A Control Method for Intelligent Equipment for Live-Line Working in Distribution Networks Based on Sliding Mode Control

Abstract

This invention relates to the technical field of electrical automation and discloses a control method for intelligent live-line working equipment in power distribution networks based on sliding mode control. The method includes optimizing the dynamic model of the N-joint intelligent live-line working equipment to construct an error dynamic model. Simultaneously, a linear extended state observer is designed to perform real-time observation and compensation for unknown and uncertain terms in the tracking error dynamic model of the N-joint intelligent live-line working equipment. The design of a neural network adaptive global non-singular terminal sliding mode controller can achieve high-precision tracking control by ensuring finite-time convergence, avoiding singularities, and enhancing robustness while simultaneously adapting parameters.

Description

Technical Field

[0001] This invention relates to the technical field of electrical automation, and in particular to a control method for intelligent equipment for live-line work in power distribution networks based on sliding mode control. Background Technology

[0002] Bionic live-line working intelligent equipment is characterized by its adaptability to narrow spaces, diverse movement forms, fault resistance, high-precision inspection, and reduced human resource consumption. It can move flexibly in confined spaces, such as narrow gaps between power towers or complex truss structures of cables. Its ability to change body shape helps the robot climb power towers and cross complex terrains such as cable trenches to complete inspection tasks. Even if a fault occurs in one part, it will not affect the completion of the entire task. Furthermore, it is equipped with a variety of sensors to reduce human error and improve inspection accuracy.

[0003] However, in reality, modeling intelligent equipment for live-line working is complex and difficult to solve. It is often difficult to use complex control algorithms to achieve efficient tracking and control, and some simple control algorithms are difficult to achieve high-precision control. Therefore, the optimization of the model and the design of high-precision control algorithms are crucial for the control of intelligent equipment for live-line working. Summary of the Invention

[0004] The purpose of this section is to outline some aspects of embodiments of the present invention and to briefly describe some preferred embodiments. Simplifications or omissions may be made in this section, as well as in the abstract and title of this application, to avoid obscuring the purpose of these documents; however, such simplifications or omissions should not be construed as limiting the scope of the invention.

[0005] In view of the aforementioned existing problems, the present invention is proposed.

[0006] Therefore, this invention provides a control method for intelligent equipment for live-line work in distribution networks based on sliding mode control. While optimizing the mathematical model, it proposes a neural network adaptive global nonlinear terminal sliding mode control method based on a linear extended state observer.

[0007] To address the aforementioned technical problems, this invention provides the following technical solution: It includes: reconstructing the tracking error dynamic model of an N-joint live-line working intelligent device based on its dynamic model; designing a linear extended state observer to perform real-time observation and compensation for unknown and uncertain terms in the tracking error dynamic model; constructing a globally non-singular terminal sliding surface based on the characteristics of finite-time arrival of the terminal sliding mode, avoidance of convergence stagnation by non-singularity, and rapid attainment of the sliding surface by the global sliding mode; designing a neural network adaptive isotropic approach rate based on the constructed globally non-singular terminal sliding surface; and designing a neural network adaptive globally non-singular terminal sliding mode controller for the N-joint live-line working intelligent device system based on the linear extended state observer, the globally non-singular terminal sliding surface, and the neural network adaptive isotropic approach rate.

[0008] As a preferred embodiment of the intelligent equipment control method for live-line working in distribution networks based on sliding mode control described in this invention, the method includes: reconstructing the tracking error dynamic model of the N-joint intelligent equipment for live-line working, including...

[0009] The dynamic model of the N-joint live-line working intelligent equipment is as follows:

[0010]

[0011] Where, q φ =[φ1,…,φ N-1 ,φ N ,p x ,p y ] T ∈R (N+2)×1 φ i It is the i-th joint angle of the live-line working intelligent equipment, (p x ,p y ) is the centroid coordinate of the intelligent live-line working device; M(φ)∈R (N+2)×(N+2) It is the system's inertia matrix. It is the matrix of Coriolis force and centripetal force. G(φ)∈T (N+2)×2N and These are the matrices of gravity and friction, respectively. u is the joint input torque, u = [u1, ..., u] N-1 ,0,0,0] T ∈R (N+2)×1 .

[0012] The tracking error of the N-joint live-line working intelligent device is defined as:

[0013]

[0014] in, It is the target trajectory of the N-joint live-line working intelligent equipment; q φ (t) is the actual trajectory of the N-joint live-line working intelligent equipment; e(t)∈R (N+2)×1 It is the tracking error of the N-joint live-line working intelligent equipment.

