Saturation-resistant preset performance despinning control method for failed satellite and related device

Abstract

The application discloses a kind of anti-saturation preset performance despun control methods of failed satellite and related devices, the method includes: obtaining the attitude of service spacecraft and failed satellite, establishes the dynamics model of service spacecraft and failed satellite;According to the dynamics model of service spacecraft and failed satellite, the flexible operating rod dynamics model of service spacecraft is established, the large deformation dynamics characteristics of despun brush are obtained, under the framework of the dynamics model of service spacecraft and the large deformation dynamics characteristics of despun brush, the rigid-flexible coupling dynamics model of service spacecraft is established by Lagrange multiplier method;Based on the rigid-flexible coupling dynamics model of service spacecraft, an anti-saturation preset performance controller is designed, and an anti-saturation full-state constraint control strategy is used for despun control.The application is aimed at service spacecraft with flexible operating rod, realizes efficient and accurate despun process, and greatly improves control performance.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of spacecraft control, and relates to an anti-saturation preset performance despun control method for a failed satellite and a related device. BACKGROUND

[0002] With the rapid development of space technology, a large number of launch missions are carried out every year to meet the growing demand for meteorological monitoring and communication navigation. However, the number of failed satellites caused by factors such as fuel depletion and mechanical failure is increasing day by day. These failed satellites not only occupy valuable orbital resources, but also pose a great threat to normally operating satellites in orbit. The influence of residual angular momentum and space perturbation torque causes the satellite attitude to present a complex free rolling motion, making it extremely difficult to capture directly. Therefore, the despun operation before capture is a key link. At present, using a service spacecraft equipped with a flexible operation rod to perform despun operation on a failed satellite is a novel and efficient method. However, due to the large flexible deformation of the operation rod when interacting with the satellite, the service spacecraft presents nonlinear and strong coupling characteristics, and the strong disturbance caused by contact has a great impact on its stability, which can seriously reduce its transient and steady-state response performance, making the despun process face a big problem in control strategy design.

[0003] In the despun control method of the service spacecraft, most methods usually suppress the influence of disturbance through feedback regulation. Although the designed controller can eventually suppress the disturbance through relatively slow feedback regulation, it is difficult to guarantee the desired control performance under the action of strong disturbance. Therefore, most existing methods still have certain limitations in dealing with disturbances, and cannot achieve the preservation of transient and steady-state response performance.

[0004] For the despun process of the failed satellite, a new control method needs to be designed to effectively suppress the adverse effects of disturbance and achieve the preset transient and steady-state response performance, thereby improving the anti-interference performance of the service spacecraft and providing necessary conditions for efficient and accurate despun operation. SUMMARY

[0005] The application aims to provide an anti-saturation preset performance despun control method for a failed satellite and a related device, which solves the problem that the existing control method has a greater impact on transient and steady-state response performance.

[0006] To achieve the above-mentioned purpose, the application adopts the following technical solutions:

[0007] An anti-saturation preset performance despun control method for a failed satellite, comprising:

[0008] Obtaining the attitude of the service spacecraft and the failed satellite, and establishing a dynamic model of the service spacecraft and the failed satellite;

[0009] According to the dynamics model of the servicing spacecraft and the failed satellite, a flexible manipulator dynamics model of the servicing spacecraft is established, and large deformation dynamics characteristics of the despinning brush are obtained. Under the framework of the dynamics model of the servicing spacecraft and the large deformation dynamics characteristics of the despinning brush, a rigid-flexible coupling dynamics model of the servicing spacecraft is established by the Lagrange multiplier method.

[0010] Based on the rigid-flexible coupling dynamics model of the servicing spacecraft, an anti-windup preset performance controller is designed, and an anti-windup full-state constraint control strategy is used for despinning control.

[0011] Further, the dynamics model of the servicing spacecraft is:

[0012]

[0013] wherein ω = [ω x ω y ω z ] represents an attitude angular velocity vector of the servicing spacecraft, σ = [φ θ ψ ] represents an Euler angle vector of the servicing spacecraft, J represents a moment of inertia of the servicing spacecraft, r represents a center of mass position vector of the servicing spacecraft, m represents a mass of the servicing spacecraft, f(t) represents a control force, u(t) represents a control torque, D represents a despinning force, and T represents a despinning torque. φ ω θ ω ψ ] T ω T ω c ω c ω c ω

[0014] Further, the dynamics model of the failed satellite is:

[0015]

[0016] wherein ω = [ω x ω y ω z ] represents an attitude angular velocity vector of the failed satellite, σ = [φ θ ψ ] represents an Euler angle vector of the failed satellite, J represents a moment of inertia of the failed satellite, r represents a center of mass position vector of the failed satellite, m represents a mass of the failed satellite, F represents a despinning force, T represents a despinning torque, and D represents a despinning force. t ω tφ ω tθ ω tψ ] T ω t ω t ω t ω t ω T ω t ω t ω t ω c ω c ω t ω

[0017] Further, the flexible manipulator dynamics model of the servicing spacecraft is:

[0018]

[0019] wherein Q c represents a contact force vector, represents a stiffness matrix related to axial deformation, represents a stiffness matrix related to bending deformation, C=aM e +b(K t +K l represents a damping matrix, a and b represent proportional coefficients, and e(t) represents a node coordinate vector.

