High-speed train operation control method based on adaptive neural network

Abstract

The invention discloses a high-speed train operation control method based on an adaptive neural network. The method comprises the steps that a longitudinal dynamic model of a high-speed train is established, the speed and acceleration states of the train are observed in real time through a high-order sliding mode observer, the unknown system dynamic state is recognized in combination with the neural network, and the dynamic approximation precision is improved. And by utilizing a self-adaptive output feedback controller and combining the observed train state and the approached unknown dynamic state, the accurate tracking control of the train displacement and speed is realized. According to the controller, the accumulation of parameter estimation errors is inhibited by introducing a leakage item, and the adaptability of a train to uncertainty is enhanced. The control method provided by the invention can effectively improve the running stability and trajectory tracking precision of the train, and ensures the safe and reliable running of the train under unknown dynamic interference.

Description

Technical Field

[0001] The present invention relates to the field of high-speed train operation control, and in particular to a high-speed train operation control method based on an adaptive neural network. Background Art

[0002] With the rapid development of the global economy and the acceleration of urbanization, high-speed trains, as an important part of the modern transportation system, are increasingly becoming the main means of efficient transportation between cities. With its high speed, high comfort and high energy efficiency, high-speed trains have significantly improved people's travel efficiency. In this context, ensuring the safe, stable and reliable operation of high-speed trains has become the focus of technical research. Especially in complex and changeable operating environments, the control system of high-speed trains needs to have high precision and high reliability to cope with external disturbances and internal uncertainties of the system.

[0003] The control of high-speed trains faces many challenges. First, during the operation of the train, it is affected by many factors such as environmental changes, track conditions, and traffic flow, resulting in a high degree of uncertainty and nonlinearity in the dynamic behavior of the train. This uncertainty makes it difficult for traditional control methods to achieve precise control, especially when rapid response is required. In addition, the state variables of the train (such as displacement, velocity, and acceleration) are often difficult to measure directly in practical applications, which further increases the complexity of control. Therefore, researchers are in urgent need of developing new control methods to improve the adaptability and control performance of high-speed trains under uncertain conditions.

[0004] Although some progress has been made in the field of high-speed train control, there are still some problems that need to be solved in practical applications. For example, the existing control strategies are often unable to ensure the safety and stable operation of the train when dealing with rapidly changing external disturbances. In addition, traditional control methods are highly dependent on system models. When there is a difference between the actual system and the model, the control effect will be significantly reduced. Therefore, developing a method that can identify unknown dynamic disturbances in real time and perform adaptive control can not only improve the operating safety of high-speed trains, but also improve their operating efficiency and comfort. These are the key issues that need to be overcome in current high-speed train control technology. Summary of the invention

[0005] In order to overcome the shortcomings and deficiencies of the prior art, the present invention provides a high-speed train operation control method based on an adaptive neural network.

[0006] A high-speed train operation control method based on an adaptive neural network, the method comprising:

[0007] Step S1: using Newton's second law to establish a dynamic model of the train, the dynamic model combines the change of the train mass, the relationship between the speed and acceleration, and the control input and total resistance of the train;

[0008] Step S2: Observe the train speed and acceleration using a high-order sliding mode observer; estimate the two unknown dynamic parameters of the train total resistance and mass;

[0009] Step S3: using two radial basis function neural networks to estimate the unknown dynamics of the train control system and define the tracking error;

[0010] Step S4: Based on the use of a neural network to approximate the unknown parameters, the derivative of the error is controlled;

[0011] Step S5: filtering the control error and the system recursive vector to extract the auxiliary error vector for subsequent adaptive law design;

[0012] Step S6: Define two auxiliary variables and represents a square matrix with 2m rows and 2m columns, Representing a vector space with 2m rows and 1 column, based on the auxiliary variables P(t) and Q(t), the vector Ξ containing the unknown dynamic estimation error is calculated, and the expression is:

[0013]

[0014] in, is the estimated value of the neural network weight W*(t).

