A Fuzzy Control Method for Tether Deployment of a Two-Body Tethered Satellite

Abstract

This embodiment discloses a fuzzy control method for tether deployment of a two-body tethered satellite, which belongs to the field of aerospace technology. It is to solve the problem that the existing technology cannot take into account both the nonlinear dynamics characterization and the controller design of the tethered satellite system at the same time. The fuzzy control method includes: establishing the nonlinear dynamic equation of the two-body tethered satellite system according to the Euler-Lagrange equation; selecting the nonlinear function from the established nonlinear dynamic equation; respectively constructing the fuzzy expression forms of the nonlinear functions; substituting the fuzzy expressions into the system nonlinear dynamic equation, and designing the fuzzy description rules of the system to establish a fuzzy dynamic model; based on the fuzzy dynamic model, through the parallel distributed compensation principle, designing the fuzzy controller rules based on state feedback to establish a fuzzy controller; using the fuzzy controller to control the tether release process of the two-body tethered satellite system.

Description

Technical Field

[0001] The present invention relates to the field of aerospace technology, and in particular to a fuzzy control method for tether deployment of a two-body tethered satellite system. Background Art

[0002] At present, tethered satellite technology has become the most attractive emerging space science and technology, showing broad application prospects in the fields of space exploration, national defense security, etc.

[0003] A tethered satellite refers to a combined flight system formed by connecting two or more artificial satellites through a tether. By means of a retractable mechanism installed on the satellite, the deployment, retention, and recovery operations of the tether can be realized, and then space tasks such as detection, capture, and on-orbit service at distances ranging from several meters to dozens of kilometers can be completed.

[0004] Due to the flexible characteristics of the tether, the motion processes of the deployment, retention, and recovery of the tethered satellite show strong nonlinear and time-varying characteristics. In addition, factors such as multi-physical field coupling in space, rigid-flexible coupling, and coupling of slow orbital variation and fast attitude variation will further induce complex nonlinear phenomena such as chaos, buckling, and bifurcation in the system. It can be seen that the tethered satellite system is a complex nonlinear dynamic system with multiple variables, strong coupling, easy perturbation of physical parameters, and continuous influence of external disturbances. At present, it is difficult to simultaneously meet the requirements of accurately describing the nonlinear dynamic behavior of the system and facilitating the design of the controller in the research on the dynamic modeling of tethered satellites. Summary of the Invention

[0005] An embodiment of the present invention provides a fuzzy control method for tether deployment of a two-body tethered satellite system, which can simultaneously take into account the accuracy of the nonlinear dynamics description of the tethered satellite system and the problem of facilitating the design of the controller.

[0006] To achieve the above object, the embodiment of the present invention adopts the following technical solutions:

[0007] S1. Establish a nonlinear dynamic model for the two-body tethered satellite system;

[0008] S2. Extract the nonlinear function information from the nonlinear dynamic model, and construct fuzzy expression data according to the extracted nonlinear function information;

[0009] S3. Import the constructed fuzzy expression data into the nonlinear dynamic model, and obtain the fuzzy dynamic model of the two-body tethered satellite system;

[0010] S4. Establish a fuzzy controller by using the fuzzy dynamic model;

[0011] S5. Deploy the fuzzy controller to a control device for tether deployment of a two-body tethered satellite system, and use the fuzzy controller to control a tether release process of the two-body tethered satellite system.

[0012] At present, it is difficult to simultaneously take into account the requirements of accurate description of the nonlinear dynamic behavior of the system and convenience of controller design in the dynamic modeling research of tethered satellites. In order to solve the above-mentioned existing problems, this embodiment discloses a fuzzy control scheme for a two-body tethered satellite system. On the basis of sufficient nonlinear dynamic analysis, a fuzzy dynamic model of the system is established. The established fuzzy dynamic model can not only accurately characterize the complex nonlinear dynamic characteristics of the system, but also facilitate controller design and motion stability analysis. The problem that the nonlinear dynamic characterization and controller design of the tethered satellite system cannot be taken into account at the same time in the prior art is solved. Among them, the nonlinear dynamic equation of the two-body tethered satellite system is established according to the Euler-Lagrange equation; a nonlinear function is selected from the established nonlinear dynamic equation; and the fuzzy expression form of the nonlinear function is constructed respectively; then the fuzzy expression is substituted into the nonlinear dynamic equation of the system, and the fuzzy description rule of the system is designed to establish a fuzzy dynamic model; based on the fuzzy dynamic model, a fuzzy controller rule based on state feedback is designed through the parallel distributed compensation principle to establish a fuzzy controller; and the fuzzy controller is used to control the tether release process of the two-body tethered satellite system. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0014] Figure 1 The length of the tether provided in the embodiment of the present invention Schematic diagram of the response curve under control action;

