Anti-saturation preset performance racemization control method of failed satellite and related device

Abstract

The invention discloses an anti-saturation preset performance racemization control method for a failed satellite and a related device, and the method comprises the steps: obtaining the attitudes of a service spacecraft and the failed satellite, and building a dynamic model of the service spacecraft and the failed satellite; establishing a dynamic model of a flexible operating rod of the service spacecraft according to the dynamic models of the service spacecraft and the failure satellite to obtain large-deformation dynamic characteristics of the racemization brush, and establishing a dynamic model of the flexible operating rod of the service spacecraft under a framework of the dynamic model of the service spacecraft and the large-deformation dynamic characteristics of the racemization brush; establishing a service spacecraft rigid-flexible coupling dynamic model through a Lagrangian multiplier method; and designing an anti-saturation preset performance controller based on the rigid-flexible coupling dynamic model of the service spacecraft, and performing racemization control by using an anti-saturation full-state constraint control strategy. According to the invention, for the service spacecraft with the flexible operating rod, the efficient and accurate racemization process is realized, and the control performance is greatly improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of spacecraft control, and relates to an anti-saturation preset performance despin control method and related device for a failed satellite. Background Art

[0002] With the rapid development of space technology, a large number of launch missions are carried out every year to meet the growing demands such as meteorological monitoring and communication navigation. However, the number of failed satellites caused by factors such as fuel exhaustion and mechanical failures is increasing day by day. These failed satellites not only occupy precious orbital resources, but also pose a huge threat to the satellites operating normally in orbit. Affected by the residual angular momentum and space perturbation torque, the attitude of the satellite presents complex free tumbling motion, making direct capture extremely difficult. Therefore, the despin operation before capture is a key link. At present, using a servicing spacecraft equipped with a flexible operating rod to perform the despin operation on a failed satellite is an efficient and novel method. However, due to the large flexible deformation generated when the operating rod interacts with the satellite, the servicing spacecraft exhibits non-linear and strong coupling characteristics. At the same time, the strong disturbance caused by the contact has a greater impact on its stability, seriously reducing its transient and steady-state response performance, resulting in greater difficulties in the design of the control strategy for the despin process.

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

[0004] For the despin process of a failed satellite, it is necessary to design a new control method to effectively suppress the adverse effects brought by disturbances, and at the same time achieve the preset transient and steady-state response performance, so as to improve the anti-interference performance of the servicing spacecraft and provide necessary conditions for realizing efficient and accurate despin operation. Summary of the Invention

[0005] The purpose of the present invention is to provide an anti-saturation preset performance despin control method and related device for a failed satellite, so as to solve the problem that the existing control methods have a greater impact on the transient and steady-state response performance.

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

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

[0008] Obtain the attitudes of the servicing spacecraft and the failed satellite, and establish the dynamic models of the servicing spacecraft and the failed satellite;

[0009] Based on the dynamic models of the servicing spacecraft and the failed satellite, establish the dynamic model of the flexible operating rod of the servicing spacecraft, obtain the large deformation dynamic characteristics of the despin brush. Under the framework of the dynamic model of the servicing spacecraft and the large deformation dynamic characteristics of the despin brush, establish the rigid-flexible coupling dynamic model of the servicing spacecraft by the Lagrange multiplier method;

[0010] Based on the rigid-flexible coupling dynamic model of the servicing spacecraft, design an anti-saturation preset performance controller and use the anti-saturation full state constraint control strategy for despin control.

[0011] Furthermore, the dynamic model of the servicing spacecraft is:

[0012]

[0013] where ω = [ω φ ω θ ω ψ T represents the attitude angular velocity vector of the servicing spacecraft, σ = [φ θ ψ] T represents the Euler angle vector of the servicing spacecraft, J represents the moment of inertia of the servicing spacecraft, r c represents the position vector of the center of mass of the servicing spacecraft, m c represents the mass of the servicing spacecraft, f(t) represents the control force, u(t) represents the control torque, D c is expressed as

[0014] Furthermore, the dynamic model of the failed satellite is:

[0015]