[0015] Step S7: Design an adaptive law using the auxiliary error vector Ξ to obtain an estimated value of the neural network weight W*(t)

[0016]

[0017] Among them, Γ>0 represents the adaptive law learning gain, and δ>0 represents the adaptive law correction coefficient.

[0018] Step S8: Make the two neural networks approximate the unknown lumped dynamics to obtain effective estimation. The estimated value expression is: and and are two ideal weight vectors of radial basis function neural networks, represents the jth value of the ith weight, and m is the dimension of the vector space. and are two radial basis function neural network basis vectors, Denotes the j-th value of the i-th basis vector.

[0019] Furthermore, the train dynamics model has the following expression:

[0020]

[0021] where \(t\in[0,T]\) is the time variable and \(T\) is the train's running termination time; \(M(t)>0\) represents the time-varying mass of the train, and \(1 / M(t)\) satisfies \(0 < b_1\leq1 / M(t)\leq b_2\), where \(b_1>0\) and \(b_2>0\) are two constants; \(p(t)\), \(v(t)\), and \(a(t)\) represent the displacement, velocity, and acceleration of the train respectively; the control input signal is denoted by \(u(t)\); \(f\) d \(f(v(t),p(t))\) represents the total resistance acting on the train. The total resistance consists of two parts: basic resistance and additional resistance, and the total resistance is:

[0022] \(f\) d \((v(t),p(t)) = c_0(t)+c\) v (t) \(v(t)+c\) a (t) \(v\) 2 (t)+\(f\) a (p(t))

[0023] where the unknown time-varying parameters \(c_0(t)\), \(c\) v (t) and \(c\) a (t) are the basic damping coefficients of the train, which are affected by factors such as train type or structure, and the unknown continuous function \(f\) a (p(t)) is the additional resistance encountered by the train during operation.

[0024] Furthermore, the high-order sliding mode observer has the following expression:

[0025]

[0026] where \(k_1\), \(k_2\), and \(k_3\) are the observation gains of the high-order sliding mode observer and are all greater than zero, and are the observed values of the system's unknown state variables \(p\), \(v\), and \(a\) respectively;

[0027] Furthermore, the estimation of the system's lumped unknown dynamics has the following expression:

[0028]

[0029] where, and are the ideal weight vectors of two radial basis function neural networks respectively, represents the m-dimensional vector space, and \(T\) represents the matrix transpose operation, represents the jth value of the i-th weight, m ​​is the dimension of the vector space, and are two radial basis function neural network basis vectors, φ ij (t)(i=1,2,j=1,…,m) represents the jth value of the ith basis vector. ε1(t) and ε2(t) are radial basis function neural network errors, and satisfy |ε1(t)|≤ε 1N and |ε2(t)|≤ε 2N (ε 1N and ε 2N is a positive constant);

[0030] Define tracking error, the expression is:

[0031] e(t)=[e1(t),e2(t)] T =[p(t)-p r (t),v(t)-v r (t)] T

[0032]

[0033] Among them, p r (t) and v r (t) are the bounded displacement and velocity references given by the train, p(t) and v(t) are the actual displacement and velocity of the train, Λ is a positive constant greater than zero; e(t) represents the tracking error vector, e1(t) represents the displacement tracking error, e2(t) represents the velocity tracking error, and τ(t) represents the scalar value containing the error.

[0034] Using a high-order sliding mode observer to observe the state and Replace, get

[0035]

[0036] in, represents the observer tracking vector, represents the observed displacement tracking error, represents the observed velocity tracking error, Represents a scalar value containing the observation error.

[0037] Derivative of control error The following form can be obtained:

[0038]

[0039] Furthermore, the derivative of the control error The expression is:

[0040]

[0041] Among them, ζ(t) is the bounded error caused by the observer error.

[0042] The controller u(t) is used to complete the convergence of the tracking error τ(t), and the expression is:

[0043]

[0044] Furthermore, based on the high-order sliding mode observer and neural network, the system expression is:

[0045]

[0046] in, is a bounded estimation error.