[0015] Figure 2 A schematic diagram of a response curve of the in-plane angle ρ under control provided by an embodiment of the present invention;

[0016] Figure 3 The tether tension provided by the embodiment of the present invention Schematic diagram of the response curve;

[0017] Figure 4 A schematic diagram of a two-body tethered satellite system provided in an embodiment of the present invention.

[0018] Figure 5Schematic diagram of the method flow provided by the embodiments of the present invention. Detailed implementation manners

[0019] To enable those skilled in the art to better understand the technical solutions of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings and specific implementation manners. The embodiments of the present invention will be described in detail below. Examples of the embodiments are shown in the accompanying drawings, where the same or similar reference numerals indicate the same or similar elements or elements with the same or similar functions from beginning to end. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and cannot be construed as a limitation to the present invention. Those skilled in the art of the present technology can understand that, unless specifically stated otherwise, the singular forms "a", "an", "the" and "said" used herein may also include the plural forms. It should be further understood that the term "comprising" used in the description of the present invention means the presence of the described features, integers, steps, operations, elements and / or components, but does not exclude the presence or addition of one or more other features, integers, steps, operations, elements, components and / or their groups. It should be understood that when we say that an element is "connected" or "coupled" to another element, it can be directly connected or coupled to other elements, or there may also be intermediate elements. In addition, the "connection" or "coupling" used here may include wireless connection or coupling. The phrase "and / or" used here includes any unit and all combinations of one or more related listed items. Those skilled in the art of the present technology can understand that, unless otherwise defined, all terms (including technical terms and scientific terms) used here have the same meaning as the general understanding of those of ordinary skill in the art to which the present invention belongs. It should also be understood that terms such as those defined in a general dictionary should be understood to have a meaning consistent with the meaning in the context of the prior art, and will not be interpreted with an idealized or overly formal meaning unless defined as here.

[0020] The embodiments of the present invention provide a fuzzy control method for tether deployment of a two-body tethered satellite, which relates to the dynamics and control problems of a two-body tethered satellite system in the orbital plane. This method can be applied to a tether deployment scenario of a two-body tethered satellite as shown in Figure 4 In the tether deployment scenario of a two-body tethered satellite as shown. In this two-body tethered satellite system, the sub-satellite and the mother satellite are connected by a straight, extremely low-mass (the mass of the tether can be ignored in actual calculations) and inextensible tether, and operate in a circular orbit around the Earth. The mother satellite releases the sub-satellite to the expected orbit through the tether. For Figure 4For the two-body tethered satellite system shown, the following coordinate systems and parameters are defined first: OXYZ represents the Earth inertial coordinate system, oxyz represents the orbital coordinate system, ox′y′z′ represents the body coordinate system fixed to the two-body tethered satellite system, the parameter ρ represents the in-plane angle, β represents the length of the tether that has been released, L represents the total length of the tether to be released, Ψ represents the orbital velocity, m 1 and m 2 represent the masses of the mother satellite and the daughter satellite respectively, represents F represents the tension on the tether.

[0021] As Figure 5 shown, the fuzzy control method provided in this embodiment for the tether deployment of the two-body tethered satellite system can be implemented in the form of a computer program and deployed on the mother satellite as shown in Figure 4 . Among them, an on-board control computer is installed on the mother satellite, and this method is executed by the on-board control computer. This method mainly includes:

[0022] S1. Establish a nonlinear dynamic model for the two-body tethered satellite system.

[0023] In this embodiment, the nonlinear dynamic equation of the two-body tethered satellite system can be established according to the Euler-Lagrange equation.

[0024] S2. Extract the nonlinear function information from the nonlinear dynamic model, and construct fuzzy expression data according to the extracted nonlinear function information.

