Iterative learning control method, system and equipment for train speed and storage medium

Abstract

The invention relates to the technical field of train speed control, and discloses a train speed iterative learning control method, system and device and a storage medium, and the method comprises the steps: building a spatial domain model of a train, and obtaining an actual speed sequence of the train according to the spatial domain model; obtaining an expected speed sequence of the train, and calculating a speed tracking error between the expected speed sequence and the actual speed sequence; according to the speed tracking error, a spatial domain iterative learning law based on an information compensation item is established, and the information compensation item is determined based on speed information delay; and determining the optimal control input of the train according to a spatial domain iterative learning law. According to the method, two control strategies of self-adaptive control and iterative learning control are combined, an information compensation item is designed for speed information receiving delay, meanwhile, limitation on traction force / braking force of the train is added into the control strategy, the convergence speed of the control strategy for speed tracking errors is effectively increased, and the speed tracking accuracy is improved. Complete tracking of the train speed in the whole operation interval is achieved.

Description

Technical Field

[0001] The present invention relates to the technical field of train speed control, and in particular to an iterative learning control method, system, device and storage medium for train speed. Background Art

[0002] Control methods for automated high-speed train driving include PID control, adaptive control, iterative learning control, and other strategies. While these traditional control strategies can effectively control train speed, they still have certain limitations. For one thing, both PID control and adaptive control require a precise model of the system, and the error converges only when the running process approaches infinite length. However, in practical applications, obtaining a precise train model is difficult.

[0003] Therefore, the control strategy based on the precise model of the system cannot accurately control the train's speed, and since the train's running time is limited, it is theoretically impossible to achieve the convergence of the speed tracking error using these control strategies.

[0004] On the other hand, while iterative learning control can gradually achieve complete tracking of train speed by collecting information generated during repeated train operations, traditional iterative learning control is designed for systems that operate repeatedly in the time domain. In real-world applications, trains may not depart or arrive at their scheduled times due to various reasons, meaning that the duration of each train run is not fixed.

[0005] Furthermore, during actual operation, trains inevitably experience delays in receiving speed information. Existing control strategies for train speed tracking mostly ignore this issue. However, due to various factors, sensors on trains can malfunction, leading to speed information delays. This can affect the controller's ability to control the train's real-time speed, complicating controller design. Consequently, traditional iterative learning control cannot achieve precise speed control. Summary of the Invention

[0006] In order to solve the above technical problems, the present invention provides an iterative learning control method, system, device and storage medium for train speed, so as to solve the problem of errors in train speed tracking when speed information reception is delayed, thereby improving the convergence speed of tracking errors and achieving the technical effect of complete tracking of train speed in the entire operating range.

[0007] In a first aspect, the present invention provides an iterative learning control method for train speed, the method comprising:

[0008] Establishing a spatial domain model of the train, and obtaining an actual speed sequence of the train based on the spatial domain model;

[0009] Obtaining a desired speed sequence of the train, and calculating a speed tracking error between the desired speed sequence and the actual speed sequence;

[0010] establishing a spatial domain iterative learning law based on an information compensation term according to the speed tracking error, wherein the information compensation term is determined based on a speed information delay;

[0011] An optimal control input of the train is determined according to the spatial domain iterative learning law, and the train speed is controlled according to the optimal control input.

[0012] Furthermore, the spatial domain model is expressed using the following formula:

[0013]

[0014] Where, represents the rate of change of the train's velocity at displacement s in the jth iteration, v j (s) represents the speed of the train at the jth iteration displacement s, F j (s) represents the control input of the train at displacement s in the jth iteration, d(s) represents the speed information delay at displacement s, and f(v j (sd(s)), s) represents the running resistance of the train when the speed information is delayed by d(s) at the displacement s in the jth iteration, Gv j (s) / represents the inverse of the speed of the train at the jth iteration displacement s;

[0015] The constraints of the spatial domain model include:

[0016] v j (s)≥v min >0

[0017] v j (0) = v d (0)

[0018] |f(v j )-f(v d )|≤k(v j ,v d )|v j -v d |

[0019]

[0020] Where, v min Indicates the minimum speed of the train, v j(0) represents the initial velocity of the jth iteration, v d (0) represents the initial velocity of the desired velocity sequence, k(v j ,v d ) represents the first speed drag coefficient related function, v j represents the actual velocity sequence of the jth iteration, v d represents the expected velocity sequence, represents the rate of change of velocity information delay at displacement s, and ξ represents the upper limit of the rate of change of velocity information delay.

