Discrete fractional-order integral terminal sliding mode control method, device and medium for high-speed train

Abstract

The present invention discloses a discrete fractional-order integral terminal sliding mode control method, device and medium for a high-speed train, and relates to the technical field of tracking control. The method comprises: performing force analysis on a power unit of a high-speed train to establish a three-particle model; adjusting the state variables of the high-speed train based on a fractional-order integral terminal sliding mode controller of the high-speed train according to a target speed to obtain an output speed; judging whether the output speed converges to a target speed curve; if so, updating the state variables based on the output speed, and adjusting the state variables based on a controller according to a target speed at the next moment; if not, updating the state variables based on the output speed, and adjusting the state variables of the high-speed train based on a controller according to the target speed at the next moment. The present invention can perform accurate speed tracking control on a high-speed EMU based on a discrete fractional-order integral terminal sliding mode controller.

Description

Technical Field

[0001] The present invention relates to the field of tracking control technology, and in particular to a discrete fractional-order integral terminal sliding mode control method, equipment and medium for a high-speed train. Background Art

[0002] High-speed trains have become one of the most popular modes of travel due to their comfort, punctuality, and low impact from weather. In order to ensure the stable operation of trains, research on automatic train driving will become one of the focuses of high-speed train research. The basis and premise for research on the optimization of automatic train driving control strategy is first to establish a reasonable and accurate high-speed train dynamics model, and design an accurate control method for the model to achieve automatic and precise control of traction / braking force under complex disturbance conditions, thereby achieving accurate tracking of the train to the expected speed.

[0003] The operating environment of high-speed trains is often complex and changeable, so the system control algorithm needs to be highly robust and insensitive to parameter disturbances caused by environmental changes and model changes, so as to better achieve target speed curve tracking control. However, the current PID control cannot meet the high-performance requirements in complex controls such as nonlinearity, and the traditional integer-order sliding mode control has a more serious jitter problem, which makes the automatic driving control of high-speed trains face many challenges. Therefore, studying the optimization of the dynamics of the train operation process and the control method is of great practical significance for the realization of automatic driving of high-speed EMUs. Summary of the invention

[0004] The purpose of the present invention is to provide a high-speed train discrete fractional-order integral terminal sliding mode control method, device and medium, which can perform high-precision speed tracking control on high-speed EMUs.

[0005] To achieve the above object, the present invention provides the following solutions:

[0006] In a first aspect, the present invention provides a discrete fractional-order integral terminal sliding mode control method for a high-speed train, comprising:

[0007] According to Newton's laws of kinematics, the forces acting on several power units in a high-speed train are analyzed, and a three-particle model of the longitudinal dynamics of a high-speed train is established; the forces acting on the power units include traction, braking force, basic resistance and workshop force.

[0008] The current speed of each power unit in the high-speed train is set as the state variable of the high-speed train.

[0009] According to the target speed of the high-speed train, based on the fractional-order integral terminal sliding mode controller of the high-speed train, the state variables of the high-speed train are adjusted to obtain the output speed of the high-speed train at the current moment; the fractional-order integral terminal sliding mode controller of the high-speed train is a sliding mode controller that combines the Grünwald-Letnikov fractional-order definition with the integral terminal sliding mode control technology; the target speed is determined according to the target speed curve of the high-speed train.

[0010] Determine whether the output speed of the high-speed train at the current moment converges to the target speed curve of the high-speed train; if so, update the state variables of the high-speed train according to the output speed of the high-speed train at the current moment, and adjust the state variables of the high-speed train based on the fractional-order integral terminal sliding mode controller of the high-speed train according to the target speed of the high-speed train at the next moment; if not, update the state variables of the high-speed train according to the current output speed, and adjust the state variables of the high-speed train based on the fractional-order integral terminal sliding mode controller of the high-speed train according to the target speed of the high-speed train at the next moment.

[0011] Optionally, the three-mass point model of the longitudinal dynamics of the high-speed train is as follows:

[0012] .

[0013] in, Train No. The mass, velocity and displacement of the power unit; The train under different working conditions The traction or braking force that the power unit needs to generate, is the operating resistance coefficient of the basic resistance experienced by the power unit in Section 1, i =1,2,3; is the elastic coefficient of the adjacent power unit, is the damping coefficient.

[0014] Optionally, the power unit is a unit consisting of a high-speed train locomotive and several high-speed train carriages or a unit consisting of several high-speed train carriages.