[0025] Among them, 5 nonlinear functions can be selected from the established nonlinear dynamic equation. And the fuzzy expression forms of these 5 nonlinear functions are constructed respectively.

[0026] S3. Import the constructed fuzzy expression data into the nonlinear dynamic model, and obtain the fuzzy dynamic model of the two-body tethered satellite system.

[0027] Among them, the above 5 fuzzy expressions can be substituted into the system nonlinear dynamic equation, and the fuzzy description rules of the system are designed to establish a fuzzy dynamic model.

[0028] S4. Establish a fuzzy controller by using the fuzzy dynamic model.

[0029] Among them, based on the fuzzy dynamic model, the fuzzy controller rules based on state feedback can be designed through the parallel distributed compensation principle, so as to establish a fuzzy controller.

[0030] S5. Deploy the fuzzy controller to the control device for the tether deployment of the two-body tethered satellite system, and use the fuzzy controller to control the tether release process of the two-body tethered satellite system.

[0031] In the practical application of this embodiment, the son-satellite and the mother-satellite are connected by a straight, extremely low-mass and inextensible tether and operate in a circular orbit around the Earth. The mother-satellite releases the son-satellite to the expected orbit through the tether, as Figure 4 shown. Based on the Euler-Lagrange equation, the following nonlinear dynamic equations are established for the two-body tethered satellite system:

[0032]

[0033] In this embodiment, the established nonlinear dynamic model includes:

[0034] New parameters will be designed α = Ψt, ()' = Ψ( · ) and substituting them into the above equations, the following nonlinear dynamic equations can be transformed:

[0035]

[0036] Among them, the son-satellite and the mother-satellite are connected by a straight and inextensible tether and operate in a circular orbit around the Earth. OXYZ represents the Earth inertial coordinate system, oxyz represents the orbital coordinate system, ox'y'z' represents the body coordinate system fixed to the two-body tethered satellite system. The parameter ρ represents the in-plane angle, β represents the length of the tether that has been released, L represents the total length of the tether to be released, m 1 and m 2 represent the masses of the mother-satellite and the son-satellite respectively, F represents the tension on the tether, α = Ψt represents the dimensionless time, t represents the time, Ψ represents the orbital rate, represents the first derivative with respect to α, represents the second derivative with respect to α, represents the first derivative of ρ with respect to α, represents the second derivative of ρ with respect to α.

[0037] In this embodiment, after establishing the nonlinear dynamic model, the state-space model of the nonlinear dynamic model is obtained, including: Among them, x 1 = δ, x 3 = ρ,

[0038] In the process of importing the constructed fuzzy expression data into the nonlinear dynamics model, it includes: using the state space model to obtain the nonlinear terms, and then obtaining the fuzzy forms of each nonlinear term and recording them as the fuzzy expression data. The nonlinear terms at least include: σ 1 = cos 2 (x 3 ), σ 2 = sin(x 3 ), σ 3 = x 1 x 4 + 2x 1 + x 4 + 2, The obtaining of the fuzzy forms of each nonlinear term includes:

[0039] For the nonlinear term σ 1 , set max(σ 1 ) = μ 1 and min(σ 1 ) = μ 2 , and obtain the fuzzy form σ 1 of the nonlinear term σ 1 = P 1 (σ 1 )μ 1 + P 2 (σ 1 )μ 2 , where where, μ 1 , μ 2 respectively represent the maximum and minimum values of σ 1 .

[0040] For the nonlinear term σ 2 , set max(σ 2 ) = φ 1 and min(σ 2 ) = φ 2 , and obtain the fuzzy form σ 2 of the nonlinear term σ 2 = Q 1 (σ 2 ) = φ 1 + Q 2 (σ 2 ) = φ 2 , where where, φ 1 , φ 2 respectively represent the maximum and minimum values of σ 2 .

[0041] For the nonlinear term σ 3 , set max(σ 3 ) = θ1 and min(σ 3 ) = θ 2 , the fuzzy form σ 3 of the non - linear term σ 3 = R 1 (σ 3 )θ 1 + R 2 (σ 3 )θ 2 , where where, θ 1 , θ 2 respectively represent the maximum and minimum values of σ 3 .