[0021] Furthermore, the step of establishing a spatial domain iterative learning law based on an information compensation item according to the speed tracking error, wherein the information compensation item is determined based on speed information delay, includes:

[0022] Establishing a Lyapunov-based controller design auxiliary function according to the speed tracking error and the train speed information delay;

[0023] According to the controller design auxiliary function and system stability theory, a constraint condition of a change rate of the controller design auxiliary function is obtained;

[0024] According to the constraint conditions of the change rate of the controller design auxiliary function and the speed information delay, a spatial domain iterative learning law of the information compensation term is established.

[0025] Furthermore, the following formula is used to express the spatial domain iterative learning law:

[0026]

[0027] The following formula is used to express the convergence condition of the spatial domain iterative learning law:

[0028]

[0029] Where sat(·) represents the saturation operator, F j+1 (s) represents the control input at the j+1th iteration displacement s, Q represents the control gain, represents the estimation of the second velocity drag coefficient correlation function at the j+1th iteration displacement s, e j+1 (s) represents the velocity tracking error at the j+1th iteration displacement s, v j+1 (s) represents the speed of the train at the j+1th iteration displacement s, ξ represents the upper limit of the speed information delay change rate, and γ represents the parameter learning gain.

[0030] In a second aspect, the present invention provides an iterative learning control system for train speed, the system comprising:

[0031] A model building module is used to establish a spatial domain model of the train and obtain the actual speed sequence of the train based on the spatial domain model;

[0032] an error calculation module, configured to obtain a desired speed sequence of the train and calculate a speed tracking error between the desired speed sequence and the actual speed sequence;

[0033] a learning law building module, configured to build a spatial domain iterative learning law based on an information compensation term according to the speed tracking error, wherein the information compensation term is determined based on a speed information delay;

[0034] The train control module is used to determine the optimal control input of the train according to the spatial domain iterative learning law, and control the train speed according to the optimal control input.

[0035] Furthermore, the model building module is further configured to express the spatial domain model using the following formula:

[0036]

[0037] Where, represents the rate of change of the train's velocity at displacement s in the jth iteration, v j (s) represents the speed of the train at the jth iteration displacement s, F j (s) represents the control input of the train at displacement s in the jth iteration, d(s) represents the speed information delay at displacement s, and f(v j (sd(s)), s) represents the running resistance of the train when the speed information is delayed by d(s) at the displacement s at the jth iteration;

[0038] The constraints of the spatial domain model include:

[0039] v j (s)≥v min >0

[0040] v j (0) = v d (0)

[0041] |f(v j )-f(v d )|≤k(v j ,v d )|v j -v d |

[0042]

[0043] Where, v min Indicates the minimum speed of the train, v j(0) represents the initial velocity of the jth iteration, v d (0) represents the initial velocity of the desired velocity sequence, k(v j ,v d ) represents the first speed drag coefficient related function, v j represents the actual velocity sequence of the jth iteration, v d represents the expected velocity sequence, represents the rate of change of velocity information delay at displacement s, and ξ represents the upper limit of the rate of change of velocity information delay.

[0044] Furthermore, the learning law building module is further used to establish a Lyapunov-based controller design auxiliary function according to the speed tracking error and the train speed information delay;

[0045] According to the controller design auxiliary function and system stability theory, a constraint condition of a change rate of the controller design auxiliary function is obtained;

[0046] According to the constraint conditions of the change rate of the controller design auxiliary function and the speed information delay, a spatial domain iterative learning law of the information compensation term is established.

[0047] Furthermore, the learning law construction module is further configured to express the spatial domain iterative learning law using the following formula:

[0048]

[0049] The following formula is used to express the convergence condition of the spatial domain iterative learning law:

[0050]

[0051] Where sat(·) represents the saturation operator, F j+1 (s) represents the control input at the j+1 iteration displacement s, Q represents the control gain, represents the estimation of the second velocity drag coefficient correlation function at the j+1th iteration displacement s, e j+1 (s) represents the velocity tracking error at the j+1th iteration displacement s, v j+1 (s) represents the speed of the train at the j+1th iteration displacement s, ξ represents the upper limit of the speed information delay change rate, and γ represents the parameter learning gain.