[0016] where ω t = [ω tφ ω tθ ω tψ T represents the attitude angular velocity vector of the failed satellite, σ t = [φ t θ t ψ t T represents the Euler angle vector of the failed satellite, J t represents the moment of inertia of the failed satellite, r t represents the position vector of the center of mass of the failed satellite, m t represents the mass of the failed satellite, F c represents the despin force, T c represents the despin torque, D t is expressed as ​​​

[0017] Furthermore, the dynamic model of the flexible operating rod of the servicing spacecraft is as follows:

[0018]

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

[0020] Furthermore, the rigid-flexible coupling dynamic model of the servicing spacecraft is as follows:

[0021]

[0022] where M q represents the system mass matrix, q represents the system generalized coordinate, 0 6×6 represents a 6×6 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, β 1 and β 2 represent the feedback control parameters to prevent constraint violation.

[0023] Furthermore, the design process of the anti-saturation preset performance controller includes:

[0024] Define the state tracking error, introduce the finite-time preset performance function, consider the barrier Lyapunov function, and impose constraints on the state tracking error;

[0025] Design the virtual control input, define the virtual state tracking error, impose constraints on each element of the virtual state tracking error, and design the anti-saturation compensator;

[0026] Use a fixed-time disturbance observer to estimate the disturbance of the anti-saturation compensator, obtain the disturbance estimate value, consider the Lyapunov function, and make the disturbance estimation error converge to the origin in a fixed time to obtain the anti-saturation preset performance controller.

[0027] Furthermore, the anti-saturation full-state constraint control strategy is as follows:

[0028]

[0029] where ζ represents the state variable of the anti-windup compensator, 0 n×m is an n×m zero matrix. K 2 >0 represents a positive constant, K 3 >0 represents a positive constant, α represents the virtual tracking error, μ 2 represents the set performance constraint function, represents the disturbance estimation value, x 2 represents the velocity-level state of the service spacecraft, x d represents the desired state.

[0030] An anti-windup preset performance despin control system for a failed satellite, comprising:

[0031] An acquisition module, which is used to acquire the attitudes of the service spacecraft and the failed satellite and establish the dynamic models of the service spacecraft and the failed satellite;

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

[0033] A control module, which is used 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 the anti-windup full state constraint control strategy.

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

[0035] A computer-readable storage medium stores a computer program, and the steps of the method are implemented when the computer program is executed by a processor.

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

[0037] The present invention provides a desaturation preset performance despin control method for a failed satellite. By obtaining the attitudes of the servicing spacecraft and the failed satellite and establishing the dynamic models of the servicing spacecraft and the failed satellite, the interaction between the two can be more accurately simulated, thereby more effectively planning and executing the despin operation on the failed satellite. Then, based on the dynamic models of the servicing spacecraft and the failed satellite, the dynamic model of the flexible operating rod of the servicing spacecraft is established to obtain the large deformation dynamic characteristics of the despin brush, which helps to enhance the accuracy and stability of the despin control and reduce the control error caused by inaccurate models. Furthermore, within the framework of the dynamic model of the servicing spacecraft and the large deformation dynamic characteristics of the despin brush, the rigid-flexible coupling dynamic model of the servicing spacecraft is established by the Lagrange multiplier method to more comprehensively reflect the dynamic behavior of the system, providing a basis for designing more complex control strategies. Finally, an anti-saturation preset performance controller is designed, and the anti-saturation full-state constraint control strategy is used for despin control. This controller can cope with the saturation phenomenon during the control process, ensure that the control command is within a reasonable range, and prevent the system from becoming unstable 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 present invention is aimed at a servicing spacecraft with a flexible operating rod. Without the information of the upper bounds of the disturbance and its derivatives, it can accurately estimate the strong disturbance caused by contact, achieve a fast response speed and high steady-state accuracy of the spacecraft, and significantly improve the anti-interference performance. In the presence of input saturation and strong disturbance caused by contact, it can not only ensure the preset dynamic and steady-state response performance of the servicing spacecraft, but also contribute to realizing an efficient and accurate despin process. At the same time, an anti-saturation compensator is introduced to effectively compensate for the control input saturation, significantly reducing the actuator saturation degree, effectively suppressing the negative impact of saturation on the servicing spacecraft, and greatly improving the control performance. The control method of the present invention is simple. It not only priori guarantees the transient and steady-state performance, but also involves fewer control parameters, reducing the difficulty of parameter selection and the computational complexity, which is beneficial to practical engineering applications. Description of the Drawings

[0038] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for use in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention, and thus should not be regarded as limiting the scope. For those of ordinary skill in the art, other related drawings can be obtained based on these drawings without creative efforts.