[0015] Optionally, after establishing the three-mass model of the longitudinal dynamics of the high-speed train, it also includes:

[0016] The three-particle model of the longitudinal dynamics of the high-speed train is expressed in continuous time form; the formula expression of the continuous time form is:

[0017] .

[0018] in, , , , , , ; A1, B1 are train system parameter matrices; n ( t ) is the basic resistance matrix of each power unit when the train is running; Train No. The mass, velocity and displacement of the power unit; The train under different working conditions The traction or braking force that the power unit needs to generate, is the operating resistance coefficient of the basic resistance experienced by the power unit in Section 1, i =1,2,3; is the elastic coefficient of the adjacent power unit, is the damping coefficient.

[0019] Optionally, after expressing the three-particle model of the high-speed train longitudinal dynamics in a continuous time form, the method further includes:

[0020] Based on the discrete time control input law, the formula of the continuous time form of the three-particle model of the longitudinal dynamics of the high-speed train is discretized to obtain the discrete time form of the three-particle model of the longitudinal dynamics of the high-speed train; the formula expression of the discrete time form of the three-particle model of the longitudinal dynamics of the high-speed train is:

[0021] .

[0022] Among them, A is the discretized matrix of matrix A1, , B is the discretized matrix of matrix B1, , x(k) is the discrete form of the train state variable x(t), u(k) is the discrete form of the control input u(t); n(k) is the discrete form of the basic resistance matrix n(t); x(k+1) is the train state at the next moment, h Refers to the sampling period, is the integration variable.

[0023] Optionally, the high-speed train fractional-order integral terminal sliding mode controller is specifically:

[0024] .

[0025] in, is the arrival law of the terminal sliding model, is the equivalent control input.

[0026] Optionally, the solution formula of the terminal sliding model arrival law is as follows:

[0027] .

[0028] in, ; B is the discretized matrix of matrix B1, , , , For odd ratios, , h refers to the sampling period, δ is the order of fractional difference, c1 is the sliding surface parameter, c2 is the gain parameter of the integral error term, e1(k) is the displacement tracking error, e2(k) is the velocity tracking error, is the gain parameter of the fractional-order difference function, is the integral error term, and k represents the kth moment.

[0029] Optionally, the solution formula for the equivalent control input is as follows:

[0030] .

[0031] in, , h is the sampling period, B is the discretized matrix of matrix B1, A is the discretized matrix of matrix A1, x(k) is the discrete form of the train state variable x(t), n(k) is the discrete form of the basic resistance matrix n(t), δ is the order of fractional difference, 0<γ<1, γ is the fractional power, k represents the kth moment, R1 is the displacement and velocity matrix of the next moment, c1 is the sliding surface parameter, c2 is the gain parameter of the integral error term, e1(k) is the displacement tracking error, e2(k) is the velocity tracking error, is the gain parameter of the fractional-order difference function.

[0032] In a second aspect, the present invention provides a computer device including a memory and a processor, wherein the memory stores a computer program, and when the computer program is executed by the processor, the processor executes a discrete fractional-order integral terminal sliding mode control method for a high-speed train.

[0033] In a third aspect, the present invention provides a computer-readable storage medium storing a computer program, wherein the computer program is suitable for being loaded by a processor and executing a discrete fractional-order integral terminal sliding mode control method for a high-speed train.

[0034] According to the specific embodiments provided by the present invention, the present invention discloses the following technical effects:

[0035] The present invention provides a discrete fractional-order integral terminal sliding mode control method, device and medium for a high-speed train. The method comprises: according to Newton's laws of kinematics, a force analysis is performed on several power units in a high-speed train, and a three-particle model of the longitudinal dynamics of the high-speed train is established; the forces on the power units include traction, braking force, basic resistance and workshop force; the current speed of each power unit in the high-speed train is set as the state variable of the high-speed train; according to the target speed of the high-speed train, based on the high-speed train fractional-order integral terminal sliding mode controller, the state variable of the high-speed train is adjusted to obtain the output speed of the high-speed train; the high-speed train fractional-order integral terminal sliding mode controller is a sliding mode controller combining the Grünwald-Letnikov fractional-order definition and the integral terminal sliding mode control technology; it is judged whether the output speed converges to the target speed curve; if so, the state variable is updated according to the output speed, and the state variable is adjusted based on the controller according to the target speed at the next moment; if not, the state variable is updated based on the output speed, and the state variable of the high-speed train is adjusted based on the controller according to the target speed at the next moment. The present invention designs a discrete fractional-order integral terminal sliding mode controller suitable for a high-speed train multi-particle model to perform speed tracking control on a high-speed EMU. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0037] Figure 1 A flowchart of a discrete fractional-order integral terminal sliding mode control method for a high-speed train is provided in Example 1 of the present invention.

