

[0078] V i-1 (T) = V i (0);

[0079] The initial and final states of the reference speed should be the same:

[0080] V r (T) = V r (0);

[0081] The initial and final states of the tracking error need to be consistent:

[0082] e i-1 (T) = e i (0);

[0083] By taking the derivative of the tracking error e i (t) and combining it with the system dynamics model, we can obtain:

[0084]

[0085] As Figure 5 shown, Figure 5 are the maximum absolute displacement and velocity tracking errors along the iteration axis;

[0086] Define the iterative learning control strategy:

[0087] It is defined as:

[0088]

[0089] In the formula, Β -1 is the inverse of matrix Β, is a symmetric positive definite matrix, representing the control gain, is the estimated parameter in the i-th iteration, and α(t) represents a non-linear function based on error and velocity.

[0090] The parameter adopts the following iterative update rule:

[0091]

[0092] In the formula, and t ∈ [0, T], μ > 0 is the learning gain, which determines the learning speed, and η ∈ (0, 1) is the decay factor, used to improve stability.

[0093] The non-linear function α(t) is defined as:

[0094]

[0095] In the formula, is the design parameter, used to adjust the non-linear amplitude of the function, and tanh(·) is the hyperbolic tangent function, used to limit the error growth and improve the robustness of the control.

[0096] Through the above steps, the precise trajectory tracking control of high-speed trains in different operation stages is achieved.

[0097] In the present invention, by effectively dealing with the non-linear uncertainties during the train operation, such as wind resistance, coupler force, mechanical resistance, etc., and adopting a control strategy of alignment condition and composite energy function, the rapid convergence of the control error is achieved, thereby improving the control accuracy; it is applicable to the precise displacement and speed control of the train in the traction, cruise, coasting and braking stages. Compared with the traditional method, the present invention improves the train running safety while reducing the risk of deviating from the track; reduces unnecessary acceleration and deceleration through precise trajectory tracking, thereby improving the energy-saving effect; adapts to various disturbances during operation, and improves the train punctuality rate and operation reliability. At the same time, the present invention uses the alignment condition to replace the traditional reset condition, simplifies the control process, and reduces the complexity and maintenance cost of the system.

[0098] By combining the multi-particle dynamic model with the control scheme based on the repetitive operation mode, the present invention can effectively capture the complex interactions between different carriages and solve the bounded uncertainty problem, thus significantly improving the practical applicability and robustness of the train control system, and having more advantages than the traditional iterative learning control method based on the single-particle model.

[0099] The iterative learning control algorithm proposed by the present invention can achieve precise control in the four operation stages of traction, cruise, coasting and braking, and ensure the strict convergence of the control error. Compared with the existing controllers, the algorithm of the present invention can handle non-linear uncertainties, avoiding the limitations of relying on Lipschitz continuous uncertainties and model linearization, and thus showing better adaptability and control accuracy under complex operation conditions.

[0100] By adopting the alignment condition to replace the traditional reset condition, the present invention reduces the complexity of the system, enhances the continuity and stability of the control system, is particularly applicable to the actual operation environment of high-speed trains, improves the smoothness and safety of train operation, and has high practical application value.

[0101] After considering the specification and the content disclosed herein, those skilled in the art will readily think of other embodiments of the present application. The present application is intended to cover any variations, uses or adaptations of the present application, which follow the general principles of the present application and include the common general knowledge or conventional technical means in the technical field not disclosed in the present application.

[0102] It should be understood that the present application is not limited to the precise structures described above and shown in the drawings, and various modifications and changes can be made without departing from its scope.

Claims

1. A full-stage trajectory iterative learning control method for a multi-particle high-speed train, characterized in that, It includes the following steps: Describe the dynamic behavior of a high-speed train based on its multi-particle model and establish a dynamic model of the train; Introduce an iterative learning control strategy based on the dynamic model and control objectives; Define the tracking error of the train speed during the iterative process; Analyze the dynamic behavior of the tracking error, obtain dynamic behavior data, and complete the precise trajectory tracking control of the high-speed train at different operating stages, including the following steps: In each iterative process, the initial state of the high-speed train needs to meet the following alignment conditions: The speed at the end of each iteration should be equal to the initial speed of the next iteration: ； The initial and final states of the reference speed should be the same: ； The initial and final states of the tracking error need to remain the same: ； By taking the derivative of the tracking error and combining it with the system dynamics model, we can obtain: 。 2. The full-stage trajectory iterative learning control method for a multi-particle high-speed train according to claim 1, wherein In the step of describing the dynamic behavior of a high-speed train based on its multi-particle model and establishing a dynamic model of the train: The dynamic model is: ； In the formula, is the order of the high-speed train, is the displacement of the j-th carriage, in m, represents the speed of the j-th carriage, in m / s, represents the mass of the j-th carriage, in kg, is the traction / braking force of the j-th carriage, and represent unknown resistance coefficients, is the other resistance of the j-th carriage.

3. The full-stage trajectory iterative learning control method for a multi-particle high-speed train according to claim 2, characterized in that, In the step of introducing an iterative learning control strategy based on the dynamic model and control objectives: Define: ； In the formula, and respectively represent the displacement and velocity of the j-th carriage in the i-th iteration, represents the control input signal; The dynamic model of the high-speed train can be expressed in the iterative framework as: 。 4. The full-stage trajectory iterative learning control method for a multi-particle high-speed train according to claim 3, characterized in that In the step of defining the tracking error of the train speed during the iterative process: Obtain the total resistance during train operation Range: ； wherein, is a known locally Lipschitz continuous function used to limit the upper bound of the total resistance; Define the tracking error of the train speed in the i-th iterative process: ； Wherein, represents the speed tracking error of the j-th carriage in the i-th iteration, is the reference speed.

5. The full-stage trajectory iterative learning control method for a multi-particle high-speed train according to claim 1, characterized in that In the step of analyzing the dynamic behavior of the tracking error and obtaining dynamic behavior data: Define the iterative learning control strategy: ； wherein, is the inverse of the matrix , is a symmetric positive definite matrix, representing the control gain, is the estimated parameter in the i-th iteration, represents a non-linear function based on the error and speed.

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