A self-adaptive anti-swing control method for double-pendulum bridge crane

Abstract

The application discloses a self-adaptive double-swing bridge type crane anti-swing control method and belongs to the technical field of intelligent control. The method constructs a double-swing dynamic model containing a trolley, a hook and a load mass coupling through Euler-Lagrange equation, and proposes a hybrid strategy combining PD control and RBF neural network hierarchical sliding mode control: PD control is used to realize basic position tracking, RBF neural network is used to online approximate unknown nonlinear dynamics of the system, a composite sliding surface and a smooth saturation function are designed in combination with hierarchical sliding mode control, and multiple targets of position tracking and double-swing suppression are coordinated and chattering is suppressed. The application solves the problems of modeling deviation of a traditional single pendulum, insufficient nonlinear control precision and multiple target coordination, significantly improves the robustness and engineering practicability of the system, and provides a novel technical scheme for intelligent anti-swing control of a crane.

Description

Technical Field

[0001] This invention relates to the field of anti-sway control technology for cranes, and in particular to an adaptive double-sway bridge crane anti-sway control method. Background Technology

[0002] Bridge cranes, as core material handling equipment in the industrial field, are widely used in large warehouses, factories, docks, and construction sites due to their advantages such as small footprint, high efficiency, simple structure, and strong load capacity. They achieve vertical lifting and horizontal transport of heavy objects through a wire rope sling system. However, this system is essentially a typical underactuated nonlinear system, inevitably facing load sway during operation, which severely restricts operational efficiency and safety.

[0003] Traditional control methods generally use a single pendulum model to describe crane lifting systems, neglecting the double pendulum coupling characteristics between the hook and the load, i.e., the secondary oscillation between the lifting rope and the load. In reality, when the trolley starts, stops, accelerates, decelerates, or turns, the hook and load will generate complex coupled oscillations. The single pendulum model cannot accurately reflect the dynamic characteristics of the system, leading to a mismatch between the control algorithm and the physical model, thus affecting control accuracy.

[0004] Gantry cranes are underactuated systems, with the control input dimension being smaller than the system's degrees of freedom. Their dynamic equations exhibit strong nonlinearity and strong coupling characteristics. Control methods based on simplified linear models (such as traditional PID control) struggle to handle the system's nonlinear dynamics, especially when the load mass changes or external disturbances occur, easily leading to large trajectory tracking errors and poor sway suppression. While current crane anti-sway control schemes based on neural networks possess nonlinear approximation capabilities, they lack rigorous stability theory support, have slow convergence speeds, and cannot guarantee real-time dynamic response when used alone, making it difficult to meet the requirements for rapid sway suppression in engineering applications.

[0005] Therefore, the present invention provides a new solution to this problem. Summary of the Invention

[0006] In view of the above situation and to overcome the defects of the prior art, the purpose of this invention is to provide an adaptive anti-sway control method for a double-swing bridge crane, so as to solve the above problems existing in the prior art. The specific solution is as follows:

[0007] An adaptive anti-sway control method for a double-swing bridge crane includes the following steps:

[0008] S1. Based on the actual operating parameters of the bridge crane, construct a double pendulum mathematical model that includes key elements such as trolley, load mass, hook mass, rope swing angle and pendulum length ratio.

[0009] S2. Decompose the double pendulum system into two subsystems: position tracking and angle control. Design a sliding surface for each subsystem and form a unified sliding control surface through a composite strategy.

[0010] S3. Based on the sliding mode control principle, design the overall control law, which includes equivalent control terms, switching control terms, PD control terms, and angle compensation terms.

[0011] S4. Utilize the RBF neural network's ability to approximate unknown dynamics of the system to adjust key parameters in the overall control law in real time, thereby achieving precise position tracking and sway suppression.

[0012] Optionally, the mathematical model of the double pendulum in step S1 is derived using the Euler-Lagrange equations to derive the system dynamics equations, and its mathematical expression is:

[0013]

[0014] Among them, M and m f m g Let θ1 represent the trolley mass, load mass, and hook mass, respectively; θ2 represent the swing angle of the rope l1 relative to the vertical direction; and θ2 represent the swing angle of l2 relative to the vertical direction, with the swing length ratio defined as l1:l2; F represents the trolley driving force; and f represents the coefficient of friction between the trolley and the slide rail.