[0052] In a third aspect, an embodiment of the present invention further provides a computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the steps of the above method when executing the computer program.

[0053] In a fourth aspect, an embodiment of the present invention further provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program implements the steps of the above method when executed by a processor.

[0054] The present invention provides a method, system, device, and storage medium for iterative learning control of train speed. This method combines adaptive control with iterative learning control strategies, designs an information compensation term for speed information reception delay, and incorporates limits on the train's traction and braking forces into the control strategy. This effectively improves the control strategy's convergence rate for speed tracking errors and enables complete tracking of train speed across the entire operating range. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Figure 1 1 is a flow chart of an iterative learning control method for train speed according to an embodiment of the present invention;

[0056] Figure 2 3. FIG. 4 is a comparison diagram of the speed trajectory of the iterative learning control method for train speed in an embodiment of the present invention during iteration in a simulation experiment and the expected speed trajectory;

[0057] Figure 3 1. A comparison diagram of the speed tracking error of the iterative learning control method for train speed according to an embodiment of the present invention and other control methods in a comparative experiment;

[0058] Figure 4 This is another speed tracking error comparison diagram of the iterative learning control method for train speed in an embodiment of the present invention and other control methods in a comparative experiment;

[0059] Figure 5 1 is a schematic diagram of the structure of an iterative learning control system for train speed according to an embodiment of the present invention;

[0060] Figure 6 1 is a diagram showing the internal structure of a computer device according to an embodiment of the present invention. DETAILED DESCRIPTION

[0061] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings 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 making creative efforts shall fall within the scope of protection of the present invention.

[0062] See also Figure 1 The first embodiment of the present invention provides an iterative learning control method for train speed, which includes steps S10 to S40:

[0063] Step S10, establishing a spatial domain model of the train, and obtaining the actual speed sequence of the train based on the spatial domain model;

[0064] Step S20, obtaining the desired speed sequence of the train, and calculating the speed tracking error between the desired speed sequence and the actual speed sequence;

[0065] Step S30, establishing a spatial domain iterative learning law based on an information compensation item according to the speed tracking error, wherein the information compensation item is determined based on a speed information delay;

[0066] Step S40 , determining the optimal control input of the train according to the spatial domain iterative learning law, and controlling the train speed according to the optimal control input.

[0067] The present invention provides a train speed control method for trains with speed information reception delay. Since the traditional iterative control strategy cannot meet the accuracy requirements of train speed control, and the train always runs repeatedly on the same track, the spatial interval of each operation must be equal to the length of the track. Therefore, the present invention adopts spatial domain iterative learning control to control the train speed.

[0068] First, a spatial domain model of the train based on speed information delay is established:

[0069]

[0070] Where s∈[0,S], j is the number of iterations, is an S-domain differential operator, v j (s) is the output signal, which represents the speed of the train at the jth iteration displacement s, F represents the rate of change of the train's velocity at displacement s in the jth iteration, j (s) is the input signal, which represents the traction or braking force per unit mass of the train, and d(s) is the speed information delay. r (v j (sd(s)), s) is the resistance per unit mass of the train when the velocity information is delayed d(s) at the displacement s in the jth iteration. c0(s), c v (s),c a (s) are the resistance coefficients, f a (s) is the track resistance experienced by the train, S is the total length of the track, sat(·) is the saturation operator, and sat(·) is defined as:

[0071]

[0072] Where F represents the input parameter, F uIndicates the maximum value of the parameter, F l Indicates the minimum value of the parameter.

[0073] According to the above spatial domain model, the actual input signal is input into the spatial domain model to obtain the actual speed sequence of the train. For the preset expected speed sequence, the two speed sequences are subtracted to obtain the speed tracking error of the train:

[0074] e j (s)=v j (s)-v d (s)

[0075] Where, e j (s) represents the velocity tracking error at the jth iteration displacement s, v j (s) represents the speed of the train at the jth iteration displacement s, that is, the actual speed sequence of the train, v d (s) represents the desired velocity sequence at displacement s.