[0039] Figure 1 It is a diagram of the anti-saturation preset performance despin control method for the failed satellite of the present invention.

[0040] Figure 2 It is a diagram of the change process of the position of the failed satellite in Embodiment 1 of the present invention.

[0041] Figure 3 It is the graph of the change process of the angular velocity of the failed satellite in Embodiment 1 of the present invention.

[0042] Figure 4 It is the graph of the change process of the interference estimation error in Embodiment 1 of the present invention.

[0043] Figure 5 It is the graph of the change process of the attitude angle of the servicing spacecraft in Embodiment 1 of the present invention.

[0044] Figure 6 It is the graph of the change process of the angular velocity of the servicing spacecraft in Embodiment 1 of the present invention.

[0045] Figure 7 It is the graph of the change process of the position tracking error of the servicing spacecraft in Embodiment 1 of the present invention.

[0046] Figure 8 It is the graph of the change process of the state of the anti-saturation compensator in Embodiment 1 of the present invention.

[0047] Figure 9 It is the graph of the change curve of the control torque in Embodiment 1 of the present invention.

[0048] Figure 10 It is the schematic structural diagram of the anti-saturation preset performance despin control system of the failed satellite in the preferred embodiment of the present invention.

[0049] Figure 11 It is the schematic structural diagram of the electronic device in the preferred embodiment of the present invention. Detailed implementation manners

[0050] The following makes an explanation of the exemplary embodiments of the present application in conjunction with the accompanying drawings. Various details of the embodiments of the present application are included to assist in understanding, and they should be considered merely exemplary. Therefore, those of ordinary skill in the art should recognize that various changes and modifications can be made to the embodiments described herein without departing from the scope and spirit of the present application. Similarly, for clarity and conciseness, the description of well-known functions and structures is omitted below.

[0051] Obviously, the described embodiments are part of the embodiments of the present application, rather than all of the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments in the present application without creative efforts fall within the scope of protection of the present application.

[0052] It should be noted that the terminals involved in the embodiments of the present application may include, but are not limited to, mobile phones, personal digital assistants (PDAs), wireless handheld devices, tablet computers, personal computers (PCs), MP3 players, MP4 players, wearable devices (such as smart glasses, smart watches, smart bracelets, etc.), and smart home devices and other intelligent devices.

[0053] In addition, the term "and / or" in this article is merely a description of the association relationship of associated objects, indicating that three relationships may exist. For example, A and / or B may represent: A exists alone, A and B exist simultaneously, and B exists alone. In addition, the character " / " in this article generally represents an "or" relationship between the preceding and following associated objects.

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

[0055] See Figure 1 , the present invention provides a desaturation preset performance despin control method for a failed satellite, specifically including the following steps:

[0056] Step 1: Establish the dynamic models of the service spacecraft and the failed satellite.

[0057] The attitudes of the service spacecraft and the failed satellite are described by Euler angles, and the six-degree-of-freedom pose dynamics of the service spacecraft are expressed as

[0058]

[0059] The six-degree-of-freedom pose dynamics of the failed satellite are expressed as

[0060]

[0061] where, ω t = [ω tφ ω tθ ω tψ T and ω = [ω φ ω θ ω ψ T respectively represent the attitude angular velocity vectors of the service spacecraft and the failed satellite, σ = [φ θ ψ] T and σ t = [φ t θ t ψ t T respectively represent the Euler angle vectors of the service spacecraft and the failed satellite, J and J trespectively represent the moments of inertia of the service spacecraft and the failed satellite, r c and r t respectively represent the position vectors of the centers of mass of the service spacecraft and the failed satellite, m c and m t respectively represent the masses of the service spacecraft and the failed satellite, f(t) represents the control force, u(t) represents the control torque, F c represents the despin force, T c represents the despin torque, D c and D t have a similar expression form, D c is expressed as

[0062]

[0063] Step 2: Establish a dynamic model of the flexible operating rod.