[0015] The system dynamics equations are expressed in matrix form as follows:

[0016]

[0017] Where M(q) is a positive definite symmetric mass matrix. Let G(q) be the damping matrix, G(q) be the gravity vector, and Q be the generalized force vector of the system.

[0018] Optionally, step S2 decomposes the double pendulum system into two subsystems: position tracking and angle control. A sliding surface is designed for each subsystem, and the specific steps are as follows:

[0019] Define the desired displacement as x d Then the error between the expected displacement and the actual output displacement x is:

[0020] e = xx d

[0021] Design the sliding surface, where:

[0022] Crane trolley position tracking sliding surface s1:

[0023]

[0024] Hook angle sliding surface s2 and load angle sliding surface s3:

[0025]

[0026] Where λ1 is the position tracking gain parameter, λ2 is the hook angle gain parameter, and λ3 is the load angle gain parameter, and λ1, λ2, and λ3 are all greater than 0;

[0027] Define the new sliding surface as a composite sliding control with three sliding controls:

[0028] S = s1 + β1s2 + β2s3

[0029] Where S is the composite sliding surface, β1 and β2 are the coupling coefficients of the hook angle and the load angle, respectively, used to adjust the weight relationship between position tracking and anti-sway control, and both β1 and β2 are greater than 0.

[0030] Optionally, the mathematical expression for the total control law u in step S3 is:

[0031]

[0032] Among them, u eq This is an equivalent control term used to offset known system dynamics;

[0033] u sw To switch control terms, a smooth saturation function is used to suppress chattering;

[0034] u pd This is a PD control term; used to improve transient response.

[0035] u a This is an angle compensation term used to suppress angular coupling, and it satisfies the following equation:

[0036]

[0037] Where, k a The gain is controlled by the angle.

[0038] Optionally, the RBF neural network described in step S4 is a multi-layer feedforward network, including an input layer, hidden layers, and an output layer, wherein:

[0039] The input layer is used to receive the system's state information, which is a 6-dimensional vector z, and its mathematical expression is:

[0040]

[0041] The hidden layer employs a predetermined number of Gaussian function nodes, and the basis function expression for each node is as follows:

[0042]

[0043] Where σ is the width parameter, C j The center of the j-th node;

[0044] The output layer updates its weights through an online adaptive law, which is based on a composite sliding surface S-design.

[0045] Optionally, the hidden layer employs 49 Gaussian function nodes.

[0046] Optionally, the output layer updates the weights through an online adaptive law, which is designed based on a composite sliding surface S and specifically includes:

[0047] Define the weight estimation error:

[0048]

[0049] Where w is the actual weight vector, w * These are the ideal weights for an RBF neural network;

[0050] The error approximation can then be expressed as:

[0051]

[0052] Where f(z) is the unknown dynamic function value of the system. This is an approximation value for the unknown dynamics of the system; Let z be the hidden layer output vector, and ε(z) be the approximation error.

[0053] The differential equation for weight estimation is:

[0054]

[0055] Among them, α1 and α2 are positive design parameters;

[0056] Based on the aforementioned adaptive law, at each sampling time, the current composite sliding surface S and the hidden layer output vector are used. Update the actual weight vector w.

[0057] Through the above technical solutions, the beneficial effects of this invention are as follows: This application accurately characterizes the coupling characteristics of the system by constructing a double pendulum dynamic model, adopts a hybrid strategy combining PD control and RBF neural network hierarchical sliding mode control, utilizes RBF neural network to approximate unknown nonlinear dynamics online to compensate for model uncertainty, enhances robustness and coordinates position tracking and double pendulum suppression of multiple objectives through hierarchical sliding mode control, and introduces boundary layer design to eliminate chattering, thereby achieving strong adaptability to changes in system parameters and external disturbances, significantly improving trajectory tracking accuracy and swing suppression effect, and providing an efficient solution for intelligent control of bridge cranes that combines theoretical rigor and engineering practicality. Attached Figure Description