[0038] Figure 2 A model diagram of a high-speed train power unit provided in Example 1 of the present invention.

[0039] Figure 3 This is a schematic diagram of force analysis of a power unit provided in Embodiment 1 of the present invention.

[0040] Figure 4 This is a control block diagram provided for Embodiment 1 of the present invention.

[0041] Figure 5 This is a target speed curve diagram provided in Example 1 of the present invention.

[0042] FIG6( a ) is a comparison diagram of accelerations of three controllers provided in the first embodiment of the present invention, and FIG6( b ) is a comparison diagram of speed tracking errors of three controllers provided in the first embodiment of the present invention.

[0043] Figure 7 (a) is a speed tracking error comparison diagram of power unit 1 under the DFOITSM method provided in Example 1 of the present invention; Figure 7 (b) is a speed tracking error comparison diagram of power unit 2 under the DFOITSM method provided in Example 1 of the present invention; Figure 7 (c) is a speed tracking error comparison diagram of power unit 3 under the DFOITSM method provided in Example 1 of the present invention.

[0044] Figure 8 (a) is a speed tracking error comparison diagram of power unit 1 under the DITSMC method provided in Example 1 of the present invention; Figure 8 (b) is a speed tracking error comparison diagram of power unit 2 under the DITSMC method provided in Example 1 of the present invention; Figure 8 (c) is a speed tracking error comparison diagram of power unit 3 under the DITSMC method provided in Example 1 of the present invention.

[0045] Figure 9 (a) is a speed tracking error comparison diagram of power unit 1 under the DLSMC method provided in Example 1 of the present invention; Figure 9 (b) is a speed tracking error comparison diagram of power unit 2 under the DLSMC method provided in Example 1 of the present invention; Figure 9 (c) is a speed tracking error comparison diagram of power unit 3 under the DLSMC method provided in Example 1 of the present invention.

[0046] FIG10( a ) is a speed tracking error comparison diagram of two controllers after adding disturbance provided in the first embodiment of the present invention, and FIG10( b ) is an acceleration comparison diagram of two controllers after adding disturbance provided in the first embodiment of the present invention.

[0047] Fig.11 This is a diagram of the internal structure of a computer device provided in Embodiment 2 of the present invention. DETAILED DESCRIPTION

[0048] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0049] The purpose of the present invention is to provide a high-speed train discrete fractional-order integral terminal sliding mode control method, device and medium, which can perform high-precision speed tracking control on high-speed EMUs.

[0050] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0051] Embodiment 1

[0052] like Figure 1As shown, this embodiment provides a discrete fractional-order integral terminal sliding mode control method for a high-speed train, comprising:

[0053] Step 101: According to Newton's laws of kinematics, a force analysis is performed on several power units in a high-speed train, and a three-particle model of the longitudinal dynamics of the high-speed train is established; the forces on the power units include traction, braking force, basic resistance and workshop force.

[0054] Step 102: setting the current speed of each power unit in the high-speed train as the state variable of the high-speed train.

[0055] Step 103: According to the target speed of the high-speed train, based on the fractional-order integral terminal sliding mode controller of the high-speed train, the state variable of the high-speed train is adjusted to obtain the output speed of the high-speed train at the current moment; the fractional-order integral terminal sliding mode controller of the high-speed train is a sliding mode controller that combines the Grünwald-Letnikov fractional-order definition with the integral terminal sliding mode control technology; the target speed is determined according to the target speed curve of the high-speed train.

[0056] Step 104: Determine whether the output speed of the high-speed train at the current moment converges to the target speed curve of the high-speed train; if so, update the state variables of the high-speed train according to the output speed of the high-speed train at the current moment, and adjust the state variables of the high-speed train based on the high-speed train fractional-order integral terminal sliding mode controller according to the target speed of the high-speed train at the next moment; if not, update the state variables of the high-speed train according to the current output speed, and adjust the state variables of the high-speed train based on the high-speed train fractional-order integral terminal sliding mode controller according to the target speed of the high-speed train at the next moment.