[0076] The above spatial domain model can be expressed as follows:

[0077]

[0078] in:

[0079]

[0080] Where, represents the rate of change of the train's velocity at displacement s in the jth iteration, v j (s) represents the speed of the train at the jth iteration displacement s, F j (s) represents the control input of the train at displacement s in the jth iteration, d(s) represents the speed information delay at displacement s, and f(v j (sd(s)), s) represents the running resistance of the train when the speed information is delayed by d(s) at the displacement s at the jth iteration, f r (v j (sd(s)), s) represents the running resistance per unit mass of the train when the speed information is delayed by d(s) at the displacement s in the jth iteration, Gv j (s) / represents the inverse of the speed of the train at the j-th iteration displacement s.

[0081] According to the above spatial domain model, by changing the input F of the train j The train's speed change rate can be controlled Then control the speed v of the train j Therefore, the control goal of this invention is to design a suitable iterative learning control controller F j , to achieve train speed vj For the expected speed v d Tracking over the entire operating range.

[0082] Before designing the controller, it is necessary to explain the constraints of the above-mentioned spatial domain model. In this embodiment, the constraints include speed constraints, namely constraint ①:

[0083] v j (s)≥v min >0

[0084] v j (0) = v d (0)

[0085] Where, v min Indicates the minimum speed of the train, v j (0) represents the initial velocity of the jth iteration, v d (0) represents the initial velocity of the desired velocity sequence.

[0086] Since the spatial domain model is a nonlinear function, it needs to satisfy the local Lipschitz condition. The local Lipschitz condition is a mathematical condition used to describe the condition that the rate of change of a function in a local area is limited. It is mainly used in the stability analysis of differential equations and nonlinear systems to ensure the existence and uniqueness of the solution. Therefore, the constraints also include constraint ②:

[0087] |f(v j )-f(v d )|≤k(v j ,v d )|v j -v d |

[0088] In the formula, k(v j ,v d ) represents the first speed drag coefficient related function, that is, a function related to speed and drag coefficient, wherein the first speed drag coefficient related function can be expressed as:

[0089]

[0090] Where c v 、c a are the resistance coefficients, v j represents the actual velocity sequence of the jth iteration, v d represents the expected velocity sequence.

[0091] In addition, since the train has unknown speed information delay, the rate of change of the speed information delay should also meet constraint ③:

[0092]

[0093] Where, represents the rate of change of velocity information delay at displacement s, and ξ represents the upper limit of the rate of change of velocity information delay.

[0094] Based on the above spatial domain model and constraints, the steps for establishing a spatial domain iterative learning law for controlling train speed include:

[0095] Establishing a Lyapunov-based controller design auxiliary function according to the speed tracking error and the train speed information delay;

[0096] According to the controller design auxiliary function and system stability theory, a constraint condition of a change rate of the controller design auxiliary function is obtained;

[0097] According to the constraint conditions of the change rate of the controller design auxiliary function and the speed information delay, a spatial domain iterative learning law of the information compensation term is established.

[0098] In this embodiment, since the train system contains a speed information acquisition delay assumed to be n, the speed of the next point can only be calculated using the speed of the previous n points. However, the speed of the next point calculated in this way is incorrect. Under normal circumstances, the speed of the next point should be calculated using the speed of the current point. In order to solve the speed information reception delay problem that may occur during train operation, before designing the controller, we first establish a controller design auxiliary function based on Lyapunov based on the speed tracking error and the train speed information delay:

[0099]

[0100] Where, L j (s) represents the controller design auxiliary function at the j-th iteration displacement s, and λ represents a preset constant, which is greater than zero.

[0101] In the above controller design auxiliary function, represents the energy of velocity tracking error, Represents the energy of information that is not accurately obtained due to delay.

[0102] By taking the derivative of the displacement s in the controller design auxiliary function, we can obtain:

[0103]

[0104] At the same time, the speed tracking error e j Taking the derivative of s in (s) and combining it with constraint ②, we can get:

[0105]

[0106] Where, v max Indicates the maximum operating speed, v max >0,F d (s) is the expected input signal, is the rate of change of speed tracking error, Design the auxiliary function rate of change for the controller.