[0058] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention, and the embodiments in the accompanying drawings do not constitute any limitation on the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0059] Figure 1 A flowchart illustrating an adaptive double-swing bridge crane anti-swing control method provided in an embodiment of this application;

[0060] Figure 2 Force analysis diagram of a crane double pendulum mathematical model provided in an embodiment of this application;

[0061] Figure 3 A simulation diagram of the vehicle displacement curve provided in one embodiment of this application;

[0062] Figure 4 A simulation curve of the swing angle θ1 provided in an embodiment of this application;

[0063] Figure 5 A simulation curve of the swing angle θ2 provided in an embodiment of this application;

[0064] Figure 6 A simulation curve of the driving force of a vehicle provided in an embodiment of this application.

[0065] The realization of the purpose, functional features and advantages of this application will be further explained in conjunction with the embodiments and with reference to the accompanying drawings. Detailed Implementation

[0066] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments, which are preferred embodiments of the present invention. It should be understood that the described embodiments are merely some embodiments of the present invention, and not all embodiments; it should be noted that, unless otherwise specified, the embodiments and features in the embodiments of the present invention can be combined with each other. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0067] To better understand the above technical solutions, the following will provide a detailed explanation of the technical solutions in conjunction with the accompanying drawings and specific implementation methods.

[0068] like Figure 1 As shown, an adaptive anti-sway control method for a double-swing bridge crane includes the following steps:

[0069] S1. Based on the actual operating parameters of the bridge crane, construct a double pendulum mathematical model that includes key elements such as trolley, load mass, hook mass, rope swing angle and pendulum length ratio.

[0070] S2. Decompose the double pendulum system into two subsystems: position tracking and angle control. Design a sliding surface for each subsystem and form a unified sliding control surface through a composite strategy.

[0071] S3. Based on the sliding mode control principle, design the overall control law, which includes equivalent control terms, switching control terms, PD control terms, and angle compensation terms.

[0072] S4. Utilize the RBF neural network's ability to approximate unknown dynamics of the system to adjust key parameters in the overall control law in real time, thereby achieving precise position tracking and sway suppression.

[0073] In step S1, as Figure 2 As shown, the mathematical model of the double pendulum uses the Euler-Lagrange equations to derive the system's dynamic equations. The specific derivation process is as follows:

[0074] Let the coordinates of the hook be (X) 钩 Y 钩 ),but:

[0075]

[0076] Hook speed:

[0077]

[0078] The load location coordinates are (X) 负 Y 负 ),but:

[0079]

[0080] Load speed:

[0081]

[0082] The kinetic energy T of the double pendulum system is:

[0083]

[0084] The potential energy V of the system is:

[0085] V=-mgl1 cosθ1-mg(l1 cosθ1+l2 cosθ2)

[0086] Constructing Lagrange operators:

[0087]

[0088] Let the generalized coordinates of the system be: q = (x, y, θ) T By the Euler-Lagrange equations:

[0089]

[0090] We can obtain:

[0091]

[0092] Based on the above, the dynamic equations of the crane double pendulum model lifting system can be simplified to:

[0093]

[0094] Among them, M and m f m g Let θ1 represent the trolley mass, load mass, and hook mass, respectively; θ2 represent the swing angle of the rope l1 relative to the vertical direction; and θ2 represent the swing angle of l2 relative to the vertical direction, with the swing length ratio defined as l1:l2; F represents the trolley driving force; and f represents the coefficient of friction between the trolley and the slide rail.

[0095] The system dynamics equations are expressed in matrix form as follows:

[0096]

[0097] Where M(q) is a positive definite symmetric mass matrix. Let G(q) be the damping matrix, and G(q) be the gravity vector. Q is the generalized force vector of the system, expressed as:

[0098]

[0099]

[0100] In step S2, the double pendulum system is decomposed into two subsystems: position tracking and angle control. A sliding surface is designed for each subsystem to effectively suppress the swaying of the hook and load while the trolley moves along the target position, and finally the control force for controlling the trolley is obtained.