[0015] The second-order differential of the tracking error of the aforementioned N-joint live-line working intelligent device is:

[0016]

[0017] in, It is the second differential of e(t). yes The second derivative, It is q φ The second derivative of (t).

[0018] definition The matrix is ​​used to modify the dynamic model of the N-joint live-line working intelligent equipment as follows:

[0019]

[0020] in, It is a dimensionless parameter-tuning gain matrix.

[0021] Substituting the second derivative of the tracking error, we construct a dynamic model of the tracking error of the N-joint live-line working intelligent equipment:

[0022]

[0023] As a preferred embodiment of the intelligent equipment control method for live-line working in distribution networks based on sliding mode control described in this invention, the method includes: designing a linear extended state observer, comprising,

[0024] The linear extended state observer is defined as follows:

[0025]

[0026] Where z1 is the actual trajectory q of the N-joint live-line working intelligent device. φ The observed value of (t), z2 is the observed value of F(t) for uncertainties and unknown disturbances in the dynamic model of the N-joint live-line working intelligent equipment, e1=z1(t)-q φ (t) is the observation error of the linear extended state observer on the actual output trajectory.

[0027] As a preferred embodiment of the intelligent equipment control method for live-line working in distribution networks based on sliding mode control described in this invention, the method includes: designing a globally non-singular terminal sliding mode surface, comprising,

[0028] The global non-singular terminal sliding surface is designed as follows:

[0029]

[0030]

[0031] Where ηe(t) is the tracking error proportional term of the N-joint live-line working intelligent equipment, and η is the proportional term parameter adjustment gain; For non-singular terms, ω, And σ are non-singular term tuning gains, which must satisfy: and σ is a positive odd number.

[0032] The first-order differential of the globally nonsingular terminal sliding surface is as follows:

[0033]

[0034] in, It is the first differential of s(t) with respect to time t. They are s1(t), s2(t), ..., s N (t),S N+1 (t),s N+2 (t) is the first differential of time t.

[0035] As a preferred embodiment of the intelligent equipment control method for live-line working in distribution networks based on sliding mode control described in this invention, the method includes: designing an adaptive constant-rate approaching law for a neural network, comprising,

[0036] The adaptive constant velocity approach law design is as follows:

[0037]

[0038] in, It is the adaptive term parameter of the constant velocity approach rate.

[0039] As a preferred embodiment of the intelligent equipment control method for live-line working in distribution networks based on sliding mode control described in this invention, it further includes:

[0040] The neural network adaptive rate is designed as follows:

[0041]

[0042] in, It is the parameter of the constant velocity approach rate adaptive term. The approximation is given by ζ, where ζ is the control gain of the adaptive rate, and h(x) is the activation function of the hidden layer of the neural network observer. Γ represents the optimal weights from the hidden layer to the output layer of the neural network, where Γ is the weight between... and The approximate error, It is W * The estimated value, yes The adaptive rate.

[0043] The activation function for the hidden layer is chosen to be a cubic B-spline basis function, defined as:

[0044] h(x) = [h1(t),h2(t),…,h N (t),h N+1 (t),h N+2 (t)]

[0045]

[0046] When ||xo i ||≤h i When, and i = 1, 2, ..., N+2

[0047]

[0048] When h i <||xo i ||≤2h i When, and i = 1, 2, ..., N+2

[0049]

[0050] When 2h i <||xo i When ||, and i = 1, 2, ..., N+2

[0051] h i (x) = 0;

[0052] Among them, ||xo i || represents the Euclidean distance between the input vector and the center vector; x is the input vector; o and o i It is the center vector; h i It is the width of the cubic B-spline function.

[0053] As a preferred embodiment of the intelligent equipment control method for live-line working in distribution networks based on sliding mode control described in this invention, the designed controller includes:

[0054] Combining a linearly extended state observer, a globally non-singular terminal sliding mode surface, and a neural network adaptive isotropic approach rate, the N-joint live-line working intelligent equipment system is designed with a neural network adaptive globally non-singular terminal sliding mode controller based on a linearly extended state observer as follows:

[0055]

[0056] The beneficial effects of this invention are as follows: This invention optimizes the dynamic model of an N-joint live-line working intelligent device and constructs an error dynamic model. Simultaneously, a linear extended state observer is used to observe uncertainties and disturbances, thereby compensating for them in the constructed error dynamic model of the live-line working intelligent device. The design of the adaptive global non-singular terminal sliding mode controller can adapt parameters while ensuring finite-time convergence, avoiding singular phenomena, and enhancing robustness, achieving high-precision tracking control. Attached Figure Description

[0057] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. Wherein:

[0058] Figure 1 This is a schematic diagram of the principle control framework of the intelligent equipment control method for live-line working in distribution networks based on sliding mode control according to the present invention.