[0042] For the non - linear term σ 4 , set max(σ 4 ) = τ 1 and min(σ 4 ) = τ 2 , the fuzzy form σ 4 of the non - linear term σ 4 = S 1 (σ 4 )τ 1 + S 2 (σ 4 )τ 2 , where where, τ 1 , τ 2 respectively represent the maximum and minimum values of σ 4 .

[0043] For the non - linear term σ 5 , set Get the fuzzy form σ 5 = T 1 (σ 5 )ξ 1 x 3 + T 2 (σ 5 )ξ 2 x 3 , where

[0044] In this embodiment, the importing the constructed fuzzy expression data into the non - linear dynamics model includes:

[0045] Obtain the non - linear dynamic characteristics of the two - body tethered satellite system and characterize them through fuzzy rules.

[0046] Superimpose the fuzzy rules to obtain the fuzzy dynamic model of the two - body tethered satellite system.

[0047] Substitute the fuzzy expressions of the five constructed non - linear terms into the state - space model, then as Figure 4 shown, the non - linear dynamic characteristics of the two - body tethered satellite can be characterized by the following fuzzy rules. Rule i: If σ 1 is and σ 2 is and σ 3 is and σ 4 is and σ 5 is then where the parameter λ 1 ∈{1, 2}, λ 2 ∈{1, 2}, λ 3 ∈{1, 2}, λ 4 ∈{1, 2}, λ 5 ∈{1, 2}, i ∈{1, 2, 3, …32}, represents the i - th system matrix, represents the i - th input matrix.

[0048] Through singleton fuzzification, product inference, and center - average defuzzification methods, multiple fuzzy rules ( i.e., 32 rules) can be superimposed into the global fuzzy dynamic model of the two - body tethered satellite system, expressed as where σ = [σ 1 σ 2 σ 3 σ 4 σ 5 T , T represents the transpose of a vector or matrix, represents the number of fuzzy rules.

[0049] Using the fuzzy dynamic model of the two - body tethered satellite system, a fuzzy controller is established, including: Characterizing the controller v using the following fuzzy rules. Rule i: If σ 1 is and σ 2 is and σ 3 is and σ 4 is and σ 5 is then v = K i x, i ∈{1, 2, 3, …32}, K i represents the i - th feedback gain matrix.

[0050] ​By means of single-point fuzzification, product inference, and center-average defuzzification, multiple fuzzy controller rules can be superimposed into a global fuzzy controller, expressed as

[0051] where ε i () represents the i-th membership function, and K i represents the i-th feedback gain matrix.

[0052] Bring the established fuzzy controller into the established global fuzzy dynamics model to generate a closed-loop control system

[0053] Furthermore, it also includes: obtaining the positive definite matrix W and the general matrix X according to the solution of the linear matrix inequality . Obtain the feedback gain matrix K j . j = X j W -1 , and import K j into the fuzzy controller to obtain the fuzzy controller for tether deployment For example: the specific values of matrices W and X can be solved according to the linear inequality. The linear matrix inequality is solved by a ground computer before deploying the controller. Only by solving this linear matrix inequality can W and X be obtained j . With W and X j , there is the specific value of the feedback gain matrix K j , that is, K j = X j W j W -1 . With the specific value of the feedback gain matrix K j , substituting it into the fuzzy controller can the specific expression of the fuzzy controller be obtained Finally, deploy the fuzzy controller to the airborne control computer of the mother star.

[0054] This embodiment can verify the effectiveness of the proposed fuzzy control method through the following numerical examples.

[0055] The initial conditions of the tether release process are defined as ρ 0 = 0, Select the operating threshold of the system state variable as -0.99 ≤ x 1 ≤ 0.2, -0.2 ≤ x 2 ≤ 1.3, -0.99 ≤ x 4 ​≤0.5. In addition, the fuzzification parameters related to the selected five non-linear terms are defined as μ 1 = 1, μ 2 = 0.5, φ 1 = 0.7071, φ 2 = -0.7071, θ 1 = 3, θ 2 = 0.0101, τ 1 = 150, τ 2 = 0.0083, ξ 1 = 1, Tether tension is restricted to vary within a range. According to the above design parameters, a fuzzy controller for the tether release process can be obtained by the design method proposed in this embodiment. Applying the fuzzy controller can obtain the tether release process as shown in Figure 4 . It can be seen from the figure that under the action of the designed fuzzy controller, the tether can be quickly and smoothly deployed to the desired length. During the deployment process, the change range of the in-plane angle ρ is small, suppressing the tether vibration to a small extent and being quickly suppressed.