[0057] In some implementations of this embodiment, when executing step 101, the specific steps may be as follows:

[0058] This embodiment takes the CRH380A EMU as an example to establish a three-point train model, whose structure is as follows: Figure 2 As shown. The hollow wheel pair vehicle represents a trailer, and the solid wheel pair vehicle represents a motor vehicle. The power unit is subjected to dynamic analysis, and each power unit generates traction or braking force. The power unit is a unit composed of a high-speed train head and a plurality of high-speed train carriages or a unit composed of a plurality of high-speed train carriages.

[0059] The established train three-mass model has only one workshop force on the first and last power units, and the force analysis of other power units is the same. Figure 3 As shown, according to Newton's law of kinematics, the force condition of the train power unit is analyzed. Each power unit is subject to traction / braking force, basic resistance and workshop force.

[0060] According to the dynamic process analysis of each power unit, the mathematical equation of the three-point model of the train is expressed as:

[0061] (1).

[0062] (2).

[0063] (3).

[0064] in, , Train No. The mass, velocity and displacement of the power unit; The train under different working conditions i The traction or braking force that the power unit needs to generate, For train operation i The basic resistance of the power unit, is the running resistance coefficient; For the i Power unit and The workshop force of the power unit is reduced. is the elastic coefficient of the adjacent power unit, is the damping coefficient.

[0065] Will and Substituting into equation (1), we get the three-particle model of high-speed train longitudinal dynamics:

[0066] (4).

[0067] Among them, after establishing the three-particle model of high-speed train longitudinal dynamics, it can also include:

[0068] The three-particle model of the high-speed train longitudinal dynamics is represented in continuous time form.

[0069] Specifically, the actual speed and displacement of each power unit are defined as train state variables , the system input variable is recorded as According to equation (4), the high-speed train longitudinal dynamics model can be expressed as the following state space description:

[0070] (5).

[0071] in, , , , , , ; A1, B1 are train system parameter matrices; n ( t ) is the basic resistance matrix of each power unit when the train is running; Train No. The mass, velocity and displacement of the power unit; The train under different working conditions The traction or braking force that the power unit needs to generate, For train operation The basic resistance of the power unit, is the running resistance coefficient; For the Power unit and The workshop force of the power unit is reduced. is the elastic coefficient of the adjacent power unit, is the damping coefficient.

[0072] After expressing the three-mass point model of the high-speed train longitudinal dynamics in a continuous time form, the method further comprises:

[0073] Based on the discrete time control input law, the formula of the continuous time form of the three-particle model of the longitudinal dynamics of the high-speed train is discretized to obtain the discrete time form of the three-particle model of the longitudinal dynamics of the high-speed train; the formula expression of the discrete time form of the three-particle model of the longitudinal dynamics of the high-speed train is:

[0074] (6).

[0075] Among them, A is the discretized matrix of matrix A1, , B is the discretized matrix of matrix B1, , x(k) is the discrete form of the train state variable x(t), u(k) is the discrete form of the control input u(t); n(k) is the discrete form of the basic resistance matrix n(t); x(k+1) is the train state at the next moment, h Refers to the sampling period, is the integration variable.

[0076] In some implementations of this embodiment, before executing step 103, it also includes designing a high-speed train fractional-order integral terminal sliding mode controller, which can be specifically as follows:

[0077] Sliding mode variable structure control is a control method with good robustness and anti-interference performance. How to more effectively reduce the chattering phenomenon is the focus of the sliding mode controller research. Compared with the integer order, the fractional order has the memory of historical information. It can buffer the transfer of the control quantity during high-speed switching, so that the chattering phenomenon is effectively alleviated. The system state vector can reach the steady-state range faster, which not only improves the response speed of the system but also reduces the vibration wear and consumption of the controlled object. Therefore, this embodiment designs a high-speed train fractional-order integral terminal sliding mode controller. The control block diagram is as follows: Figure 4 shown.

[0078] Among them, the application of fractional calculus in control science has two directions: fractional order system and fractional order controller. The significance of fractional order controller lies in the controller itself, so it can be used for integer order system.

[0079] In the development of fractional calculus over hundreds of years, many definitions have emerged, among which the more famous ones are the Riemann-Liouville definition, the Caputo definition and the Grünwald-Letnikov definition. Among them, the Grünwald-Letnikov definition is often used to describe discrete time situations due to its clear expression.

[0080] Functions in discrete Grünwald-Letnikov form The fractional difference form of is given by:

[0081] (7).

[0082] Where: is the order of fractional differences, is the number of samples used in the calculation. As shown below:

[0083] (8).