[0047] Define the filter variable φ 1f (t),φ 2f (t),u f (t), Δ f (t) and for:

[0048]

[0049] The system expression after filtering is as follows:

[0050]

[0051] in, is the lumped error, is the radial basis function neural network augmented weight vector, Augment the regression vector for a neural network.

[0052] Furthermore, the two auxiliary variables are expressed as follows:

[0053]

[0054] in, and is a constant greater than zero.

[0055] The beneficial technical effects of the present invention are:

[0056] 1. The present invention has significant advantages in achieving high-speed train trajectory tracking control. Through the adaptive control strategy, the train can maintain consistency with the given reference trajectory under complex working conditions and unknown dynamic interference. Compared with the traditional backstepping control method, the control jitter of the present invention is smaller and the response is smoother, which significantly improves the stability and tracking accuracy of the train under high-speed conditions.

[0057] 2. Different from the traditional adaptive law gradient descent method, the present invention innovatively introduces unknown dynamic estimation error information and auxiliary error terms into the adaptive law design, ensuring the rapid convergence of neural network weights and system parameters. This design improves the accuracy of the controller, enabling the train control system to quickly and effectively respond to complex dynamic environmental changes, thereby improving the running stability and safety of the train.

[0058] 3. The present invention uses a neural network to approximate complex and unknown dynamic parameters. The present invention effectively improves the motion performance of high-speed trains under complex working conditions and has strong applicability and scalability. The control method is applicable to a variety of high-speed train models and can greatly enhance the control accuracy and practicality of the train system. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] Figure 1 It is a general step flow chart of the present invention;

[0060] Figure 2 A schematic diagram of a semi-physical simulation of an embodiment of the present invention;

[0061] Figure 3 This is a train motion state control effect diagram of an embodiment of the present invention;

[0062] Figure 4 It is a graph of the adaptive control speed curve and speed tracking error of a high-speed train according to an embodiment of the present invention;

[0063] Figure 5 It is a high-speed train adaptive operation control input curve diagram according to an embodiment of the present invention;

[0064] Figure 6 This is a comparison diagram of the unknown parameter M estimation of an embodiment of the present invention and the traditional gradient descent method;

[0065] Figure 7 The unknown parameter f in the embodiment of the present invention is d Comparison diagram of the estimated effect with the traditional gradient descent method. DETAILED DESCRIPTION

[0066] It should be noted that, in the absence of conflict, the embodiments and features described in the embodiments of the present application may be combined with each other. The present application is further described in detail below in conjunction with the accompanying drawings and specific embodiments.

[0067] like Figure 1 As shown, a high-speed train operation control method based on an adaptive neural network comprises:

[0068] Step S1: To achieve precise control of a high-speed train under unknown dynamic disturbances, a dynamic model of the train is established based on Newton's second law. This model takes into account the variation of the train's mass, the relationship between speed and acceleration, as well as the control input and total resistance acting on the train. The train dynamic model is:

[0069]

[0070] where \(t\in[0,T]\) is the time variable and \(T\) is the running termination time of the train. \(M(t)>0\) is the train mass varying with time, and \(1 / M(t)\) satisfies \(0 < b1\leq1 / M(t)\leq b2\), where \(b1>0\) and \(b2>0\) are two constants. In addition, \(p(t)\), \(v(t)\), and \(a(t)\) represent the displacement, speed, and acceleration of the train respectively. The control input signal (tractive force or braking force) is denoted by \(u(t)\). The total resistance acting on the train consists of two parts: basic resistance and additional resistance. The total resistance is:

[0071] f d (v(t),p(t)) = c0(t)+c v (t)v(t)+c a (t)v 2 (t)+f a (p(t))

[0072] where the unknown time-varying parameters \(c0(t)\), \(c v (t)\) and \(c a (t)\) are the basic damping coefficients of the train, which are affected by factors such as train type or structure, and the unknown continuous function \(f a (p(t))\) is the additional resistance encountered by the train during operation.