[0059] Figure 2 This is a comparison of the tracking performance of a three-degree-of-freedom intelligent equipment for live-line work in distribution networks with a joint angle 1 under a target trajectory (aim1) and a traditional PID control method.

[0060] Figure 3 The diagram shows the target trajectory tracking effect of a three-degree-of-freedom intelligent equipment for live-line working in a distribution network, with joint angle 2 as the target trajectory 2 (aim2), compared with the traditional PID control method.

[0061] Figure 4 This is a flowchart of a control method for intelligent equipment for live-line working in power distribution networks based on sliding mode control, according to the present invention. Detailed Implementation

[0062] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the protection scope of the present invention.

[0063] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and those skilled in the art can make similar extensions without departing from the spirit of the invention. Therefore, the invention is not limited to the specific embodiments disclosed below.

[0064] Secondly, the term "one embodiment" or "embodiment" as used herein refers to a specific feature, structure, or characteristic that may be included in at least one implementation of the present invention. The phrase "in one embodiment" appearing in different places in this specification does not necessarily refer to the same embodiment, nor is it a single or selective embodiment that is mutually exclusive with other embodiments.

[0065] This invention is described in detail with reference to the schematic diagrams. When detailing the embodiments of this invention, for ease of explanation, the cross-sectional views illustrating the device structure may be partially enlarged, not adhering to the usual scale. Furthermore, the schematic diagrams are merely examples and should not be construed as limiting the scope of protection of this invention. In actual fabrication, the three-dimensional spatial dimensions of length, width, and depth should be included.

[0066] Furthermore, in the description of this invention, it should be noted that the terms "upper," "lower," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. These terms are used solely for the convenience of describing the invention and for simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the invention. In addition, the terms "first," "second," or "third" are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0067] Unless otherwise explicitly specified and limited, the terms "installation," "connection," and "joining" in this invention should be interpreted broadly. For example, they can refer to fixed connections, detachable connections, or integral connections; similarly, they can refer to mechanical connections, electrical connections, or direct connections, or indirect connections through an intermediate medium, or internal connections between two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0068] Example 1

[0069] Reference Figure 1 , Figure 4This invention provides a control method for intelligent live-line working equipment in power distribution networks based on sliding mode control. The method reconstructs the tracking error dynamic model of the N-joint intelligent live-line working equipment based on its dynamic model. For the unknown and uncertain terms in the tracking error dynamic model, a linear extended state observer is designed for real-time observation and compensation. Based on the characteristics of finite-time arrival of terminal sliding mode, avoidance of convergence stagnation by non-singularity, and rapid attainment of the sliding surface by global sliding mode, a global non-singular terminal sliding surface is constructed. Based on the constructed global non-singular terminal sliding surface, a neural network adaptive isotropic approach rate combined with the linear extended state observer, the global non-singular terminal sliding surface, and the neural network adaptive isotropic approach rate is designed to create a neural network adaptive global non-singular terminal sliding mode controller for the N-joint intelligent live-line working equipment system based on the linear extended state observer.

[0070] S1: Based on the dynamic model of the N-joint live-line working intelligent equipment, reconstruct the tracking error dynamic model of the N-joint live-line working intelligent equipment. The following points need to be noted in this step:

[0071] The dynamic model of the N-joint live-line working intelligent device is as follows.

[0072]

[0073] Where, q φ =[φ1,…,φ N-1 ,φ N ,p x ,p y ] T ∈R (N+2)×1 φ i It is the i-th joint angle of the live-line working intelligent equipment, (p x ,p y ) is the centroid coordinate of the intelligent live-line working device; M(φ)∈R (N+2)×(N+2) It is the system's inertia matrix. It is the matrix of Coriolis force and centripetal force. G(φ)∈R (N+2)×2N and These are the matrices of gravity and friction, respectively. u is the joint input torque, u = [u1, ..., u] N-1 ,0,0,0] T ∈R (N+2)×1 .