[0084] It is clear from equation (8) that fractional calculus can be viewed as the function The weighted sum of In addition, when its step size approaches the step size When the weight is large, and when its step length is far away from the step length In practical engineering applications, especially for digital control, the sum of the items involved is usually reduced to a suitable length. Then, we can It is expressed as:

[0085] (9).

[0086] Therefore, the sum of the systems can be written as:

[0087] (10).

[0088] In the formula, f ( kj ) represents a function f(k) of kj The function value at time; is the sampling period h The order of the fractional difference of δ Power. is the Gamma function, is the Gamma function The integrand, the Gamma function, that is, Euler's second integral, is a type of function that extends the factorial function on real and complex numbers. It is a mathematical content and will not be elaborated here.

[0089] Then, the fractional-order integral terminal sliding mode controller is designed.

[0090] Let the target displacement be , For the actual displacement information, the following contents are defined:

[0091] (11).

[0092] in, , are the tracking errors of displacement and velocity respectively.

[0093] According to the design process of the traditional discrete linear sliding mode control (DLSMC) method, for the discrete time error dynamic system equation (6), the linear sliding mode surface is usually selected:

[0094] (12).

[0095] Where: , , , .

[0096] According to formula (12), the sliding mode function can be further derived :

[0097] (13).

[0098] The exponential reaching law method is applied to the design of the DLSMC control law, so that the system state is restricted to the vicinity of the origin of the switching hyperplane. By introducing the exponential reaching law:

[0099] (14).

[0100] Where: , , s(k+1) is the introduced exponential reaching law; β1 is the reaching speed parameter, which mainly affects the dynamic transition process of the switching function; β2 is the gain function of the sign function, which is the main parameter of the system to overcome perturbations and external interferences; h refers to the sampling period.

[0101] Combining equation (6), equation (13) and equation (14), we get:

[0102] (15).

[0103] In order to reduce the quasi-sliding mode bandwidth and improve tracking accuracy, an integral terminal sliding mode control (DITSMC) strategy is proposed. Compared with the linear sliding mode, the integral sliding mode has higher steady-state accuracy; the fast terminal sliding mode control can make the system state converge to zero in a finite time, breaking through the characteristic of the ordinary sliding mode control that the state converges gradually under the condition of the linear sliding mode surface, making the dynamic performance of the system better than the ordinary sliding mode control.

[0104] The designed integral terminal sliding surface is:

[0105] (16).

[0106] Where: , with the integral error term as shown in formula (17):

[0107] (17).

[0108] in, , , when the sliding surface reaches the vicinity of the origin of the switching hyperplane, the fractional power introduced Provides system status Faster convergence speed. In addition, c2=0 The integral terminal sliding mode surface of formula (16) is transformed into the traditional linear discrete time sliding mode function in formula (12).

[0109] In order to alleviate the chattering problem of sliding mode control, based on the above, this embodiment introduces fractional calculus into the sliding mode surface and constructs a fractional-order integral terminal sliding mode function as follows:

[0110] (18).

[0111] According to formula (14), the sliding mode function can be further derived :

[0112] (19).

[0113] Combining equation (6) and equation (15), the equivalent control input Given by:

[0114] (20).

[0115] in, , h is the sampling period, B is the discretized matrix of matrix B1, A is the discretized matrix of matrix A1, x(k) is the discrete form of the train state variable x(t), n(k) is the discrete form of the basic resistance matrix n(t), δ is the order of fractional difference, 0<γ<1, γ is the fractional power, k represents the kth moment, R1 is the displacement and velocity matrix of the next moment, c1 is the sliding surface parameter, c2 is the gain parameter of the integral error term, e1(k) is the displacement tracking error, e2(k) is the velocity tracking error, is the gain parameter of the fractional-order difference function.

[0116] In addition, this embodiment introduces the terminal sliding model arrival law to obtain formula (21):

[0117] (twenty one).

[0118] Where: , , , , For odd ratios, , h refers to the sampling period, δ is the order of fractional difference, B is the discretized matrix of matrix B1, c1 is the sliding surface parameter, c2 is the gain parameter of the integral error term, e1(k) is the displacement tracking error, e2(k) is the velocity tracking error, is the gain parameter of the fractional-order difference function, is the integral error term, and k represents the kth moment.

[0119] Combining the equivalent control with the reaching law, the actual control law is obtained, as shown in formula (22):

[0120] (twenty two).

[0121] In some implementations of this embodiment, stability and convergence need to be proved, which can be as follows:

[0122] Substituting the above formula (18) into formula (15), we get:

[0123] (twenty three).