[0073] Step S2: Use a high-order sliding mode observer to observe the train speed and acceleration:

[0074]

[0075] where \(k1\), \(k2\), and \(k3\) are the observation gains of the high-order sliding mode observer and are all greater than zero, and are the observed values of the system unknown state variables \(p\), \(v\), and \(a\) respectively

[0076] Since both the total resistance \(f d (v(t),p(t))\) and the mass \(M(t)\) are unknown, to estimate these two unknown dynamic parameters, the train system is reformulated as follows:

[0077]

[0078] Step S3: Use two radial basis function neural networks to estimate the unknown dynamics of the train control system. The unknown dynamics originate from the nonlinear characteristics of the system, external disturbances and parameter uncertainties, and reflect the parts of the actual high-speed train that are difficult to accurately model or predict. The estimated expression is as follows:

[0079]

[0080] in, and are two ideal weight vectors of radial basis function neural networks, represents the jth value of the ith weight, and m is the dimension of the vector space. and are two radial basis function neural network basis vectors, φ ij (t)(i=1,2,j=1,…,m) represents the jth value of the ith basis vector. ε1(t) and ε2(t) are radial basis function neural network errors, and satisfy |ε1(t)|≤ε 1N and |ε2(t)|≤ε 2N (ε 1N and ε 2N is a positive constant).

[0081] Defining the tracking error, we can get:

[0082] e(t)=[e1(t),e2(t)] T =[p(t)-p r (t),v(t)-v r (t)] T

[0083]

[0084] Among them, p r (t) and v r (t) are the bounded displacement and velocity reference given by the train, p(t) and v(t) are the actual displacement and velocity of the train, and Λ is a positive constant greater than zero.

[0085] Using a high-order sliding mode observer to observe the state and Alternative, available

[0086]

[0087] Derivative of control error The following form can be obtained:

[0088]

[0089] Step S4: Based on the use of neural network to approximate unknown parameters, the derivative of the control error The following form can be obtained:

[0090]

[0091] Among them, ζ(t) is the bounded error caused by the observer error.

[0092] In the above derivation process, in order to achieve the convergence of the tracking error τ(t), the expression of the controller u(t) is as follows:

[0093]

[0094] Step S5: Filter the control error and the system recursive vector to extract the auxiliary error vector for subsequent adaptive law design:

[0095] Based on the high-order sliding mode observer and neural network, the system expression is as follows:

[0096]

[0097] in, is a bounded estimation error.

[0098] Define the filter variable φ 1f (t),φ 2f (t),u f (t), Δ f (t) and for:

[0099]

[0100] The system expression after filtering is as follows:

[0101]

[0102] in, is the lumped error, is the radial basis function neural network augmented weight vector, Augment the regression vector for a neural network.

[0103] Step S6: Define two auxiliary variables and

[0104]

[0105] in, and is a constant greater than zero.

[0106] Based on the auxiliary variables P(t) and Q(t), the vector Ξ containing the unknown dynamic estimation error is calculated as:

[0107]

[0108] in, is the weight W * (t) is an estimated value.

[0109] Step S7: Design an adaptive law using the auxiliary error vector Ξ to obtain the neural network weight W * Estimated value of (t)

[0110]

[0111] Among them, Γ>0 is the adaptive law learning gain, and δ>0 is the adaptive law correction coefficient.

[0112] Among them, adaptive law learning is the core mechanism in adaptive control, which aims to cope with system uncertainty, external disturbances or model incompleteness by adjusting controller parameters (such as neural network weights) in real time. Its main function is to dynamically adjust control parameters according to the feedback information of the system to maintain the stability and performance of the system. In this way, adaptive control can adapt to system dynamic changes and effectively respond to various changes in complex environments without relying on accurate models.