[0101] Reference kinetic equations:

[0102]

[0103] get:

[0104]

[0105] Based on the above formula, the specific steps for designing the sliding surface are as follows:

[0106] Define the desired displacement as x dThen the error between the expected displacement and the actual output displacement x is:

[0107] e = xx d

[0108] Design the sliding surface, where:

[0109] Crane trolley position tracking sliding surface s1:

[0110]

[0111] Hook angle sliding surface s2 and load angle sliding surface s3:

[0112]

[0113] Where λ1 is the position tracking gain parameter, λ2 is the hook angle gain parameter, and λ3 is the load angle gain parameter, and λ1, λ2, and λ3 are all greater than 0;

[0114] Define the new sliding surface as a composite sliding control with three sliding controls:

[0115] S = s1 + β1s2 + β2s3

[0116] Where S is the composite sliding surface, β1 and β2 are the coupling coefficients of the hook angle and the load angle, respectively, used to adjust the weight relationship between position tracking and anti-sway control, and both β1 and β2 are greater than 0.

[0117] Differentiating with respect to the sliding surface, we get:

[0118]

[0119] Among them, λ1 determines the convergence of position and tracking displacement, and λ2 determines the convergence rate of the swing angle. λ1, λ2, β1 and β2 are all greater than 0.

[0120] In step S3, the mathematical expression for the total control law u is:

[0121]

[0122] Among them, u eq This is an equivalent control term used to offset known system dynamics;

[0123] u sw To switch control terms, a smooth saturation function is used to suppress chattering;

[0124] To achieve a smoother control effect, the smoothing saturation function is selected as the approximation function in the switching control item:

[0125]

[0126] The simplified smooth saturation function is:

[0127]

[0128] Δ represents the boundary layer, Δ>0. Using a smooth saturation function can better resist uncertainties and disturbances.

[0129] u pd This is a PD control term; used to improve transient response.

[0130] u a This is an angle compensation term used to suppress angular coupling, and it satisfies the following equation:

[0131]

[0132] Where, k a The gain is controlled by the angle.

[0133] According to the general approximation theorem, RBF neural networks can approximate continuous functions with arbitrary precision. Let the unknown dynamic function of the system be λ(Z). For any continuous function f(Z) ∈ U, where U is an R... m The compactness of the middle.

[0134] For the control law designed in this application, the RBF neural network in step S4 is a multi-layer feedforward network, including an input layer, hidden layers, and an output layer, wherein:

[0135] The input layer receives the system's state information, which is a 6-dimensional vector z, and its mathematical expression is:

[0136]

[0137] The hidden layer uses a preset number of Gaussian function nodes. In this embodiment, the hidden layer uses 49 Gaussian function nodes, and the basis function expression for each node is as follows:

[0138]

[0139] Where σ is the width parameter, C j The center of the j-th node;

[0140] The center of the j-th basis function is:

[0141] C j =[C j1 C j2 ,...,C j6 ]

[0142] The output layer updates the weights through an online adaptive law, which is based on the design of a composite sliding surface S.

[0143] In one specific embodiment, the output layer updates the weights through an online adaptive law, which is designed based on a composite sliding surface S and specifically includes:

[0144] Define the weight estimation error:

[0145]

[0146] Where w is the actual weight vector, w * These are the ideal weights for an RBF neural network;

[0147] The error approximation can then be expressed as:

[0148]

[0149] Where f(z) is the unknown dynamic function value of the system. For the approximation value of the unknown dynamics of the system Let z be the hidden layer output vector, and ε(z) be the approximation error.

[0150] The differential equation for weight estimation is:

[0151]

[0152] Among them, α1 and α2 are positive design parameters;

[0153] Based on the aforementioned adaptive law, at each sampling time, the current composite sliding surface S and the hidden layer output vector are used. Update the actual weight vector w.

[0154] The implementation process of Lyapunov stability analysis:

[0155] The Lyapunov function V1 is selected as follows:

[0156] Nof function:

[0157]

[0158] Where Γ is the gain matrix in the adaptive weight law of the RBF neural network, satisfying positive definiteness and symmetry, Γ=diag(γ,γ,...,γ)∈R 49x49 γ is the adaptive learning rate, which is set to 800 in this design.