[0064] To accurately describe the large deformation dynamic characteristics of the despin brush, the 3D absolute nodal coordinate method is used to describe its dynamic equation. The global position coordinates of any point on the despin brush element are expressed as

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

[0066] where S(x) = [S 1 I 3 S 2 I 3 S 3 I 3 S 4 I 3 T represents the shape function, I 3 is the 3×3 identity matrix, S 1 (x) = 1 - 3ξ 2 + 2ξ 3 , S 2 (x) = L(ξ - 2ξ 2 + ξ 3 ), S 3 (x) = 3ξ 2 - 2ξ 3 , S 4 (x) = L(-ξ 2 + ξ 3 ), ξ = x / L, x represents the material coordinate, L represents the length of the despin brush element, and e(t) represents the nodal coordinate vector.

[0067] The element mass matrix is expressed as

[0068]

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

[0070] The element 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, which is expressed as

[0071]

[0072] where E and J respectively represent the elastic modulus and the cross-sectional moment of inertia of the de-spun brush, ε represents the axial strain, and κ represents the curvature.

[0073] The elastic forces caused by axial deformation and bending deformation can be written as

[0074]

[0075] where represents the stiffness matrix related to axial deformation, is the average axial strain, and S x is the first derivative of S(x) with respect to x. represents the stiffness matrix related to bending deformation, and S xx is S x (x) the first derivative of with respect to x.

[0076] The element dynamic equation of the de-spun brush is expressed as

[0077]

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

[0079] Step 3: Establish the rigid-flexible coupling dynamic model of the service spacecraft.

[0080] Assemble the de-spun brush elements according to the traditional finite element program to obtain the dynamic equation of the de-spun brush system. Under the framework of the dynamic model of the service spacecraft and the dynamic model of the de-spun brush system, establish the rigid-flexible coupling dynamic model of the spacecraft through the Lagrange multiplier method, which is expressed in the following compact form

[0081]

[0082] where M q represents the system mass matrix, q represents the system generalized coordinates, 0 6×6 represents a 6×6 zero matrix. λ represents the Lagrange multiplier vector, Φ represents the algebraic constraint equation, and Φ q represents the Jacobian matrix of the constraint equation, Q represents the system generalized force vector, and γ represents the Lagrange multiplier vector. β 1 and β 2 represent the feedback control parameters to prevent constraint violations.

[0083] Step 4: Design an anti-saturation preset performance controller.

[0084] First, define the state tracking error as

[0085]

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

[0087] Introduce a finite-time preset performance function, denoted as

[0088]

[0089] where, μ 0j ≥ 1, μ Tj > 0, T j represents the arrival 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] Impose a constraint on the state tracking error z 1 , that is, satisfy |z 1i | ≤ μ 1 , i = 1, 2,..., 6. Consider the following barrier Lyapunov function

[0091]

[0092] where, I i is a 6×6 diagonal matrix, whose i-th diagonal element is equal to 1 and the remaining elements are equal to 0.

[0093] Take the first derivative of Equation (12) with respect to time and simplify to obtain

[0094]

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

[0096] The designed virtual control input is

[0097]

[0098] where K 1 > 0 is a positive constant.

[0099] The virtual tracking error is defined as

[0100] α = z 2 - x 2 * (15)

[0101] Substituting Equation (15) into Equation (13) and arranging, we can get

[0102]

[0103] Applying constraints to each element of the virtual tracking error α, that is, satisfying |α i | ≤ μ 2 , i = 1, 2,..., 6. Considering another barrier Lyapunov function

[0104]

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

[0106] Taking the derivative of Equation (17) with respect to time and arranging, we can get

[0107]

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

[0109] The anti - saturation 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] Taking the derivative of equation (15) with respect to time gives

[0113]

[0114] where

[0115] 0 n×m is an \(n\times m\) zero matrix.

[0116] Using a fixed-time disturbance observer to estimate the disturbance \(d(t)\), first define a new auxiliary variable, denoted as

[0117]

[0118] where \(l\) 1 > 0 represents a positive constant.