[0107] According to the above and The two formulas, combined with the three constraints of the model and Young's inequality, can be deduced as follows:

[0108]

[0109] in:

[0110]

[0111] k l =v max *k(v j ,v d )

[0112] G l is the preset speed function, and G l ≤G 2 (v j (s)),

[0113] According to the constraints, we can know that:

[0114]

[0115] Because k l is a function of the drag coefficient, Gv j (s) / is related to speed, so θ(s) is actually a function related to speed and drag coefficient. In order to j ,v d ) are distinguished, and θ(s) is named as the second speed drag coefficient related function here.

[0116] According to Lyapunov stability theory, in order to ensure the stability of the system, it is necessary to ensure Semi-negative definite, and in order to compensate for the error caused by the speed information delay, this embodiment provides a spatial domain iterative learning law with an information compensation term:

[0117]

[0118] Where sat(·) represents the saturation operator, F j+1 (s) represents the control input at the j+1th iteration displacement s, Q represents the control gain, represents the estimation of the second velocity drag coefficient correlation function at the j+1th iteration displacement s, e j+1 (s) represents the velocity tracking error at the j+1th iteration displacement s, v j+1 (s) represents the speed of the train at the j+1th iteration displacement s, ξ represents the upper limit of the speed information delay change rate, and γ represents the parameter learning gain.

[0119] In the above iterative learning law, the initial state is set to:

[0120] F0(s)=0

[0121]

[0122] Among them, F0(s) represents the initial value of the control input, Represents the initial value of the second speed drag coefficient correlation function estimate.

[0123] In addition, the control gain Q also needs to meet the following convergence conditions:

[0124]

[0125] Through the iterative learning law provided in this embodiment, the speed tracking error of the train can be converged to 0 in the entire operating range within a limited number of iterative operations.

[0126] In the above iterative learning law, the information compensation term refers to:

[0127]

[0128] In the controller design auxiliary function, the energy of information that is not accurately obtained due to delay is represented by the following expression:

[0129]

[0130] Conventional spatial domain iterative learning control strategies don't account for this energy. Specifically, as discussed in the above embodiment, because the train system contains a delay in acquiring speed information, assumed to be n, the speed of the next point can only be calculated using the speed of the previous n points. However, this calculated speed is incorrect; the speed of the next point should normally be calculated using the speed of the current point. To address this issue, this embodiment incorporates this information compensation term into the iterative learning law, compensating for the speed information lost due to state delay from the previous n points to the current point, thereby achieving complete speed tracking.

[0131] The control method provided by the present invention is simulated below. The train system iteration length is set to 2000m and the sampling rate is selected to be 0.1. Other simulation parameters are set as follows:

[0132] Q=5, γ=10, ξ=0.8, F u =0.5, F l =-0.7;

[0133] c0(s)=0.081*sin(0.000067*(s))+0.088

[0134] c v (s)=0.000007*sin(0.000067*(s))+0.000074

[0135] c a (s)=0.00001*sin(0.000067*(s))+0.00011

[0136]

[0137]

[0138] Figure 2 The velocity trajectory of the control strategy proposed in this invention at the 2nd, 5th and 10th iterations is given by Figure 2 It can be seen that the speed trajectory gradually approaches the expected speed trajectory as the number of iterations increases. The iterative learning control method provided by the present invention can achieve complete tracking of the train speed in the entire operating range.

[0139] The control effect of the control strategy provided by the present invention is further verified by comparative experiments. The control algorithm used in the comparative experiments is a spatial domain iterative learning control strategy without an information compensation term, and the error index functions used are:

[0140] E1=max|v k (s)-v d (s)|,s∈{1,2…S+1}

[0141]

[0142] Figure 3 and Figure 4 The following is a comparison of the convergence curves of the control strategy provided by the present invention and the spatial domain iterative learning control strategy without information compensation term under different error indicators, where: Figure 3 The error indicator in is the maximum speed error E1, Figure 4 The error index in is the sum of the speed errors E2, according to Figure 3 and Figure 4From the convergence comparison diagram, it can be seen that the control strategy provided by the present invention converges faster than the traditional spatial iterative learning control method.

[0143] This embodiment provides an iterative learning control method for train speed. The invention combines adaptive control with iterative learning control strategies, designs an information compensation term for speed information reception delays, and incorporates limits on the train's traction and braking forces into the control strategy. This effectively improves the control strategy's convergence rate for speed tracking errors, enabling complete tracking of train speed across the entire operating range. This improved convergence rate further reduces energy loss. Furthermore, because the iterative control strategy provided by the invention does not require support from a precise system model, it is applicable not only to train models but also to other systems with spatially repetitive operations, demonstrating excellent applicability and scalability.