[0159] Differentiate with respect to V1:

[0160]

[0161] Substitute the control law into have to:

[0162]

[0163] right Upper bound estimate:

[0164]

[0165] Where ε m ρ1 and ρ2 are positive constants and represent the upper bound of the neural network approximation error.

[0166] Because of Young's inequality, we have:

[0167]

[0168] so Upper Realm:

[0169]

[0170] The values ​​of the control law parameters are shown in the table below:

[0171] Value 2 1.5 1.5 0.3 0.2 10 10 0.5 8

[0172] Because a sufficient condition for the asymptotic stability of the system is:

[0173] 1) η>ε m

[0174] 2)k P >1 / 2ρ1 2

[0175] 3)k d >1 / 2ρ2 2

[0176] 4)k a >max{ρ1,2ρ2}

[0177] Therefore, when the above conditions are met:

[0178] in, Strictly negative definite, the Lyapunov function V1 is monotonically decreasing. The values ​​of the system state variable z asymptotically converge to zero, and the weight estimation error... Maintaining boundedness. This means that when the load is below the hook and the hook is below the trolley during operation, the following conditions are met:

[0179] (1) The position of the vehicle can asymptotically track the desired trajectory;

[0180] (2) The angle of the double pendulum can be stabilized in the vertical position;

[0181] (3) The entire closed-loop system achieves asymptotic stability.

[0182] System simulation:

[0183] To verify the effectiveness of the designed neural network adaptive controller, simulations were performed using theoretical and numerical methods based on the parameters of an actual double pendulum bridge crane platform. The feasibility of the proposed control scheme can be verified kinematically.

[0184] The simulation environment used was MATLAB / Simulink 2023B. The parameters such as trolley mass, hook and lifting weight mass, rope length, and gravitational acceleration were set as follows:

[0185] M = 10 kg, m f =1kg,m g =0.08kg, l1=1m, l2=0.5m, g=9.8m / s 2 .

[0186] The smooth trajectory from the literature "Research on Nonlinear Control Strategy of Underactuated Bridge Crane" is selected as the ideal reference trajectory for trolley positioning, and its expression is as follows:

[0187]

[0188] Where, p d k represents the target position of the crane trolley. d These represent the maximum speed and maximum acceleration of the vehicle, respectively, and parameter ε is the initial acceleration adjustment parameter of the vehicle.

[0189] The neural network controller has 49 nodes (N), with the network center points non-uniformly distributed in the range [-5, 5]. The network width is σ = 0.6, the initial weights are W(0) = 0, and the initial system state is X(0) = [0; 0; 0; 0; 0; 0]. The selected control input is:

[0190] u = u eq +u sw +u pd +u a

[0191]

[0192] Where, k P =10,k d =0.5, k a =5.

[0193] The selected adaptive law is:

[0194]

[0195] Among them, Γ=800, α1=0.2, α2=0.1.

[0196] The simulation results of the car's position are as follows: Figure 3As shown. By Figure 3 As can be seen, the car starts moving from its initial position of 0 meters and reaches the desired position of approximately 20 meters in about 20 seconds, after which it remains stable. This demonstrates that the designed adaptive controller based on the RBF neural network can effectively track the predetermined target and exhibits good dynamic response characteristics.

[0197] Figure 4 and Figure 5 The changes in the hook swing angle θ1 and the load swing angle θ2 are shown separately. As can be seen from the figure, during the trolley's movement, the maximum deviation of both swing angles is controlled within ±3 degrees, and they converge rapidly to near 0 degrees after t = 40 seconds, indicating that the controller has good anti-sway performance. The trends of the two swing angles are basically consistent, indicating that the system has good coordination.

[0198] Figure 6 The curve of the driving force of the vehicle is presented. The control force fluctuates within ±6N, peaking at approximately t=20s, which corresponds to the acceleration and sway angle suppression phases of the vehicle. Afterward, the control force gradually approaches zero, and the system reaches a steady state. The control input is smooth, without any violent oscillations, indicating that the designed controller has good robustness.