[0124] In order to complete the stability analysis of the discrete time control strategy, this embodiment makes the following assumptions on the sliding surface.

[0125] Assumption 1: For a practical discrete-time control system, the sampling interval and the sliding surface should satisfy the following relationship:

[0126] (twenty four).

[0127] Where: .

[0128] 1) Discrete-time sliding mode dynamics can be Step is driven to the area In the area It can be described by the following formula:

[0129] (25).

[0130] Where: , ; , , .

[0131] 2) Once the sliding mode enters the region , it will stay there and will not escape at a later time, which means that if but .

[0132] Select the Lyapunov function , we can get:

[0133] (26).

[0134] Therefore, the relationship in formula (27) needs to be satisfied:

[0135] (27).

[0136] Case 1: When When , we can get equations (28) and (29):

[0137] (28).

[0138] (29).

[0139] From assumption 1, we can get:

[0140] (30).

[0141] From this we can get:

[0142] (31).

[0143] Combining equations (28), (29), and (31), we can obtain that hour, .

[0144] Case 2: When It can also be proved that .

[0145] Depend on have to: .

[0146] Then we have the relationship in formula (32):

[0147] (32).

[0148] (33).

[0149] Therefore, there are .

[0150] In this embodiment, simulation results and analysis are also performed.

[0151] The CRH380A EMU is equipped with three independent traction power units. The basic information of each vehicle section of the EMU is shown in Table 1.

[0152] Table 1 CRH380A EMU model parameters

[0153]

[0154] Among them, the expected running speed curve is designed as follows Figure 5 The running process of the train within 3000 seconds is simulated, and the running distance is about 230km, including two acceleration stages, three constant speed stages, one deceleration stage and one braking stage.

[0155] In order to verify the superiority of the designed controller, the traditional discrete linear sliding mode (DLSMC) controller and discrete integral terminal sliding mode (DITSMC) controller are selected as comparison objects. Figure 6 (a) and Figure 6 (b) are the acceleration change comparison diagram and speed tracking error comparison diagram of the three methods of DLSMC, DITSMC and DFOITSM. Figure 7 (a)-Figure 7 (c), Figure 8 (a)-Figure 8 (c) and Figure 9 (a)-Figure 9 (c) describe in more detail the changes in the speed tracking error of each power unit of the EMU under the designed controller.

[0156] It can be seen from Figure 6 (a)-Figure 6 (b) that the traditional DLSMC has a poor effect in the train startup phase, and the error is greater than that of DITSMC and DFOITSM. The initial error is between [-0.5m / s, -0.4m / s], and it can only be stable between [0.01m / s, 0.015m / s] when stable; the initial error of integer-order DITSMC is between [-0.45m / s, 0.4m / s], and the error can be stable between [0.01m / s, 0.12m / s] when stable, which is smaller than the error of DLSMC. This is because the integral sliding mode can improve the steady-state control accuracy of the system compared with the linear sliding mode; in addition, DFOITSM has the best effect in the startup phase, with a starting error between [-0.35m / s, -0.3m / s], and the error can be stable between [-0.003m / s, 0.006m / s] when stable. From Figure 6 (a)-Figure 6 (b), Figure 7 (a)-Figure 7 (c), Figure 8 (a)-Figure 8 (c) and Figure 9 (a)-Figure 9 (c), it can be seen that the traditional DLSMC has obvious chattering problems and cannot track the desired trajectory well. Both integer-order DITSMC and DFOITSM control methods can solve the chattering problem caused by DLSMC well. This is because compared with linear sliding mode control, terminal sliding mode control has no switching terms, so it can suppress chattering well.

[0157] Therefore, high-speed trains will be subject to external interference during operation. In order to prove the anti-interference ability of DFOITSM, white noise interference is introduced in this embodiment. Figure 10 (a) and Figure 10 (b) are the comparisons of the speed tracking error and acceleration of the two controllers after the interference is added. It can be seen from the figure that the anti-interference ability of the DFOITSM proposed in this embodiment is better than that of the integer-order DITSMC. This is because the fractional-order calculus calculation follows the order of integration first and then differentiation. And the function calculation process processes the global information in a weighted form, which retains the memory of the function's historical data. Therefore, the anti-interference performance shows a stronger quality when the controller contains fractional-order calculus.

[0158] Embodiment 2

[0159] The present invention also provides a computer device, including a memory and a processor, wherein the memory stores a computer program, and when the computer program is executed by the processor, the processor executes the above-mentioned discrete fractional-order integral terminal sliding mode control method for high-speed trains.