[0020] Further, the rigid-flexible coupling dynamics model of the servicing spacecraft is:

[0021]

[0022] wherein M q represents a system mass matrix, q represents a system generalized coordinate, 0 6×6 represents a 6x6 zero matrix. λ represents a Lagrange multiplier vector, Φ represents an algebraic constraint equation, Φ q represents a Jacobian matrix of the constraint equation, Q represents a system generalized force vector, γ represents a Lagrange multiplier vector, β1 and β2 represent feedback control parameters for preventing constraint violation.

[0023] Further, the design process of the anti-windup pre-specified performance controller comprises:

[0024] defining a state tracking error, introducing a finite-time pre-specified performance function, considering an obstacle Lyapunov function, and imposing a constraint on the state tracking error;

[0025] designing a virtual control input, defining a virtual state tracking error, imposing a constraint on each element of the virtual state tracking error, and designing an anti-windup compensator;

[0026] adopting a fixed-time disturbance observer to estimate the disturbance of the anti-windup compensator, obtaining a disturbance estimation value, considering a Lyapunov function, and making the disturbance estimation error converge to the origin in a fixed time, thereby obtaining the anti-windup pre-specified performance controller.

[0027] Further, the anti-windup full-state constraint control strategy is:

[0028]

[0029] wherein ζ represents a state variable of the anti-windup compensator, 0 n×m is an n x m dimensional zero matrix. K2 is a positive constant, K3 is a positive constant, alpha is a virtual tracking error, mu2 is a set performance constraint function, is an interference estimate, x2 is a service spacecraft velocity level state, x d is a desired state.

[0030] A kind of failure satellite anti-saturation preset performance despin control system, comprising:

[0031] An acquisition module is used to acquire the attitude of service spacecraft and failure satellite, and establish the dynamics model of service spacecraft and failure satellite;

[0032] A modeling module is used to establish the flexible operating rod dynamics model of service spacecraft according to the dynamics model of service spacecraft and failure satellite, obtain the large deformation dynamics characteristics of despin brush, and establish the rigid-flexible coupling dynamics model of service spacecraft under the framework of the dynamics model of service spacecraft and the large deformation dynamics characteristics of despin brush by Lagrange multiplier method;

[0033] A control module is used to design anti-saturation preset performance controller based on the rigid-flexible coupling dynamics model of service spacecraft, and utilize anti-saturation full state constraint control strategy to carry out despin control.

[0034] A terminal device, comprising a memory, a processor and a computer program stored on the memory and executable on the processor, wherein the processor implements the steps of the method when executing the computer program.

[0035] A computer-readable storage medium stores a computer program, wherein the computer program is executed by a processor to implement the steps of the method.

[0036] Compared with the prior art, the present application has the following beneficial effects:

[0037] The application provides a kind of anti-saturation preset performance despun control method of failed satellite, the attitude of service spacecraft and failed satellite is obtained, the dynamic model of service spacecraft and failed satellite is established, the interaction between the two can be simulated more accurately, so that the despun operation to failed satellite is more effectively planned and executed.Then according to the dynamic model of service spacecraft and failed satellite, the flexible operating rod dynamic model of service spacecraft is established, the large deformation dynamic characteristics of despun brush are obtained, which helps to enhance the accuracy and stability of despun control, and reduce the control error caused by inaccurate model.Again under the framework of dynamic model of service spacecraft and large deformation dynamic characteristics of despun brush, the rigid-flexible coupling dynamic model of service spacecraft is established by Lagrange multiplier method to more comprehensively reflect the dynamic behavior of the system, which provides a basis for designing more complex control strategy.Finally, an anti-saturation preset performance controller is designed, and an anti-saturation full-state constraint control strategy is used for despun control.This controller can deal with the saturation phenomenon in the control process, ensure that the control command is within a reasonable range, and avoid system instability due to excessive control.At the same time, the preset performance control strategy can ensure that the system reaches the predetermined performance index within a certain time, improving the reliability and robustness of the control.The application accurately estimates the strong disturbance caused by contact without the need for upper bound information of disturbance and its derivative for service spacecraft with flexible operating rod, realizes fast response speed and high steady-state accuracy of spacecraft, and significantly improves the anti-interference performance.In the presence of input saturation and strong disturbance caused by contact, not only the dynamic and steady-state response performance of service spacecraft is guaranteed, but also the efficient and accurate despun process is realized.Meanwhile, an anti-saturation compensator is introduced to effectively compensate for the control input saturation, significantly reduce the actuator saturation degree, effectively suppress the negative impact of saturation on service spacecraft, and greatly improve the control performance.The control method is simple, which not only guarantees the transient and steady-state performance, but also involves fewer control parameters, reduces the difficulty of parameter selection, reduces the computational complexity, and is conducive to practical engineering application. BRIEF DESCRIPTION OF DRAWINGS

[0038] In order to more clearly illustrate the technical solutions of the embodiments of the application, the following will briefly introduce the drawings needed to be used in the embodiments. It should be understood that the following drawings only show some embodiments of the application, and therefore should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can also be obtained without creative labor under the premise of these drawings.

[0039] Figure 1 The figure is a despun control method of failed satellite of the application.