[0119] The estimation algorithm of \(\xi\) is designed as

[0120]

[0121] where represents the estimation error of \(\xi\), \(l\) 2 > 0 represents a positive constant, \(\alpha\) 1 > 1, \(\alpha\) 2 and \(\alpha\) 3 are positive odd numbers, and satisfy \(\alpha\) 2 < \(\alpha\) 3 . The symbol where \(sgn(\cdot)\) is the sign function.

[0122] The estimated value of the disturbance is designed as

[0123]

[0124] According to equations (21) and (22), we can obtain

[0125]

[0126] Consider the following Lyapunov function

[0127]

[0128] Taking the first derivative of equation (25) with respect to time and substituting equation (24) gives

[0129]

[0130] where represents a positive constant, denotes a positive constant, denotes a positive constant, denotes a positive constant.

[0131] When t≥T p then V ξ =0, at this time where T p has an upper bound of According to Equation (26), it can be obtained that Therefore, the disturbance estimation error will converge to the origin in a fixed time.

[0132] Substituting Equation (20) into Equation (18) gives

[0133]

[0134] where, Φ 2i is expressed as satisfies μ 2 2 (0)≥α i 2 (0), i = 1, 2,..., 6, K 1 >0 is a positive constant, Φ 1i is expressed as satisfies μ 1 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-saturation preset performance decoupling control strategy is designed as

[0136]

[0137] where, ζ represents the state variable of the anti-saturation compensator, K 2 >0 represents a positive constant, K 3 >0 represents a positive constant, α represents the virtual tracking error, μ 2 represents the preset performance function, represents the disturbance estimation value, x 2 * represents the virtual control input, x d represents the desired pose state.

[0138] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments:

[0139] Embodiment 1:

[0140] In this embodiment, taking the spacecraft despin system composed of a servicing spacecraft, a flexible operating rod, and a failed satellite as an example, the effectiveness of the anti-saturation preset performance despin control method of the present invention is illustrated. The simulation parameters of the despin system are shown in Table 1, which includes the dynamic parameters of the servicing spacecraft, the flexible operating rod, and the failed satellite.

[0141] Table 1 Physical parameters of the despin system

[0142]

[0143]

[0144] The anti-saturation preset performance despin control method for the failed satellite specifically includes the following steps:

[0145] Step 1: Establish the dynamic models of the servicing spacecraft and the failed satellite

[0146] The dynamic model of the servicing 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 respectively represent the attitude angular velocity vectors of the servicing spacecraft and the failed satellite. σ = [φ θ ψ] T and σ t = [φ t θ t ψ t ] T respectively represent the Euler angle vectors of the servicing spacecraft and the failed satellite. J and J t respectively represent the moments of inertia of the servicing spacecraft and the failed satellite. r c and r t respectively represent the centroid position vectors of the servicing spacecraft and the failed satellite. m c and m t respectively represent the masses of the servicing spacecraft and the failed satellite. f(t) represents the control force, and u(t) represents the control torque. F c represents the despin force, and T c represents the despin torque. Dc and D t is expressed as

[0151]

[0152] Step 2: Establish the dynamic model of the flexible operating rod

[0153] In order to accurately describe the large deformation dynamic characteristics of the de-spinning brush, the 3D absolute nodal coordinate method is used to describe its dynamic equation, and the element dynamic equation of the de-spinning 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, C = aM e + b(K t + K l ) is the damping matrix, a and b are proportionality coefficients, and e(t) represents the nodal coordinate vector.

[0156] Step 3: Rigid-flexible coupling dynamic model of the service spacecraft

[0157] Assemble the brush elements according to the traditional finite element program to obtain the dynamic equation of the brush system. Under the framework of the dynamic model of the service spacecraft formula (1) and the dynamic model of the brush system, establish the rigid-flexible coupling dynamic model of the spacecraft through 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 coordinate, 0 6×6 is expressed as a 6×6 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 generalized force vector of the system, γ represents the Lagrange multiplier vector, β 1 and β 2 represent the feedback control parameters to prevent constraint violation.