[0113] Step S8: Through steps S1 to S7, the train speed is controlled according to the given speed trajectory; while ensuring the weight of the neural network On the basis of convergence, the two neural networks are able to approximate the unknown lumped dynamics and obtain effective estimates, and the estimated values ​​are: and

[0114] like Figure 2 As shown, a real-time hardware-in-the-loop simulation test platform for a high-speed train operation control method based on an adaptive neural network is provided. The platform consists of the StarSim MT1070 rapid prototyping collaborative operation controller, which is mainly used to perform real-time control tasks and work in conjunction with the simulation target machine to apply simulation and control algorithms to the actual hardware environment; the StarSimMT6060 collaborative control real-time simulation target machine, which undertakes the real-time simulation task of the train model, runs the dynamic model exported from Simulink in the hardware environment, provides real-time dynamic data for control algorithm testing, and acts as a development and monitoring terminal with the computer. The train model and the adaptive controller are debugged in MATLAB / Simulink and can be downloaded and executed on the real-time simulation target machine. According to the above implementation process, the real-time hardware-in-the-loop simulation results of the train can be obtained. Figure 3-Figure 7.

[0115] The reference curve of the train mainly includes the acceleration phase, the cruising phase and the braking phase, covering all the running states of the train. The maximum running speed reaches 83.5 m / s, which is approximately equivalent to a speed of 300 km / h. In the HIL simulation, the parameter in step S1 is f a (p(t)) = -sin(πp(t)) as additional resistance M = 345kg, c0(t) = -275sin(0.0037t) -2977N, c v (t)=-2.5sin(0.0037t)-25.17NS / m, c a (t)=-0.04sin(0.0037t)-0.3864NS 2 / m; in step S2, the parameters are k1=40, k2=65, k3=0.3; in step S3, the neural network node m=16; in step S4, the controller parameter is set to Λ=10 3 k=10 4 In step S4, the adaptive law parameters are δ=200, Γ=4,

[0116] like Figure 3 As shown in FIG. 1 , it is a diagram showing the displacement tracking performance and speed tracking error control effect under the train reference curve. From the tracking performance of the reference signal, it can be seen that the application of the control algorithm of the present invention can obtain satisfactory tracking results. Figure 4 As shown, the tracking error curves of train displacement and speed show that these error curves converge to near zero after a short oscillation, further confirming the convergence of the tracking error. In addition, Figure 5 As shown, the control signal u(t) of the train is described, further proving that all relevant variables are bounded throughout the entire operation cycle.

[0117] like Figure 6 and Figure 7 As shown in the figure, it means that under the same parameter setting, the traditional adaptive law and the designed adaptive law respectively affect the parameters M and f d The simulation results show that the adaptive control based on neural network designed by the present invention can achieve the expected identification and tracking performance by using the newly designed adaptive law method.

[0118] Emphasis should be placed on the fact that these configurations are intended exclusively for testing purposes and not for controller design and implementation. Any additional information can be obtained from the train design manual.

[0119] Although embodiments of the present invention have been shown and described, it will be understood by those skilled in the art that various equivalent changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A high-speed train operation control method based on adaptive neural network, characterized in that , the method comprises: Step S1: using Newton's second law to establish a dynamic model of the train, the dynamic model combines the change of the train mass, the relationship between the speed and acceleration, and the control input and total resistance of the train; Step S2: Observe the train speed and acceleration using a high-order sliding mode observer; estimate the two unknown dynamic parameters of the train total resistance and mass; Step S3: using two radial basis function neural networks to estimate the unknown dynamics of the train control system and define the tracking error; Step S4: Based on the use of a neural network to approximate the unknown parameters, the derivative of the error is controlled; Step S5: filtering the control error and the system recursive vector to extract the auxiliary error vector for subsequent adaptive law design; Step S6: Define two auxiliary variables and represents a square matrix with 2m rows and 2m columns, Representing a vector space with 2m rows and 1 column, based on the auxiliary variables P(t) and Q(t), the vector Ξ containing the unknown dynamic estimation error is calculated, and the expression is: in, is the neural network weight W * (t) is an estimated value; Step S7: Design an adaptive law using the auxiliary error vector Ξ to obtain the neural network weight W * Estimated value of (t) Among them, Γ>0 represents the adaptive law learning gain, δ>0 represents the adaptive law correction coefficient; Step S8: Make the two neural networks approach the unknown dynamics respectively, and complete the estimation of the unknown dynamics of the train. The estimated value expression is: and and are two ideal weight vectors of radial basis function neural networks, represents the jth value of the i-th weight, and m is the dimension of the vector space; and are two radial basis function neural network basis vectors, Represents the jth value of the ith basis vector.