[0160] See also Fig.11 , Fig.11 Schematic diagram of the structure of a computer device provided by this application. Fig.11As shown, the computer device 1000 may include: a processor 1001, a network interface 1004 and a memory 1005. In addition, the computer device 1000 may also include: a user interface 1003, and at least one communication bus 1002. The communication bus 1002 is used to realize the connection and communication between these components. The user interface 1003 may include a display screen (Display), a keyboard (Keyboard), and the user interface 1003 may optionally include a standard wired interface and a wireless interface. The network interface 1004 may optionally include a standard wired interface and a wireless interface (such as a WI-FI interface). The memory 1005 may be a high-speed RAM memory, or a non-volatile memory (non-volatile memory), such as at least one disk storage. The memory 1005 may optionally be at least one storage device located away from the aforementioned processor 1001. As Fig.11 As shown, the memory 1005 as a computer storage medium may include an operating system, a network communication module, a user interface module, and a device control application program.

[0161] exist Fig.11 In the computer device 1000 shown, the network interface 1004 can provide network communication functions; the user interface 1003 is mainly used to provide an input interface for the user; and the processor 1001 can be used to call the device control application stored in the memory 1005 to implement the high-speed train discrete fractional-order integral terminal sliding mode control method described in the above embodiment, which will not be repeated here.

[0162] Embodiment 3

[0163] The present invention also provides a computer-readable storage medium, which stores a computer program. The computer program is suitable for being loaded by a processor and executing the discrete fractional-order integral terminal sliding mode control method for high-speed trains described in the above embodiment, which will not be repeated here.

[0164] The above program can be deployed and executed on a computer device, or deployed and executed on multiple computer devices located in one location, or executed on multiple computer devices distributed in multiple locations and interconnected through a communication network. Multiple computer devices distributed in multiple locations and interconnected through a communication network can form a blockchain network.

[0165] The computer-readable storage medium may be an internal storage unit of the computer device, such as a hard disk or memory of the computer device. The computer-readable storage medium may also be an external storage device of the computer device, such as a plug-in hard disk, a smart media card (SMC), a secure digital (SD) card, a flash card, etc. equipped on the computer device. Further, the computer-readable storage medium may include both an internal storage unit and an external storage device of the computer device. The computer-readable storage medium is used to store the computer program and other programs and data required by the computer device. The computer-readable storage medium may also be used to temporarily store data that has been output or is to be output.

[0166] The various embodiments in this specification are described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the various embodiments can be referenced to each other.

[0167] In this embodiment, specific examples are used to illustrate the principle and implementation of the present invention. The above description of the embodiment is only used to help understand the method and core idea of ​​the present invention; at the same time, for those skilled in the art, according to the idea of ​​the present invention, there will be changes in the specific implementation and application scope. In summary, the content of this specification should not be understood as limiting the present invention.