[0040] Figure 2 The figure is a change history diagram of failed satellite position in embodiment 1 of the application.

[0041] Figure 3 A plot of the variation of the failure satellite angular velocity in the embodiment 1 of the present application.

[0042] Figure 4 A plot of the variation of the failure satellite angular velocity in the embodiment 1 of the present application.

[0043] Figure 5 A plot of the variation of the failure satellite angular velocity in the embodiment 1 of the present application.

[0044] Figure 6 A plot of the variation of the failure satellite angular velocity in the embodiment 1 of the present application.

[0045] Figure 7 A plot of the variation of the failure satellite angular velocity in the embodiment 1 of the present application.

[0046] Figure 8 A plot of the variation of the failure satellite angular velocity in the embodiment 1 of the present application.

[0047] Figure 9 A plot of the variation of the failure satellite angular velocity in the embodiment 1 of the present application.

[0048] Figure 10 A plot of the variation of the failure satellite angular velocity in the embodiment 1 of the present application.

[0049] Figure 11 A plot of the variation of the failure satellite angular velocity in the embodiment 1 of the present application. DETAILED DESCRIPTION

[0050] The exemplary embodiments of this application are described herein with reference to the accompanying drawings, which are meant to be exemplary, and various changes and modifications can be made thereto without departing from the scope and spirit of the application. It is to be understood that the following description is purely exemplary in nature and is intended to illustrate, but not limit, the scope of the present application. Therefore, specific details disclosed herein are not to be interpreted in an absolute sense, but are merely intended to illustrate this application.

[0051] It is apparent that the described embodiments are only part of the embodiments of the present application, but not all. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative work are within the scope of protection of the present application.

[0052] It should be noted that the terminal involved in the embodiments of the present application can include, but is not limited to, a mobile phone, a personal digital assistant (PDA), a wireless handheld device, a tablet computer, a personal computer (PC), an MP3 player, an MP4 player, a wearable device (for example, smart glasses, a smart watch, a smart bracelet, etc.), a smart home device, and the like.

[0053] In addition, the term "and / or" in the present application is only used to describe the association relationship of the associated objects, and can represent three relationships, for example, A and / or B can represent three cases of A alone, A and B together, and B alone. In addition, the character " / " in the present application generally represents an "or" relationship between the front and rear associated objects.

[0054] The application will be further described in detail below with reference to the accompanying drawings:

[0055] Referring to Figure 1 The application provides a kind of anti-saturation preset performance despin control method of failed satellite, specifically includes the following steps:

[0056] Step 1: establish the dynamics model of service spacecraft and failed satellite.

[0057] The attitude of service spacecraft and failed satellite is described using Euler angles, and the 6-DOF pose dynamics of service spacecraft is represented as

[0058]

[0059] The 6-DOF pose dynamics of failed satellite is represented as

[0060]

[0061] Wherein, ω t =[ω tφ ω tθ ω tψ ] T And ω=[ω φ ω θ ω ψ ] T Respectively represent the attitude angular velocity vector of service spacecraft and failed satellite, σ=[φ θ ψ] T And σ t =[φ t θ t ψ t ] T Respectively represent the Euler angle vector of service spacecraft and failed satellite, J and J tLet r represent the moments of inertia of the servicing spacecraft and the failed satellite, respectively. c and r t Let m represent the position vectors of the center of mass of the servicing spacecraft and the failed satellite, respectively. c and m t Let f(t) represent the mass of the servicing spacecraft and the failed satellite, respectively, and let u(t) represent the control force and the control torque. c T represents the derotation force. c D represents the derotation torque. c and D t The expression is similar, D c Represented as

[0062]

[0063] Step 2: Establish a dynamic model of the flexible control lever.

[0064] To accurately describe the large deformation dynamics of the deswirl brush, its dynamic equations are described using the 3D absolute nodal coordinate method. The global position coordinates of any point on the deswirl brush element are represented as follows:

[0065] r=S(x)e(t)(4)

[0066] Where S(x) = [S1I3 S2I3 S3I3 S4I3] T Let I3 be a 3×3 identity matrix, and S1(x) = 1 - 3ξ. 2 +2ξ 3 S2(x)=L(ξ-2ξ) 2 +ξ 3 S3(x) = 3ξ 2 -2ξ 3 S4(x)=L(-ξ) 2 +ξ 3 ), ξ=x / L, where x represents the material coordinates, L represents the length of the devortex brush element, and e(t) represents the nodal coordinate vector.

[0067] The element mass matrix is ​​represented as

[0068]

[0069] In the formula: ρ and A represent the density and cross-sectional area of ​​the deswirl brush, respectively.

[0070] The elemental strain energy is divided into two parts: one part is the strain energy caused by axial deformation, and the other part is the strain energy caused by bending deformation, expressed as follows:

[0071]

[0072] where E and J denote the elastic modulus and the cross-sectional moment of inertia of the bristle, respectively, ε denotes the axial strain, and κ denotes the curvature.

[0073] The elastic forces due to axial and bending deformations can be written as

[0074]

[0075] where, denotes the stiffness matrix associated with axial deformations, is the average axial strain, S x is the first derivative of S(x) with respect to x. denotes the stiffness matrix associated with bending deformations, S xx is the first derivative of S x (x) with respect to x.