2. A high-speed train operation control method based on an adaptive neural network as claimed in claim 1, characterized in that: The train dynamics model is expressed as: where \(t\in[0,T]\) is the time variable and \(T\) is the running termination time of the train; \(M(t)>0\) represents the mass of the train varying with time, and \(1 / M(t)\) satisfies \(0 < b_1\leq1 / M(t)\leq b_2\), where \(b_1 > 0\) and \(b_2 > 0\) are two constants; \(p(t)\), \(v(t)\), \(a(t)\) represent the displacement, velocity and acceleration of the train respectively; the control input signal is denoted by \(u(t)\); \(f d (v(t), p(t))\) represents the total resistance acting on the train. The total resistance consists of two parts: basic resistance and additional resistance. The expression for the total resistance is: f d (v(t),p(t))=c0(t)+c v (t)v(t)+c a (t)v 2 (t)+f a (p(t)) Among them, the unknown time-varying parameters c0(t),c v (t) and c a (t) is the basic damping coefficient of the train, which is affected by the type of train or structural factors. The unknown continuous function f a (p(t)) is the additional resistance encountered by the train during operation.

3. A high-speed train operation control method based on adaptive neural network as claimed in claim 1, characterized in that: The high-order sliding mode observer is expressed as: Among them, k1, k2 and k3 are the observation gains of the high-order sliding mode observer and are all greater than zero. and are the observed values ​​of the unknown state variables p, v and a of the system respectively.

4. A high-speed train operation control method based on adaptive neural network as claimed in claim 1, characterized in that: The unknown dynamics of the train control system are estimated, and the expression is: in, and are two ideal weight vectors of radial basis function neural networks, represents an m-dimensional vector space, T represents a matrix transpose operation, represents the jth value of the i-th weight, m ​​is the dimension of the vector space, and are two radial basis function neural network basis vectors, φ ij (t)(i=1,2,j=1,…,m) represents the jth value of the ith basis vector, ε1(t) and ε2(t) are radial basis function neural network errors, and satisfy |ε1(t)|≤ε 1N and |ε2(t)|≤ε 2N , ε 1N and ε 2N is a positive constant; Define tracking error, the expression is: e(t)=[e1(t),e2(t)] T =[p(t)-p r (t),v(t)-v r (t)] T Among them, p r (t) and v r (t) are the bounded displacement and velocity references given by the train, p(t) and v(t) are the actual displacement and velocity of the train, Λ is a positive constant greater than zero; e(t) represents the tracking error vector, e1(t) represents the displacement tracking error, e2(t) represents the velocity tracking error, and τ(t) represents the scalar value containing the error; Using a high-order sliding mode observer to observe the state and Replace, get in, represents the observer tracking vector, represents the observed displacement tracking error, represents the observed velocity tracking error, represents a scalar value that includes observation errors; Derivative of control error Get the following form:

5. A high-speed train operation control method based on adaptive neural network as claimed in claim 1, characterized in that: The derivative of the control error The expression is: Among them, ζ(t) is the bounded error, which is caused by the observer error; The controller u(t) is used to complete the convergence of the tracking error τ(t), and the expression is:

6. A high-speed train operation control method based on adaptive neural network as claimed in claim 1, characterized in that: Based on the high-order sliding mode observer and neural network, the train control system expression is: in, is a bounded estimation error; Define the filter variable φ 1f (t),φ 2f (t),u f (t), Δ f (t) and for: The system expression after filtering is as follows: in, is the lumped error, is the radial basis function neural network augmented weight vector, Augment the regression vector for a neural network.

7. A high-speed train operation control method based on adaptive neural network as claimed in claim 1, characterized in that: The two auxiliary variables are expressed as: Among them, l and is a constant greater than zero.

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