[0074] The tracking error of the N-joint live-line working intelligent device is defined as:

[0075]

[0076] in, It is the target trajectory of the N-joint live-line working intelligent equipment; q φ (t) is the actual trajectory of the N-joint live-line working intelligent equipment; e(t)∈R (N+2)×1 It is the tracking error of the N-joint live-line working intelligent equipment.

[0077] The second-order differential of the tracking error of the aforementioned N-joint live-line working intelligent device is:

[0078]

[0079] in, It is the second differential of e(t). yes The second derivative, It is q φ The second derivative of (t).

[0080] definition The matrix is ​​used to modify the dynamic model of the N-joint live-line working intelligent equipment as follows:

[0081]

[0082] in, It is a dimensionless parameter-tuning gain matrix.

[0083] Substituting the second derivative of the tracking error, we construct a dynamic model of the tracking error of the N-joint live-line working intelligent equipment:

[0084]

[0085] S2: For the unknown and uncertain terms in the dynamic model of the tracking error of the intelligent equipment for live-line working at joint N, a linear extended state observer is designed to perform real-time observation and compensation. The following points need to be noted in this step:

[0086] The linear extended state observer is defined as follows:

[0087]

[0088] Where z1 is the actual trajectory q of the N-joint live-line working intelligent device. φ The observed value of (t), z2 is the observed value of F(t) for uncertainties and unknown disturbances in the dynamic model of the N-joint live-line working intelligent equipment, e1=z1(t)-q φ(t) is the observation error of the linear extended state observer on the actual output trajectory.

[0089] S3: Based on the characteristics of finite-time arrival of the terminal sliding mode, avoidance of convergence stagnation by non-singularity, and rapid arrival of the global sliding mode at the sliding surface, a globally non-singular terminal sliding surface is constructed. The following points need to be explained in this step:

[0090] The global non-singular terminal sliding surface is designed as follows:

[0091]

[0092] Where ηe(t) is the tracking error proportional term of the N-joint live-line working intelligent equipment, and η is the proportional term parameter adjustment gain; For non-singular terms, ω, And σ are non-singular term tuning gains, which must satisfy: and σ is a positive odd number.

[0093] The first-order differential of the globally nonsingular terminal sliding surface is as follows:

[0094]

[0095] in, It is the first differential of s(t) with respect to time t. They are s1(t), s2(t), ..., s N (t),s N+1 (t),S N+2 (t) is the first differential of time t.

[0096] S4: Based on the constructed global non-singular terminal sliding mode surface, design an adaptive isorhythmic approach rate for the neural network. The following points need to be explained in this step:

[0097] The adaptive constant velocity approach law design is as follows:

[0098]

[0099] in, It is the adaptive term parameter of the constant velocity approach rate.

[0100] The neural network adaptive rate is designed as follows:

[0101]

[0102] in, It is the parameter of the constant velocity approach rate adaptive term. The approximation is given by ζ, where ζ is the control gain of the adaptive rate, and h(x) is the activation function of the hidden layer of the neural network observer. Γ represents the optimal weights from the hidden layer to the output layer of the neural network, where Γ is the weight between... and The approximate error, It is W * The estimated value, yes The adaptive rate.

[0103] The activation function for the hidden layer is chosen to be a cubic B-spline basis function, defined as:

[0104] h(x) = [h1(t),h2(t),…,h N (t),h N+1 (t),h N+2 (t)]

[0105]

[0106] When ||xo i ||≤h i When, and i = 1, 2, ..., N+2

[0107]

[0108] When h i <||xo i ||≤2h i When, and i = 1, 2, ..., N+2

[0109]

[0110] When 2h i <||xo i When ||, and i = 1, 2, ..., N+2

[0111] h i (x) = 0;

[0112] Among them, ||xo i || represents the Euclidean distance between the input vector and the center vector; x is the input vector; o and o i It is the center vector; h i It is the width of the cubic B-spline function.