[0076] The element dynamics of the bristle are given by

[0077]

[0078] where Q c denotes the contact force vector, C = aM e +b(K t +K l ) denotes the damping matrix, and a and b denote the proportional coefficients.

[0079] Step 3: Establish the rigid-flexible coupled dynamics model of the servicing spacecraft.

[0080] The bristle system dynamics equations are obtained by assembling the bristle elements according to the traditional finite element procedure. Under the framework of the servicing spacecraft dynamics model and the bristle system dynamics model, the spacecraft rigid-flexible coupled dynamics model is established by the Lagrange multiplier method, which is expressed in the following compact form

[0081]

[0082] where M q denotes the system mass matrix, q denotes the system generalized coordinates, 0 6×6 denotes a 6x6 zero matrix. λ denotes the Lagrange multiplier vector, Φ denotes the algebraic constraint equation, Φ q denotes the Jacobian matrix of the constraint equation, Q denotes the system generalized force vector, γ denotes the Lagrange multiplier vector, β1 and β2 denote the feedback control parameters to prevent constraint violation.

[0083] Step 4: Design the anti-windup pre-specified performance controller.

[0084] First, define the state tracking error as

[0085]

[0086] where x d and denote the desired pose state and its derivative, respectively.

[0087] A finite-time prescribed performance function is introduced as

[0088]

[0089] where μ 0j ≥ 1, μ Tj > 0, T j denotes the reaching time, j = 1, 2. It can be seen that the above μ j (t) is a smooth function. When t = T j , μ j (t) converges to μ Tj . When t ≥ T j , μ j (t) = μ Tj .

[0090] The constraints on the state tracking error zi, i.e., |zi 1i | ≤ μi, i = 1, 2,..., 6, are imposed. Consider the barrier Lyapunov function as

[0091]

[0092] where I i is a 6 × 6 diagonal matrix with the ith diagonal element equal to 1 and the rest equal to 0.

[0093] Taking the first-order derivative of (12) with respect to time and rearranging, we have

[0094]

[0095] where satisfies μi 2 (0) ≥ zi 1i 2 (0), i = 1, 2,..., 6.

[0096] The virtual control input is designed as

[0097]

[0098] where Ki > 0 is a positive constant.

[0099] The virtual tracking error is defined as

[0100] α = z2- x2 * (15)

[0101] Substituting equation (15) into equation (13) and rearranging gives

[0102]

[0103] A constraint is imposed on each element of the virtual tracking error a, i.e., satisfies |a i |≤μ2, i = 1, 2,..., 6. Consider another barrier Lyapunov function

[0104]

[0105] where ζ i represents the state variable of the anti-windup compensator, i = 1, 2,..., 6.

[0106] Differentiating equation (17) with respect to time and rearranging gives

[0107]

[0108] where satisfies μ2 2 (0) ≥ a i 2 (0), i = 1, 2,..., 6.

[0109] The anti-windup compensator is designed as

[0110] ζ i = - (k a + k b φ 2i ) ζ i + Δτ i , i = 1, 2,..., 6 (19)

[0111] where k a > 0, k b > 0, Δτ i = sat(τ i ) - τ i .

[0112] Differentiating equation (15) with respect to time gives

[0113]

[0114] where

[0115] 0 n×m is an n x m zero matrix.

[0116] The fixed-time disturbance observer is used to estimate the disturbance d(t). A new auxiliary variable is defined as

[0117]

[0118] where l1>0 is a positive constant.

[0119] The estimation algorithm of ξ is designed as

[0120]

[0121] where is the estimation error of ξ, l2>0 is a positive constant, α1>1, α2 and α3 are positive odd numbers, and satisfy α2<α3. The symbol where sgn(·) is the sign function.

[0122] The disturbance estimation value is designed as

[0123]

[0124] According to equation (21) and equation (22), we can get

[0125]

[0126] Consider the following Lyapunov function

[0127]

[0128] Take the first-order derivative of equation (25) with respect to time, and substitute equation (24) into it, we can get

[0129]

[0130] where is a positive constant, is a positive constant, is a positive constant, is a positive constant.

[0131] When t≥T p , V ξ =0, at this time where the upper bound of T p is According to equation (26), we can get Therefore, the disturbance estimation error will converge to the origin in fixed time.

[0132] Substitute equation (20) into equation (18), we can get

[0133]

[0134] where Φ2i is expressed as satisfies μ2 2 (0)≥α i 2 (0), i = 1, 2,..., 6, K1>0 is a constant, Φ 1i is expressed as satisfies μ1 2 (0)≥z 1i 2 (0), i = 1 , 2,..., 6. Δτ represents Δτ i = sat(τ i )-τ i .

[0135] Based on the above steps, the anti-windup pre-specified performance spin-down control strategy is designed as

[0136]

[0137] wherein ζ represents a state variable of the anti-windup compensator, K2>0 represents a constant, K3>0 represents a constant, and α represents a virtual tracking error, μ2 represents a pre-specified performance function, represents a disturbance estimation value, x2 * represents a virtual control input, x d represents an expected pose state.