[0144] See also Figure 5 Based on the same inventive concept, a second embodiment of the present invention proposes an iterative learning control system for train speed, comprising:

[0145] The model building module 10 is used to establish a spatial domain model of the train and obtain the actual speed sequence of the train based on the spatial domain model;

[0146] an error calculation module 20 for obtaining a desired speed sequence of the train and calculating a speed tracking error between the desired speed sequence and the actual speed sequence;

[0147] A learning law construction module 30 is used to establish a spatial domain iterative learning law based on an information compensation term according to the speed tracking error, wherein the information compensation term is determined based on a speed information delay;

[0148] The train control module 40 is used to determine the optimal control input of the train according to the spatial domain iterative learning law, and control the train speed according to the optimal control input.

[0149] In a preferred embodiment, the model building module is further configured to express the spatial domain model using the following formula:

[0150]

[0151] Where, represents the rate of change of the train's velocity at displacement s in the jth iteration, v j (s) represents the speed of the train at the jth iteration displacement s, F j (s) represents the control input of the train at displacement s in the jth iteration, d(s) represents the speed information delay at displacement s, and f(v j(sd(s)), s) represents the running resistance of the train when the speed information is delayed by d(s) at the displacement s at the jth iteration;

[0152] The constraints of the spatial domain model include:

[0153] v j (s)≥v min >0

[0154] v j (0) = v d (0)

[0155] |f(v j )-f(v d )|≤k(v j ,v d )|v j -v d |

[0156]

[0157] Where, v min Indicates the minimum speed of the train, v j (0) represents the initial velocity of the jth iteration, v d (0) represents the initial velocity of the desired velocity sequence, k(v j ,v d ) represents the first speed drag coefficient related function, v j represents the actual velocity sequence of the jth iteration, v d represents the expected velocity sequence, represents the rate of change of velocity information delay at displacement s, and ξ represents the upper limit of the rate of change of velocity information delay.

[0158] In a preferred embodiment, the learning law building module is further used to establish a Lyapunov-based controller design auxiliary function according to the speed tracking error and the train speed information delay;

[0159] According to the controller design auxiliary function and system stability theory, a constraint condition of a change rate of the controller design auxiliary function is obtained;

[0160] According to the constraint conditions of the change rate of the controller design auxiliary function and the speed information delay, a spatial domain iterative learning law of the information compensation term is established.

[0161] In a preferred embodiment, the learning law construction module is further configured to express the spatial domain iterative learning law using the following formula:

[0162]

[0163] The following formula is used to express the convergence condition of the spatial domain iterative learning law:

[0164]

[0165] Where sat(·) represents the saturation operator, F j+1 (s) represents the control input at the j+1 iteration displacement s, Q represents the control gain, represents the estimation of the second velocity drag coefficient correlation function at the j+1th iteration displacement s, e j+1 (s) represents the velocity tracking error at the j+1th iteration displacement s, v j+1 (s) represents the speed of the train at the j+1th iteration displacement s, ξ represents the upper limit of the speed information delay change rate, and γ represents the parameter learning gain.

[0166] The technical features and effects of the iterative learning control system for train speed proposed in the embodiments of the present invention are the same as those of the method proposed in the embodiments of the present invention and are not further elaborated here. Each module in the iterative learning control system for train speed described above can be implemented in whole or in part through software, hardware, or a combination thereof. Each of these modules can be embedded in or independent of a processor in a computer device in hardware form, or stored in a memory in the computer device in software form, so that the processor can call and execute the corresponding operations of each of these modules.

[0167] In addition, an embodiment of the present invention further provides a computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the steps of the above method when executing the computer program.

[0168] See also Figure 6 , an internal structural diagram of a computer device in one embodiment, which may specifically be a terminal or a server. The computer device includes a processor, a memory, a network interface, a display, and an input device connected via a system bus. The processor of the computer device is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system and a computer program. The internal memory provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. The network interface of the computer device is used to communicate with an external terminal via a network connection. When the computer program is executed by the processor, an iterative learning control method for train speed is implemented. The display screen of the computer device may be a liquid crystal display or an electronic ink display screen, and the input device of the computer device may be a touch layer covering the display screen, or a key, trackball, or touchpad provided on the computer device housing, or an external keyboard, touchpad, or mouse.