[0199] Simulation results show that the adaptive control method based on RBF neural network proposed in this invention can simultaneously achieve precise positioning of the vehicle and effective suppression of double sway, demonstrating strong engineering application value. The controller exhibits excellent performance in terms of system state convergence, anti-sway performance, and control input stability.

[0200] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (devices), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0201] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1The function specified in one or more boxes.

[0202] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0203] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0204] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. An adaptive double-swing bridge crane anti-swing control method, characterized in that, Includes the following steps: S1. Based on the actual operating parameters of the bridge crane, construct a double pendulum mathematical model that includes the trolley mass, load mass, hook mass, rope swing angle, pendulum length ratio, trolley driving force, and friction coefficient between the trolley and the slide rail. S2. Decompose the double pendulum system into two subsystems: position tracking and angle control. Design a sliding surface for each subsystem and form a unified sliding control surface through a composite strategy. S3. Based on the sliding mode control principle, design the overall control law, which includes equivalent control terms, switching control terms, PD control terms, and angle compensation terms. S4. Utilize the RBF neural network's ability to approximate unknown dynamics of the system to adjust key parameters in the overall control law in real time, so as to achieve precise position tracking and sway suppression. The mathematical model of the double pendulum described in step S1 uses the Euler-Lagrange equations to derive the system dynamics equations, and its mathematical expression is as follows: in, , , These represent the trolley mass, the load mass, and the hook mass, respectively. For the suspension rope The angle of swing relative to the vertical direction; for The angle of the pendulum relative to the vertical direction, and the ratio of the pendulum length is defined as... : ; F This provides the driving force for the car. f The coefficient of friction between the trolley and the slide rail; The system dynamics equations are expressed in matrix form as follows: in, It is a positive definite symmetric mass matrix. Here is the damping matrix. The gravity vector The generalized force vector of the system; Step S2 decomposes the double pendulum system into two subsystems: position tracking and angle control. A sliding surface is designed for each subsystem. The specific steps are as follows: Define the desired displacement as The expected displacement and the actual output displacement are then... The error is: Design the sliding surface, where: Crane trolley position tracking slip surface : Hook angle sliding surface and load angle sliding surface : in, For position tracking gain parameters, This refers to the hook angle gain parameter. For load angle gain parameters, and All are greater than 0; Define the new sliding surface as a composite sliding control with three sliding controls: in, It is a composite sliding surface. and These are the coupling coefficients for the hook angle and the load angle, respectively, used to adjust the weighting relationship between position tracking and anti-sway control. and All are greater than 0; The overall control law described in step S3 The mathematical expression is: in, This is an equivalent control term used to offset known system dynamics; To switch control terms, a smooth saturation function is used to suppress chattering; This is a PD control term; used to improve transient response. This is an angle compensation term used to suppress angular coupling, and it satisfies the following equation: in, Gain is controlled by angle; The RBF neural network described in step S4 is a multi-layer feedforward network, including an input layer, hidden layers, and an output layer, wherein: The input layer is used to receive the system's state information, which is a 6-dimensional vector. Its mathematical expression is: The hidden layer employs a predetermined number of Gaussian function nodes, and the basis function expression for each node is as follows: in, It is the width parameter. For the first Each node center; The output layer updates the weights through an online adaptive law, which is based on a composite sliding surface. .

2. The method according to claim 1, characterized in that, The hidden layer uses 49 Gaussian function nodes.

3. The method according to claim 2, characterized in that, The output layer updates the weights through an online adaptive law, which is based on a composite sliding surface. Specifically, it includes: Define the weight estimation error: in, This is the actual weight vector. These are the ideal weights for an RBF neural network; The error approximation is then expressed as: in, For unknown dynamic function values ​​of the system, This is an approximation value for the unknown dynamics of the system; This is the output vector of the hidden layer. To approximate the error; The differential equation for weight estimation is: in, , Positive design parameters; According to the above adaptive law, at each sampling time, the current composite sliding surface is used. and hidden layer output vector For the actual weight vector Update.

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