[0138] The application will be described in further detail below in combination with the drawings and specific embodiments:

[0139] Embodiment 1:

[0140] In this embodiment, the spacecraft spin-down system composed of a service spacecraft, a flexible operating rod and a failed satellite is taken as an example to illustrate the effectiveness of the anti-windup pre-specified performance spin-down control method of the application. The spin-down system simulation parameters are shown in Table 1, which include the dynamics parameters of the service spacecraft, the flexible operating rod and the failed satellite.

[0141] Table 1 Physical parameters of the spin-down system

[0142]

[0143]

[0144] The anti-windup pre-specified performance spin-down control method for the failed satellite specifically includes the following steps:

[0145] Step 1: Establishing the dynamics model of the service spacecraft and the failed satellite

[0146] The dynamics model of the service spacecraft is

[0147]

[0148] The dynamics of the failed satellite is expressed as

[0149]

[0150] where ω t = [ω tφ ω tθ ω tψ ] T and ω = [ω φ ω θ ω ψ ] T are the attitude angular velocity vectors of the servicing spacecraft and the failed satellite, respectively. σ = [φ θ ψ] T and σ t = [φ t θ t ψ t ] T are the Euler angle vectors of the servicing spacecraft and the failed satellite, respectively. J and J t are the moments of inertia of the servicing spacecraft and the failed satellite, respectively. r c and r t are the position vectors of the center of mass of the servicing spacecraft and the failed satellite, respectively. m c and m t are the masses of the servicing spacecraft and the failed satellite, respectively. f(t) represents the control force, and u(t) represents the control torque. F c represents the antisymmetric force, and T c represents the antisymmetric torque. D c and D t are expressed as

[0151]

[0152] Step 2: Establish the dynamics model of the flexible manipulator

[0153] In order to accurately describe the large deformation dynamics characteristics of the antisymmetric brush, the three-dimensional absolute node coordinate method is used to describe the dynamics equation, and the element dynamics equation of the antisymmetric brush is expressed as

[0154]

[0155] where Q c represents the contact force vector, represents the stiffness matrix related to the axial deformation, represents the stiffness matrix related to the bending deformation, and C = aM e +b(K t +K l) is the damping matrix, a and b are the proportional coefficients, and e(t) represents the node coordinate vector.

[0156] Step 3: Servicing spacecraft rigid-flexible coupling dynamics model

[0157] The brush system dynamics equation is obtained by assembling the brush unit according to the traditional finite element program. Under the framework of the servicing spacecraft dynamics model (1) and the brush system dynamics model, the spacecraft rigid-flexible coupling dynamics model is established by the Lagrange multiplier method, which is expressed in the following compact form

[0158]

[0159] where M q represents the system mass matrix, q represents the system generalized coordinates, 0 6×6 represents a 6x6 zero matrix. λ represents the Lagrange multiplier vector, Φ represents the algebraic constraint equation, Φ q represents the Jacobian matrix of the constraint equation, Q represents the system generalized force vector, γ represents the Lagrange multiplier vector, β1 and β2 represent the feedback control parameters to prevent constraint violation.

[0160] Step 4: Anti-windup pre-specified performance controller design

[0161] First, define the state tracking error as

[0162]

[0163] where x d and represent the desired pose state and its derivative, respectively.

[0164] A finite-time pre-specified performance function is introduced, which is expressed as

[0165]

[0166] where μ 0j ≥ 1, μ Tj > 0, T j is the arrival time, and j = 1, 2. It can be seen that the above μ j (t) is a smooth function. When t = T j , μ j (t) converges to μ Tj . When t ≥ T j , μ j (t) = μ Tj .

[0167] The state tracking error z1 is constrained, that is, it satisfies |z 1i| < μ1, i = 1, 2,..., 6. Consider the barrier Lyapunov function

[0168]

[0169] where I i is a 6x6 diagonal matrix with its ith diagonal element equal to 1 and the rest of the elements equal to 0.

[0170] Taking the first derivative of equation (8) with respect to time and rearranging, we have

[0171]

[0172] where satisfies μ1 2 (0) > z 1i 2 (0), i = 1, 2,..., 6.

[0173] The virtual control input is designed as

[0174]

[0175] where K1 > 0 is a positive constant.

[0176] The virtual tracking error is defined as

[0177] α = z2 - x2 * (11)

[0178] Substituting equation (11) into equation (9) and rearranging, we have

[0179]

[0180] A constraint is imposed on each element of the virtual tracking error α, i.e., satisfies |α i | < μ2, i = 1, 2,..., 6. Consider another barrier Lyapunov function

[0181]

[0182] where ζ i is the state variable of the anti-windup compensator, i = 1, 2,..., 6.

[0183] Taking the derivative of equation (13) with respect to time and rearranging, we have

[0184]

[0185] where satisfies μ2 2 (0) > α i 2(0), i = 1, 2,..., 6.

[0186] The anti-windup compensator is designed as

[0187] ζ i = -(k a + k b Φ 2i )ζ i + Δτ i , i = 1, 2,..., 6 (15)

[0188] where k a > 0, k b > 0, Δτ i = sat(τ i ) - τ i .

[0189] Taking the derivative of equation (11) with respect to time, we have

[0190]

[0191] where, 0 n×m is an n x m zero matrix.

[0192] The disturbance d(t) is estimated by using the fixed-time disturbance observer. First, a new auxiliary variable is defined as

[0193]

[0194] where l1> 0 is a positive constant.