[0056] At present, in the research on the dynamic modeling of tethered satellites, it is difficult to simultaneously meet the requirements of accurately describing the system's nonlinear dynamic behavior and facilitating controller design. Specifically, although traditional nonlinear models can depict the nonlinear dynamic behavior of the system, due to the extremely high degree of nonlinearity, the model form is extremely complex. For nonlinear systems, there is still no general method for controller design and analysis. Therefore, the problem of controller design and analysis for complex nonlinear systems remains a difficult problem in the academic and industrial fields. In contrast, in this embodiment, a T-S fuzzy model of a two-body tethered satellite is established based on the universal approximation principle of fuzzy logic for nonlinearity. Based on this fuzzy model, mature linear system design tools can be applied to design the controller, thereby greatly reducing the design difficulty of the controller for the two-body tethered satellite system. To solve the above existing problems, this embodiment discloses a fuzzy control scheme for a two-body tethered satellite system. Based on a sufficient nonlinear dynamic analysis, a fuzzy dynamic model of the system is established. The established fuzzy dynamic model can not only accurately depict the complex nonlinear dynamic characteristics of the system, but also facilitate controller design and motion stability analysis. It solves the problem in the prior art that it is impossible to simultaneously consider the nonlinear dynamic characterization and controller design of the tethered satellite system. The specific steps of the described fuzzy control method are as follows: establish the nonlinear dynamic equation of the two-body tethered satellite system according to the Euler-Lagrange equation; select 5 nonlinear functions from the established nonlinear dynamic equation; respectively construct the fuzzy expression forms of these 5 nonlinear functions; substitute the 5 fuzzy expressions into the system's nonlinear dynamic equation, and design the fuzzy description rules of the system to establish a fuzzy dynamic model; based on the fuzzy dynamic model, through the principle of parallel distributed compensation, design the fuzzy controller rules based on state feedback to establish a fuzzy controller; use the fuzzy controller to control the tether release process of the two-body tethered satellite system.

[0057] Each embodiment in this specification is described in a progressive manner. The same or similar parts among the embodiments can be referred to each other, and the key points of each embodiment are the differences from other embodiments. In particular, for the device embodiment, since it is basically similar to the method embodiment, the description is relatively simple, and the relevant parts can refer to the partial description of the method embodiment. As mentioned above, the above is only the specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by those skilled in the art within the technical scope disclosed by the present invention should be covered by the protection scope of the present invention. Therefore, the protection scope of the present invention should be subject to the protection scope of the claims.