[0113] S5: Combining a linear extended state observer, a global non-singular terminal sliding mode surface, and a neural network adaptive isotropic approach rate, design an N-joint live-line working intelligent equipment system based on a neural network adaptive global non-singular terminal sliding mode controller using a linear extended state observer. The following points need to be explained in this step:

[0114] The controller is designed as follows:

[0115]

[0116] Preferably, this embodiment also requires further explanation that, compared with the prior art, this embodiment discloses a control method for intelligent equipment for live-line working in power distribution networks based on sliding mode control. It uses a tracking error dynamic model to replace the complex dynamic model of the actual N joints of the intelligent equipment for live-line working, thereby simplifying the mathematical model in the control process. Simultaneously, to address uncertainties and disturbances in the system, a linear extended state observer is used for real-time compensation feedback. Furthermore, an adaptive global non-singular terminal sliding mode control method is designed, which not only ensures that the robot can achieve fast and high-precision tracking control, but also prevents convergence stagnation throughout the control process, thus effectively guaranteeing the stability and accuracy of the tracking effect.

[0117] Example 2

[0118] Reference Figures 2-3 This is another embodiment of the present invention, which differs from the first embodiment in that it provides a test verification of a control method for intelligent equipment for live-line working in distribution networks based on sliding mode control, including:

[0119] To verify the effectiveness of the technology used in this method, this embodiment compares the traditional PID control method with the method of this invention. The experimental results are compared using scientific methods to verify the actual effectiveness of this method.

[0120] The physical parameters of the three-degree-of-freedom live-line working intelligent device are as follows: N = 4 joint links; the mass of a single link is m = 0.25 kg, and the mass of each link is uniformly distributed; the joint length is l = 0.08 m; and the ground friction force is c. t =1,c n =10, J=0.0064kg×m 2 .

[0121] The vector and inertia matrices used in the three-degree-of-freedom live-line working intelligent equipment system are:

[0122]

[0123] M θ =JI N +ml 2 S θ VS θ +ml 2 Cθ VC θ V = A T (ZZ T ) -1 A; W = ml 2 S θ VC θ -ml 2 C θ VS θ ;

[0124] The input and output vectors of the intelligent live-line working device are φ = [φ1, φ2], respectively. T , u = [u1, u2] T The initial condition for the intelligent live-line working device is φ(0) = [0,0]. T rad,

[0125] The target trajectory of joint angle 1 is: The target trajectory of joint angle 2 is: φ ref2 =sin(πt).

[0126] The parameters of the global fractional-order nonsingular terminal sliding mode controller of this invention are: α=diag(0.564.22.75), β=diag(0.0820.47.53), γ=diag(37425), eta=diag(17.5,20,15,13.5,10), σ=7, h i =[1,2,5,8,1],

[0127] The controller used in comparison is a traditional PID controller: The controller parameter is k. tp =diag(3.5,2.95,0,0,0), k ti =diag(10.25,8.35,0,0,0), k td =diag(0.02.0.015,0,0,0).

[0128] Test environment: Refer to Figure 1In the MATLAB 2019a SIMULINK environment, a controlled object model of the intelligent live-line working device was built based on the existing physical parameters and mathematical models of the device. The control methods of the intelligent live-line working device, namely the neural network adaptive global terminal sliding mode control method and the traditional PID control method, were used to track and control the driven joints 1 and 2 under different target trajectories, and test results were obtained. Both methods were simulated and tested using automated testing equipment and MATLAB software programming. Simulation data was obtained based on the experimental results. Four sets of data were tested for each method, with each set sampled for 10 seconds. The input target trajectory and output tracking trajectory of each set of data were calculated and compared to verify the feasibility of the proposed algorithm.

[0129] Reference Figure 2 This invention compares the tracking performance of a neural network adaptive global terminal sliding mode control (SMC) method and a traditional PID control method under a target trajectory (aim1) with a drive joint angle 1. (Refer to...) Figure 3 This paper compares the tracking performance of the neural network adaptive global terminal sliding mode control (SMC) method and the traditional PID control method under the target trajectory 2 (aim2) of this invention. As shown in the figure, both the neural network adaptive global terminal sliding mode control (SMC) method and the traditional PID control method can track the target trajectory 1 (aim1) and the target trajectory 2 (aim2) overall. However, in terms of convergence speed, steady-state error, and stability, the neural network adaptive global terminal sliding mode control (SMC) method is superior to the traditional PID control method in all aspects. This is due to the real-time compensation of disturbances and uncertainties by the linear extended state observer, and the designed self-neural adaptive global linear terminal sliding mode controller, which can achieve global convergence, reach the sliding surface in a finite time, and solve the convergence stall problem.