[0195] The estimation algorithm of ξ is designed as

[0196]

[0197] where, is the estimation error of ξ, l2> 0 is a positive constant, a1> 1, a2 and a3 are positive odd numbers, and satisfy a2< a3. The symbol where sgn(·) is the sign function.

[0198] The disturbance estimation value is designed as

[0199]

[0200] Based on the above steps, the anti-windup full-state constrained control strategy is designed as

[0201]

[0202] wherein ζ represents a state variable of the anti-windup compensator, 0 n×m is an n x m dimensional zero matrix, represents an interference estimation value, K2>0 represents a normal number, K3>0 represents a normal number, and a represents a virtual tracking error, μ2represents a pre-set performance function, x2 * represents a virtual control input, x d represents an expected pose state, x d represents an expected pose state.

[0203] According to the above execution steps, the dynamic simulation of the despin system is performed by using the dynamic model parameters in Table 1, and on this basis, the key control parameters are selected to complete the entire despin process simulation. The controller parameters are selected as: K1=K2=K3=1; the interference observer parameters are selected as: l1=l2=l3=1, a1=1.1, a2=3, a3=11; the anti-windup compensator parameters are selected as: k a =0.3, k b =0.05. The agreed time performance function parameters are selected as: μ 0j =0.8, μ Tj =0.005, T j =15s, j=1,2. In addition, the amplitude of the control torque and the control force is limited as |τ i |≤4(N·m), i=φ,θ,ψ and |τ j |≤6(N), j=x,y,z.

[0204] The expected pose state is

[0205]

[0206] wherein, represents the displacement change amount of the satellite center of mass.

[0207] The task starting time is t=0s and the ending time is t=500s. The service spacecraft has approached the vicinity of the failed satellite and hovers in the expected position and attitude, and the flexible operating rod has entered the range of the sail envelope under the driving action of the mechanical arm. The initial speed of the satellite is [10 1 1] T deg / s. The above control parameters are applied to the above method of the embodiment to perform the despin simulation of the failed satellite, and the simulation results are obtained:

[0208] As Figure 2 and Figure 3As shown, time history graphs for the target position and angular velocity are plotted. Under the influence of the despinning force, the target position gradually moves away from the initial position. Overall, the target angular velocity ω... tψ The angular velocity decreased in a "step-like" manner. After 14 despinning operations, the angular velocity of the target satellite around its maximum inertial principal axis decreased from 10 deg / s to around 1.14 deg / s, while the angular velocities of the other two axes gradually decreased to around 0 deg / s. This reduced the angular velocity to the desired level, enabling subsequent capture operations. Furthermore, with the cumulative number of despinning operations, the target's angular velocity gradually decreased, and the contact time during each despinning operation gradually increased, leading to a gradually greater magnitude of the decrease in angular velocity.

[0209] like Figure 4 As shown, the time history of the perturbation torque and its estimation error is presented. Because the brush undergoes large deformation during each despinning, it perturbs the attitude of the servicing spacecraft through a rigid-flexible coupling effect. It can be seen that the perturbation torque / force exhibits strong time-varying characteristics during each despinning, and the amplitude shows a decaying trend, with the maximum amplitude limited to |d... ψ |≤0.04(N·m),|d rx |≤0.02(N) and |d ry |≤0.01(N). Under a fixed-time disturbance observer, the estimation error is limited to 0.01 (N). |d rx |≤1×10 -3 (N) and |d ry |≤4=10 -4 (N) can achieve the desired estimation accuracy. The above results show that the designed observer can effectively estimate disturbances and compensate for them through feedforward, thereby enhancing the system's anti-interference performance.

[0210] like Figure 5 and Figure 6 As shown, the time history plots for Euler angles and angular velocity are presented. From the magnified view, it can be seen that during despinning, the Euler angles are strictly constrained within the performance function μ1, and the angular velocity is strictly constrained within the performance function μ2. Figure 7 As shown, the time history of the position tracking error is plotted. A magnified view reveals that the position tracking error during despinning is strictly constrained within the performance function μ1. These results demonstrate that the control strategy can achieve the preset performance control objectives of the servicing spacecraft while considering all state constraints, ensuring the stable and reliable operation of the servicing spacecraft and its safe execution of the despinning mission.

[0211] like Figure 8As shown in the time history of the state variable of the anti-windup compensator, it can be seen that the state variable is bounded and converges to the equilibrium position quickly in each despinning, which indicates that the control input remains within the saturation constraint after a short saturation, showing that the compensator can reduce the adverse effects of control input saturation.

[0212] As shown in the time history of the control input, the control torque / force changes rapidly in each despinning to achieve rapid attitude stabilization and position tracking control, and always satisfies the input saturation constraint. Figure 9

[0213] From the above simulation results, it can be concluded that the control strategy proposed in the embodiment can achieve full-state constraint control performance of the service spacecraft in despinning operation, effectively compensate for the adverse effects of control input saturation on the system, and effectively suppress the influence of disturbances on the system by estimating unknown time-varying disturbances through the fixed-time disturbance observer, thereby having strong anti-interference performance.