Claims

1. A fuzzy control method for tether deployment of a two-body tethered satellite system, characterized in that, it includes: S1. Establish a nonlinear dynamic model for the two-body tethered satellite system; S2. Extract nonlinear function information from the nonlinear dynamic model, and construct fuzzy expression data according to the extracted nonlinear function information; S3. Import the constructed fuzzy expression data into the nonlinear dynamic model to obtain the fuzzy dynamic model of the two-body tethered satellite system; S4. Establish a fuzzy controller using the fuzzy dynamic model; S5. Deploy the fuzzy controller to the control device for tether deployment of the two-body tethered satellite system, and use the fuzzy controller to control the tether release process of the two-body tethered satellite system; The established nonlinear dynamic model includes: Among them, the sub-satellite and the mother-satellite are connected by a straight and inextensible tether and operate on a circular orbit around the Earth. OXYZ represents the Earth inertial coordinate system, oxyz represents the orbital coordinate system, and ox′y′z′ represents the body coordinate system fixed to the two-body tethered satellite system. The parameter ρ represents the in-plane angle, β represents the length of the tether that has been released, and L represents the total length of the tether to be released. m 1 and m 2 represent the masses of the mother-satellite and the sub-satellite respectively. F represents the tension on the tether, α = Ψt represents the dimensionless time, t represents the time, and Ψ represents the orbital velocity. denotes the first derivative with respect to α. denotes the second derivative with respect to α. denotes the first derivative of ρ with respect to α. denotes the second derivative of ρ with respect to α. It also includes: After establishing the non-linear dynamics model, obtaining the state space model of the non-linear dynamics model, including: Wherein, x 1 = δ, x 3 = ρ, represents the first derivative of δ with respect to α; Extracting nonlinear function terms from the nonlinear dynamic model includes: Using the state space model, obtain the non-linear terms, the non-linear terms at least including: σ 1 = cos 2 (x 3 ), σ 2 = sin(x 3 ), σ 3 = x 1 x 4 + 2x 1 + x 4 + 2, Constructing fuzzy expression data for the nonlinear function terms according to the extracted nonlinear function terms includes: For the non - linear term σ 1 , set max(σ 1 ) = μ 1 and min(σ 1 ) = μ 2 , and obtain the fuzzy form σ 1 of the non - linear term σ 1 = P 1 (σ 1 )μ 1 + P 2 (σ 1 )μ 2 , where where, μ 1 , μ 2 respectively represent the maximum and minimum values of σ 1 ; For the non - linear term σ 2 , set max(σ 2 ) = φ 1 and min(σ 2 ) = φ 2 , and obtain the fuzzy form σ 2 of the non - linear term σ 2 = Q 1 (σ 2 )φ 1 +Q 2 (σ 2 )φ 2 , where where, φ 1 , φ 2 represent the maximum and minimum values of σ 2 respectively; For the non - linear term σ 3 , set max(σ 3 ) = θ 1 and min(σ 3 ) = θ 2 , and obtain the fuzzy form σ 3 of the non - linear term σ 3 = R 1 (σ 3 )θ 1 + R 2 (σ 3 )θ 2 , where where, θ 1 , θ 2 respectively represent the maximum and minimum values of σ 3 ; For the non - linear term σ 4 , set max(σ 4 ) = τ 1 and min(σ 4 ) = τ 2 , and obtain the fuzzy form σ 4 of the non - linear term σ 4 = S 1 (σ 4 )τ 1 + S 2 (σ 4 )τ 2 , where where, τ 1 , τ 2 respectively represent the maximum and minimum values of σ 4 ; For the nonlinear term σ 5 , set to obtain the fuzzy form of the nonlinear term σ 5 = T 1 (σ 5 )ξ 1 x 3 + T 2 (σ 5 )ξ 2 x 3 , where Importing the constructed fuzzy expression data into the nonlinear dynamic model to obtain the fuzzy dynamic model of the two-body tethered satellite system includes: Establish a fuzzy dynamics model where \(i\in\{1, 2, 3, \cdots, 32\}\) represents the counting subscript, and \(\varepsilon\) i () represents the \(i\)-th membership function, represents the state vector, \(A\) i represents the \(i\)-th system matrix, \(B\) i represents the \(i\)-th input matrix, and \(\nu\) represents the fuzzy controller to be designed; The establishing of the fuzzy controller using the fuzzy dynamic model includes: Using the obtained fuzzy dynamic model of the two-body tethered satellite system, a fuzzy controller is established, where \(v\) represents the fuzzy controller, and represents the number of fuzzy rules, \(\varepsilon\) i () represents the \(i\)-th membership function, \(\sigma = [\sigma 1 \sigma 2 \sigma 3 \sigma 4 \sigma 5 T , \(T\) represents the transpose of a vector or matrix, \(K i represents the \(i\)-th feedback gain matrix, \(x = [x 1 x 2 x 3 x 4 x 5 T ;​​ Generate a closed-loop control system using the established fuzzy controller where A i represents the i-th system matrix, B i represents the i-th input matrix, and K j represents the j-th feedback gain matrix.

2. The method according to claim 1, characterized in that, The importing of the constructed fuzzy expression data into the nonlinear dynamic model includes: Obtaining the nonlinear dynamic characteristics of the two-body tethered satellite system and characterizing them through fuzzy rules; Superimposing the fuzzy rules to obtain the fuzzy dynamic model of the two-body tethered satellite system.

3. The method according to claim 1, characterized in that, It also includes: According to the linear matrix inequality obtain a positive definite matrix W and a general matrix X j ; Obtain the feedback gain matrix K j The specific expression of K j = X j W -1 , and substitute K j into the fuzzy controller to obtain the fuzzy controller for tether deployment

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