Claims

1. A discrete fractional-order integral terminal sliding mode control method for high-speed trains, characterized in that: include: According to Newton's laws of kinematics, the forces acting on several power units in the high-speed train are analyzed, and a three-particle model of the longitudinal dynamics of the high-speed train is established; the forces acting on the power units include traction, braking force, basic resistance and workshop force; Setting the current speed of each power unit in the high-speed train as a state variable of the high-speed train; According to the target speed of the high-speed train, based on the high-speed train fractional-order integral terminal sliding mode controller, the state variable of the high-speed train is adjusted to obtain the output speed of the high-speed train at the current moment; the high-speed train fractional-order integral terminal sliding mode controller is a sliding mode controller that combines the Grünwald-Letnikov fractional-order definition with the integral terminal sliding mode control technology; the target speed is determined according to the target speed curve of the high-speed train; Determining whether the output speed of the high-speed train at the current moment converges to the target speed curve of the high-speed train; If so, the state variables of the high-speed train are updated according to the output speed of the high-speed train at the current moment, and the state variables of the high-speed train are adjusted based on the high-speed train fractional-order integral terminal sliding mode controller according to the target speed of the high-speed train at the next moment; if not, the state variables of the high-speed train are updated according to the current output speed, and the state variables of the high-speed train are adjusted based on the high-speed train fractional-order integral terminal sliding mode controller according to the target speed of the high-speed train at the next moment; Let the target displacement be , For the actual displacement information, the following contents are defined: ； in, , are the tracking errors of displacement and velocity respectively; According to the design process of the traditional discrete linear sliding mode control method, the linear sliding mode surface is determined: ； Where: , , , ; According to the linear sliding surface, the sliding function is derived , as follows: ； The exponential reaching law method is applied to the design of the DLSMC control law, so that the system state is restricted near the origin of the switching hyperplane; the sliding mode function formula of the exponential reaching law is: ； Where: , , s(k+1) is the introduced exponential convergence law; β1 is the convergence speed parameter; β2 is the gain function of the sign function; h refers to the sampling period; According to the formula , the formula expression of the linear sliding surface and the formula expression of the sliding function with the introduction of the exponential reaching law The formula expression is: ； The designed integral terminal sliding surface is: ； In the formula, , ; , , when the sliding surface reaches the vicinity of the origin of the switching hyperplane, the fractional power introduced Provides system status Faster convergence speed; The integral terminal sliding mode surface is converted into a traditional linear discrete time sliding mode function; The fractional-order integral terminal sliding mode function is constructed as: ； Exporting Sliding Mode Function : ； Equivalent control input Given by: ； in, h is the sampling period, A is the discretized matrix of matrix A1, x(k) is the discrete form of the train state variable x(t), n(k) is the discrete form of the basic resistance matrix n(t), δ is the order of fractional difference, k represents the kth moment, R1 is the displacement and velocity matrix of the next moment, c1 is the sliding surface parameter, c2 is the gain parameter of the integral error term, is the gain parameter of the fractional-order difference function; The solution formula of the terminal sliding model arrival law is as follows: ； Among them, B is the discretized matrix of matrix B1, , , , For odd ratios, δ is the order of fractional difference, is the integral error term; The high-speed train fractional-order integral terminal sliding mode controller is specifically: ； in, is the arrival law of the terminal sliding model, is the equivalent control input.

2. A high-speed train discrete fractional-order integral terminal sliding mode control method according to claim 1, characterized in that: The three-mass point model of the longitudinal dynamics of the high-speed train is as follows: ； in, Train No. The mass, velocity and displacement of the power unit; The train under different working conditions The traction or braking force that the power unit needs to generate, For the The operating resistance coefficient of the basic resistance experienced by the power unit, i =1,2,3; is the elastic coefficient of the adjacent power unit, is the damping coefficient.

3. A high-speed train discrete fractional-order integral terminal sliding mode control method according to claim 1, characterized in that: The power unit is a unit consisting of a high-speed train locomotive and a plurality of high-speed train carriages or a unit consisting of a plurality of high-speed train carriages.

4. A high-speed train discrete fractional-order integral terminal sliding mode control method according to claim 1, characterized in that: After establishing the three-mass model of high-speed train longitudinal dynamics, it also includes: The three-particle model of the longitudinal dynamics of the high-speed train is expressed in continuous time form; the formula expression of the continuous time form is: ； in, , , , , , ; A1, B1 are train system parameter matrices; n ( t ) is the basic resistance matrix of each power unit when the train is running; Train No. The mass, velocity and displacement of the power unit; The train under different working conditions The traction or braking force that the power unit needs to generate, is the operating resistance coefficient of the basic resistance experienced by the power unit in Section 1, i =1,2,3; k is the elastic coefficient of the adjacent power unit, is the damping coefficient.

5. A high-speed train discrete fractional-order integral terminal sliding mode control method according to claim 4, characterized in that: After expressing the three-mass point model of the high-speed train longitudinal dynamics in a continuous time form, the method further comprises: Based on the discrete time control input law, the formula of the continuous time form of the three-particle model of the longitudinal dynamics of the high-speed train is discretized to obtain the discrete time form of the three-particle model of the longitudinal dynamics of the high-speed train; the formula expression of the discrete time form of the three-particle model of the longitudinal dynamics of the high-speed train is: ； Among them, A is the discretized matrix of matrix A1, , B is the discretized matrix of matrix B1, , x(k) is the discrete form of the train state variable x(t), u(k) is the discrete form of the control input u(t); n(k) is the discrete form of the basic resistance matrix n(t); x(k+1) is the train state at the next moment, h Refers to the sampling period, is the integration variable.

6. A computer device, characterized in that: The invention comprises a memory and a processor, wherein the memory stores a computer program, and when the computer program is executed by the processor, the processor executes the steps of the method according to any one of claims 1 to 5.

7. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program, and the computer program is suitable for being loaded by a processor and executing the method according to any one of claims 1 to 5.

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