[0214] The application also provides an anti-windup preset performance despinning control system for a failed satellite, as shown in Figure 10 The system comprises an acquisition module, a modeling module and a control module.

[0215] The acquisition module is used to acquire the attitude of the service spacecraft and the failed satellite, and establish a dynamics model of the service spacecraft and the failed satellite.

[0216] The modeling module is used to establish a flexible operating rod dynamics model of the service spacecraft according to the dynamics model of the service spacecraft and the failed satellite, obtain the large deformation dynamics characteristics of the despinning brush, and establish a rigid-flexible coupled dynamics model of the service spacecraft through the Lagrange multiplier method under the framework of the dynamics model of the service spacecraft and the large deformation dynamics characteristics of the despinning brush.

[0217] The control module is used to design an anti-windup preset performance controller based on the rigid-flexible coupled dynamics model of the service spacecraft, and perform despinning control by using an anti-windup full-state constraint control strategy.

[0218] It can be understood that the anti-windup preset performance despinning control system for a failed satellite provided by the application corresponds to the anti-windup preset performance despinning control method for a failed satellite provided by the above-mentioned embodiments, and the related technical features of the anti-windup preset performance despinning control system for a failed satellite can refer to the related technical features of the anti-windup preset performance despinning control method for a failed satellite, which will not be described here.

[0219] Another object of the application is to provide an electronic device, as shown in​Figure 11 The anti-saturation preset performance despun control method for the failed satellite comprises the following steps:

[0220] The anti-saturation preset performance despun control method for the failed satellite comprises the following steps:

[0221] Obtaining the attitude of the service spacecraft and the failed satellite, and establishing a dynamics model of the service spacecraft and the failed satellite;

[0222] According to the dynamics model of the service spacecraft and the failed satellite, a flexible operating rod dynamics model of the service spacecraft is established, the large deformation dynamics characteristics of the despun brush are obtained, and a rigid-flexible coupling dynamics model of the service spacecraft is established through the Lagrange multiplier method under the framework of the dynamics model of the service spacecraft and the large deformation dynamics characteristics of the despun brush;

[0223] Based on the rigid-flexible coupling dynamics model of the service spacecraft, an anti-saturation preset performance controller is designed, and the despun control is performed by using an anti-saturation full-state constraint control strategy.

[0224] A fourth object of the present application is to provide a computer readable storage medium, which stores a computer program, wherein the computer program is executed by a processor to realize the steps of the anti-saturation preset performance despun control method for the failed satellite.

[0225] The anti-saturation preset performance despun control method for the failed satellite comprises the following steps:

[0226] Obtaining the attitude of the service spacecraft and the failed satellite, and establishing a dynamics model of the service spacecraft and the failed satellite;

[0227] According to the dynamics model of the service spacecraft and the failed satellite, a flexible operating rod dynamics model of the service spacecraft is established, the large deformation dynamics characteristics of the despun brush are obtained, and a rigid-flexible coupling dynamics model of the service spacecraft is established through the Lagrange multiplier method under the framework of the dynamics model of the service spacecraft and the large deformation dynamics characteristics of the despun brush;

[0228] Based on the rigid-flexible coupling dynamics model of the service spacecraft, an anti-saturation preset performance controller is designed, and the despun control is performed by using an anti-saturation full-state constraint control strategy.

[0229] Those skilled in the art will appreciate that embodiments of the application can be devised for a method, a system, or a computer program product. Accordingly, the present application can be embodied in the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present application can take the form of a computer program product on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROMs, optical storage devices, etc.) embodying computer readable program code.

[0230] The present application is described in reference to the flowchart and / or block diagrams of the method, apparatus (system) and computer program product according to embodiments of the application. It will be understood that each block of the flowchart and / or block diagrams, and combinations of blocks in the flowchart 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 processing device 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, create means for implementing the functions specified in the flowchart and / or block diagram block or blocks. Figure 1 one or more functions specified in the flowchart and / or block diagram block or blocks. Figure 1 one or more functions specified in the flowchart and / or block diagram block or blocks.

[0231] These computer program instructions can also be stored in a computer- readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instructions which implement the function specified in the flowchart and / or block diagram block or blocks. Figure 1 one or more functions specified in the flowchart and / or block diagram block or blocks. Figure 1 one or more functions specified in the flowchart and / or block diagram block or blocks.

[0232] These computer program instructions can also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart and / or block diagram block or blocks. Figure 1 one or more functions specified in the flowchart and / or block diagram block or blocks. Figure 1 one or more functions specified in the flowchart and / or block diagram block or blocks.

[0233] Finally, it should be noted that the above-mentioned embodiments are merely intended for describing the technical solutions of the present application, but not for limiting it. Although the present application is described in detail with reference to the above embodiments, those skilled in the field should understand that the specific embodiments of the present application can be modified or replaced equivalently without departing from the spirit and scope of the present application, and any modification or equivalent replacement without departing from the spirit and scope of the present application should be covered in the protection scope of the claims of the present application.