[0130] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A control method for intelligent equipment for live-line working in distribution networks based on sliding mode control, characterized in that: include, S1, based on The dynamic model of the intelligent equipment for live-line working of joints was reconstructed. Dynamic model of tracking error of intelligent equipment for live-line working; S2, to To identify the unknown and uncertain terms in the dynamic model of tracking error of intelligent equipment for live-line work, a linear extended state observer is designed to perform real-time observation and compensation. S3. Based on the characteristics of terminal sliding mode reaching the sliding surface in a finite time, non-singularity avoiding convergence stagnation, and global sliding mode quickly reaching the sliding surface, construct a globally non-singular terminal sliding surface. S4. Based on the constructed global non-singular terminal sliding surface, design an adaptive constant velocity approach rate for the neural network. S5. Combining a linearly extended state observer, a globally non-singular terminal sliding surface, and a neural network-adaptive isotropic approaching rate, design... The intelligent equipment system for live-line working of joints is based on a neural network adaptive global non-singular terminal sliding mode controller with a linear extended state observer; The design of the globally non-singular terminal sliding surface of S3 is as follows: The global non-singular terminal sliding surface is designed as follows: ； in, for The tracking error ratio of intelligent equipment for live-line working of joints. Adjust the gain for the proportional term; For non-singular terms, , and For non-singular term parameter tuning gain, the following must be satisfied: and , It is a positive odd number; The first-order differential of the globally nonsingular terminal sliding surface is as follows: ； ； ； in, yes Regarding time The first-order differential, They are Regarding time The first differential.

2. The intelligent equipment control method for live-line working in distribution networks based on sliding mode control according to claim 1, characterized in that, The dynamic model of the N-joint live-line working intelligent device of S1 is as follows. ， in, , It is the first intelligent equipment for live-line working One joint angle, ( () represents the centroid coordinates of the intelligent live-line working equipment; It is the system's inertia matrix. ; It is the matrix of Coriolis force and centripetal force. ; These are the matrices of gravity and friction, respectively. ， ;u is the joint input torque, ; The tracking error of the N-joint live-line working intelligent device is defined as: in, It is as described The target trajectory of intelligent equipment for live-line work on joints; It is as described The actual trajectory of the intelligent equipment for live-line work on joints; It is as described Tracking error of intelligent equipment for live-line working of joints; The above Second-order differential of tracking error of intelligent equipment for live-line working of joints: in, yes The second derivative, yes The second derivative, yes The second derivative; definition Matrix, The dynamic model of the intelligent equipment for live-line working is revised as follows: in, It is a dimensionless parameter-tuning gain matrix. , ; Substituting the second derivative of the tracking error, we construct... Dynamic model of tracking error of intelligent equipment for live-line working: .

3. A control method for intelligent equipment for live-line working in distribution networks based on sliding mode control according to claim 1 or 2, characterized in that, The linear extended state observer of S2 is designed as follows: The linear extended state observer is defined as follows: in, yes The actual trajectory of the intelligent equipment for live-line work on joints The observed values, yes Uncertainties and unknown disturbances in the dynamic model of intelligent equipment for live-line working. Observations It is the observation error of the linear extended state observer on the actual output trajectory.

4. A control method for intelligent equipment for live-line working in distribution networks based on sliding mode control according to claim 1 or 2, characterized in that, The neural network adaptive constant-rate approach rate design of S4 is as follows: The adaptive constant velocity approach law design is as follows: ； in, It is the adaptive term parameter of the constant velocity approach rate. , , .

5. The intelligent equipment control method for live-line working in distribution networks based on sliding mode control according to claim 4, characterized in that, The S4 also includes, The neural network adaptive rate is designed as follows: ； in, It is the parameter of the constant velocity approach rate adaptive term. Approximate value, It is the control gain of the adaptive rate. It is the activation function of the hidden layer of the observer in the neural network. These are the optimal weights from the hidden layer to the output layer of the neural network. It is between and The approximate error, yes The estimated value, yes The adaptive rate; The activation function for the hidden layer is chosen to be a cubic B-spline basis function, defined as: when At that time, and when At that time, and when At that time, and ； in, The Euclidean norm represents the distance between the input vector and the center vector; It is the input vector; and It is the center vector; It is the width of the cubic B-spline function.

6. A control method for intelligent equipment for live-line working in distribution networks based on sliding mode control according to claim 1 or 2, characterized in that, The controller design for the S5 is as follows: Combining a linearly extended state observer, a globally non-singular terminal sliding surface, and a neural network-adaptive isotropic approach rate, The intelligent equipment system for live-line working is designed with a neural network adaptive global non-singular terminal sliding mode controller based on a linear extended state observer. 。

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