[0169] It can be understood by those skilled in the art that Figure 6 The structure shown in the figure is only a block diagram of a part of the structure related to the solution of the present application, and does not constitute a limitation on the computer device to which the solution of the present application is applied. The specific computing device may include more or fewer components than shown in the figure, or combine certain components, or have the same component arrangement.

[0170] In addition, an embodiment of the present invention further provides a computer-readable storage medium having a computer program stored thereon, which implements the steps of the above method when the computer program is executed by a processor.

[0171] In summary, embodiments of the present invention provide an iterative learning control method, system, device, and storage medium for train speed. The method establishes a spatial domain model of the train and, based on the spatial domain model, obtains the train's actual speed sequence; obtains the train's desired speed sequence and calculates the speed tracking error between the desired speed sequence and the actual speed sequence; establishes a spatial domain iterative learning law based on an information compensation term based on the speed tracking error, wherein the information compensation term is determined based on the speed information delay; determines the optimal control input for the train based on the spatial domain iterative learning law, and controls the train speed based on the optimal control input. The present invention combines adaptive control with iterative learning control strategies, designs an information compensation term for speed information reception delay, and incorporates constraints on the train's traction and braking forces into the control strategy. This effectively improves the control strategy's convergence speed for speed tracking error, achieving complete tracking of the train's speed across the entire operating range. The improved convergence speed further reduces energy loss. Furthermore, because the iterative control strategy provided by the present invention does not require the support of a precise system model, it is applicable not only to train models but also to other systems with spatially repetitive operations, demonstrating excellent applicability and generalizability.

[0172] Each embodiment in this specification is described in a progressive manner, and the same or similar parts of each embodiment can be directly referred to each other, and each embodiment focuses on the differences from other embodiments. In particular, for the system embodiment, since it is basically similar to the method embodiment, the description is relatively simple, and the relevant parts can be referred to the partial description of the method embodiment. It should be noted that the various technical features of the above embodiments can be combined arbitrarily. In order to make the description concise, not all possible combinations of the various technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0173] The above-described embodiments merely represent several preferred implementations of the present application. While the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the patent. It should be noted that a person skilled in the art could make several improvements and substitutions without departing from the technical principles of the present invention, and these improvements and substitutions should also be considered within the scope of protection of the present application. Therefore, the scope of protection of the present patent application shall be based on the scope of protection of the claims.

Claims

1. An iterative learning control method for train speed, characterized in that: include: Establishing a spatial domain model of the train, and obtaining an actual speed sequence of the train based on the spatial domain model; Obtaining a desired speed sequence of the train, and calculating a speed tracking error between the desired speed sequence and the actual speed sequence; establishing a spatial domain iterative learning law based on an information compensation term according to the speed tracking error, wherein the information compensation term is determined based on a speed information delay; An optimal control input of the train is determined according to the spatial domain iterative learning law, and the train speed is controlled according to the optimal control input.

2. The iterative learning control method for train speed according to claim 1, characterized in that: The spatial domain model is expressed using the following formula: Where, represents the rate of change of the train's velocity at displacement s in the jth iteration, v j (s) represents the speed of the train at the jth iteration displacement s, F j (s) represents the control input of the train at displacement s in the jth iteration, d(s) represents the speed information delay at displacement s, and f(v j (sd(s)), s) represents the running resistance of the train when the speed information is delayed by d(s) at the displacement s in the jth iteration, G(v j (s)) represents the inverse of the train speed at the jth iteration displacement s; The constraints of the spatial domain model include: v j (s)≥v min >0 v j (0)=v d (0) |f(v j )-f(v d )|≤k(v j ,v d )|v j -v d | Where, v min Indicates the minimum speed of the train, v j (0) represents the initial velocity of the jth iteration, v d (0) represents the initial velocity of the desired velocity sequence, k(v j ,v d ) represents the first speed drag coefficient related function, v j represents the actual velocity sequence of the jth iteration, v d represents the expected velocity sequence, represents the rate of change of velocity information delay at displacement s, and ξ represents the upper limit of the rate of change of velocity information delay.