Claims

1. A method for anti-windup preset performance despin control of a failed satellite, characterized by, The method comprises the following steps: attitude of the service spacecraft and the failed satellite is acquired, and a dynamic model of the service spacecraft and the failed satellite is established; a flexible manipulator dynamic model of the service spacecraft is established according to the dynamic model of the service spacecraft and the failed satellite, and a large deformation dynamic characteristic of the despin brush is obtained, and a rigid-flexible coupling dynamic model of the service spacecraft is established through the Lagrange multiplier method under the framework of the dynamic model of the service spacecraft and the large deformation dynamic characteristic of the despin brush; an anti-windup preset performance controller is designed based on the rigid-flexible coupling dynamic model of the service spacecraft, and the despin control is performed by using an anti-windup full-state constraint control strategy.

2. The method of claim 1, wherein the method is a method of pre- set performance despin control of a failed satellite, characterized in that, The dynamic model of the service spacecraft is: wherein denotes an Euler angle vector of the servicing spacecraft, denotes an angular velocity vector of the attitude of the servicing spacecraft, denotes a moment of inertia of the servicing spacecraft, denotes a center of mass position vector of the servicing spacecraft, denotes a mass of the servicing spacecraft, denotes a control force, denotes a control torque, denotes a control force .

3. The method of claim 1, wherein the method is a method of pre- set performance de-spin control of a failed satellite, characterized by, The dynamic model of the failed satellite is: wherein, represents an attitude angular velocity vector of the failed satellite, represents an Euler angle vector of the failed satellite, represents a moment of inertia of the failed satellite, represents a center of mass position vector of the failed satellite, represents a mass of the failed satellite, represents a despin force, represents a despin torque, represents a despin force moment, .

4. The method of claim 1, wherein the method is a method of pre- set performance de-spin control of a failed satellite, characterized by, The flexible manipulator dynamic model of the service spacecraft is: wherein denotes the mass matrix, denotes the contact force vector, denotes the stiffness matrix related to axial deformation, denotes the elastic modulus, denotes the cross-sectional area, denotes the average axial strain, denotes the shape function, is the identity matrix, , , , , , denotes the material coordinate, denotes the racemic brush element length, is a short hand for denotes the partial derivative of the shape function with respect to , denotes the stiffness matrix related to bending deformation, denotes the cross-sectional moment of inertia, denotes the second derivative of the shape function with respect to , denotes the damping matrix, and denotes the proportionality coefficient, denotes the nodal coordinate vector.

5. The method of claim 1, wherein the method is a method of pre- set performance de-spin control of a failed satellite, and wherein the method further comprises: determining a de-spin command based on the de-spin command signal; and applying the de-spin command to the failed satellite. The rigid-flexible coupling dynamic model of the service spacecraft is: wherein, denotes the system mass matrix, denotes the system generalized coordinates, denotes the system generalized velocities, denotes the zero matrix, denotes the Lagrange multiplier vector, denotes the algebraic constraint equation, denotes the Jacobian matrix of the constraint equation, denotes the system generalized force vector, denotes the Lagrange multiplier vector, , and denotes the feedback control parameter to prevent constraint violation.

6. The method of claim 1, wherein the method is a method of pre- set performance de-spin control of a failed satellite, and wherein the method further comprises: determining a de-spin command based on the de-spin command signal; and applying the de-spin command to the failed satellite. The design process of the anti-windup preset performance controller comprises the following steps: a state tracking error is defined, a finite-time preset performance function is introduced, an obstacle Lyapunov function is considered, and a constraint is applied to the state tracking error; a virtual control input is designed, a virtual state tracking error is defined, a constraint is applied to each element of the virtual state tracking error, and an anti-windup compensator is designed; a fixed-time disturbance observer is used to estimate the disturbance of the anti-windup compensator to obtain a disturbance estimation value, a Lyapunov function is considered, and the disturbance estimation error is made to converge to the origin in a fixed time, thereby obtaining the anti-windup preset performance controller.

7. The method of claim 2, wherein the method is a method of pre- set performance de-spin control of a failed satellite, characterized by, The anti-windup full-state constraint control strategy comprises the following steps: wherein denotes a state variable of an anti-windup compensator, , , , is an n x m dimensional zero matrix, , denotes a real number, denotes a real number, denotes a virtual tracking error, , denotes a disturbance estimate, denotes a service spacecraft velocity level state, denotes a desired pose state.

8. An anti-windup preset performance despun control system for a failed satellite, characterized by, The method comprises the following steps: an acquisition module is configured to acquire the attitude of the service spacecraft and the failed satellite, and establish a dynamic model of the service spacecraft and the failed satellite; a modeling module is configured to establish a flexible manipulator dynamic model of the service spacecraft according to the dynamic model of the service spacecraft and the failed satellite, obtain a large deformation dynamic characteristic of the despin brush, and establish a rigid-flexible coupling dynamic model of the service spacecraft through the Lagrange multiplier method under the framework of the dynamic model of the service spacecraft and the large deformation dynamic characteristic of the despin brush; a control module is configured to design an anti-windup preset performance controller based on the rigid-flexible coupling dynamic model of the service spacecraft, and perform despin control by using an anti-windup full-state constraint control strategy.

9. A terminal device comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that, The processor executes the computer program to realize the steps of the method in any one of claims 1-7.

10. A computer-readable storage medium storing a computer program, the computer program comprising instructions that, when executed by a computer, cause the computer to perform the method of any one of claims 1 to 9. The computer program is executed by the processor to realize the steps of the method in any one of claims 1-7.

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