3. The iterative learning control method for train speed according to claim 1, characterized in that: The step of establishing a spatial domain iterative learning law based on an information compensation item according to the speed tracking error, wherein the information compensation item is determined based on speed information delay, comprises: Establishing a Lyapunov-based controller design auxiliary function according to the speed tracking error and the train speed information delay; According to the controller design auxiliary function and system stability theory, a constraint condition of a change rate of the controller design auxiliary function is obtained; According to the constraint conditions of the change rate of the controller design auxiliary function and the speed information delay, a spatial domain iterative learning law of the information compensation term is established.

4. The iterative learning control method for train speed according to claim 3, characterized in that: The spatial domain iterative learning law is expressed by the following formula: The following formula is used to express the convergence condition of the spatial domain iterative learning law: Where sat(·) represents the saturation operator, F j+1 (s) represents the control input at the j+1th iteration displacement s, Q represents the control gain, represents the estimation of the second velocity drag coefficient correlation function at the j+1th iteration displacement s, e j+1 (s) represents the velocity tracking error at the j+1th iteration displacement s, v j+1 (s) represents the speed of the train at the j+1th iteration displacement s, ξ represents the upper limit of the speed information delay change rate, and γ represents the parameter learning gain.

5. An iterative learning control system for train speed, characterized in that: include: A model building module is used to establish a spatial domain model of the train and obtain the actual speed sequence of the train based on the spatial domain model; an error calculation module, configured to obtain a desired speed sequence of the train and calculate a speed tracking error between the desired speed sequence and the actual speed sequence; a learning law building module, configured to build a spatial domain iterative learning law based on an information compensation term according to the speed tracking error, wherein the information compensation term is determined based on a speed information delay; The train control module is used to determine the optimal control input of the train according to the spatial domain iterative learning law, and control the train speed according to the optimal control input.

6. The iterative learning control system for train speed according to claim 5, characterized in that: The model building module is further configured to express the spatial domain model using the following formula: Where, represents the rate of change of the train's velocity at displacement s in the jth iteration, v j (s) represents the speed of the train at the jth iteration displacement s, F j (s) represents the control input of the train at displacement s in the jth iteration, d(s) represents the speed information delay at displacement s, and f(v j (sd(s)), s) represents the running resistance of the train when the speed information is delayed by d(s) at the displacement s at the jth iteration; The constraints of the spatial domain model include: v j (s)≥v min >0 v j (0)=v d (0) |f(v j )-f(v d )|≤k(v j ,v d )|v j -v d | Where, v min Indicates the minimum speed of the train, v j (0) represents the initial velocity of the jth iteration, v d (0) represents the initial velocity of the desired velocity sequence, k(v j ,v d ) represents the first speed drag coefficient related function, v j represents the actual velocity sequence of the jth iteration, v d represents the expected velocity sequence, represents the rate of change of velocity information delay at displacement s, and ξ represents the upper limit of the rate of change of velocity information delay.

7. The iterative learning control system for train speed according to claim 6, characterized in that: The learning law building module is further used to establish a Lyapunov-based controller design auxiliary function based on the speed tracking error and the train speed information delay; According to the controller design auxiliary function and system stability theory, a constraint condition of a change rate of the controller design auxiliary function is obtained; According to the constraint conditions of the change rate of the controller design auxiliary function and the speed information delay, a spatial domain iterative learning law of the information compensation term is established.

8. The iterative learning control system for train speed according to claim 7, characterized in that: The learning law construction module is further used to express the spatial domain iterative learning law using the following formula: The following formula is used to express the convergence condition of the spatial domain iterative learning law: Where sat(·) represents the saturation operator, F j+1 (s) represents the control input at the j+1 iteration displacement s, Q represents the control gain, represents the estimation of the second velocity drag coefficient correlation function at the j+1th iteration displacement s, e j+1 (s) represents the velocity tracking error at the j+1th iteration displacement s, v j+1 (s) represents the speed of the train at the j+1th iteration displacement s, ξ represents the upper limit of the speed information delay change rate, and γ represents the parameter learning gain.

9. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the computer program, the steps of the method according to any one of claims 1 to 7 are implemented.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 7 are implemented.

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