[0160] Step 4: Design of the anti-saturation preset performance controller

[0161] First, define the state tracking error as

[0162]

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

[0164] Introduce a finite-time preset performance function, denoted as

[0165]

[0166] where μ 0j ≥ 1, μ Tj > 0, T j represents the time to arrival, 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] Impose a constraint on the state tracking error z 1 , that is, satisfy |z 1i | ≤ μ 1 , i = 1, 2,..., 6. Consider the following barrier Lyapunov function

[0168]

[0169] where I i is a 6×6 diagonal matrix, whose i-th diagonal element is equal to 1 and the remaining elements are equal to 0.

[0170] Take the first derivative of Equation (8) with respect to time and after rearrangement, we can get

[0171]

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

[0173] Design the virtual control input as

[0174]

[0175] where K 1 > 0 represents a positive constant.

[0176] Define the virtual tracking error as

[0177] α = z 2 - x 2 * (11)

[0178] Substitute equation (11) into equation (9) and after rearrangement, we can obtain

[0179]

[0180] Apply constraints to each element of the virtual tracking error α, that is, satisfy |α i | ≤ μ 2 , where i = 1, 2,..., 6. Consider another barrier Lyapunov function

[0181]

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

[0183] Take the derivative of equation (13) with respect to time and after rearrangement, we can obtain

[0184]

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

[0186] The anti - saturation 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 can obtain

[0190]

[0191] where 0 n×m is an n×m - dimensional zero matrix.

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

[0193]

[0194] where l 1 > 0 represents a positive constant.

[0195] The estimation algorithm of ξ is designed as

[0196]

[0197] where represents the estimation error of ξ, l 2 > 0 represents a positive constant,, α 1 > 1, α 2 and α 3 are positive odd numbers, and satisfy α 2 < α 3 . The symbol where sgn(·) is the sign function.

[0198] The disturbance estimate value is designed as

[0199]

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

[0201]

[0202] where ζ represents the state variable of the anti-saturation compensator, 0 n×m is an n×m dimensional zero matrix, represents the disturbance estimate value, K 2 > 0 represents a positive constant, K 3 > 0 represents a positive constant, α represents the virtual tracking error, μ 2 represents the pre-set performance function, x 2 * represents the virtual control input, x d represents the desired pose state, x d represents the desired pose state.

[0203] According to the above implementation steps, using the dynamic model parameters in Table 1, the dynamics simulation of the de-spin system is carried out. On this basis, the key control parameters are selected to complete the simulation of the entire de-spin process. The controller parameters are selected as: K 1 = K 2 = K3 = 1; The parameters of the disturbance observer are selected as: l 1 = l 2 = l 3 = 1, α 1 = 1.1, α 2 = 3, α 3 = 11; The parameters of the anti - saturation compensator are selected as: k a = 0.3, k b = 0.05. The parameters of the predefined time performance function are selected as: μ 0j = 0.8, μ Tj = 0.005, T j = 15 s, j = 1, 2. In addition, the amplitudes of the control torque and the control force are respectively limited to |τ i | ≤ 4 (N·m), i = φ, θ, ψ and |τ j | ≤ 6 (N), j = x, y, z.

[0204] The desired pose state is

[0205]

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

[0207] The start time of the mission is t = 0 s, and the end time is t = 500 s. The service spacecraft has approached the vicinity of the failed satellite and hovers at the desired position and attitude. At the same time, the flexible operating rod has entered the range of the solar panel envelope under the drive of the robotic arm. The initial velocity of the satellite is [10 1 1] T deg / s. Apply the above - mentioned control parameters to the above - mentioned method of this embodiment, conduct the de - spinning simulation of the failed satellite, and obtain the simulation results:

[0208] As Figure 2 and Figure 3 shown, the time - history diagrams of the target position and the angular velocity are respectively plotted. Under the action of the de - spinning force, the target position gradually moves away from the initial position. Generally speaking, the target angular velocity ω tψ shows a "step - by - step" decrease. After 14 de - spinning operations, the angular velocity of the target satellite around the maximum inertia principal axis decreases from 10 deg / s to around 1.14 deg / s, and the angular velocities of the other two axes also gradually decay to around 0 deg / s. The angular velocity has decayed to the desired level, and subsequent capture tasks can be carried out. In addition, with the accumulation of the number of de - spinning times, the target angular velocity gradually decays, and the contact time of a single de - spinning gradually extends, resulting in an increasing reduction magnitude of the angular velocity.

[0209] As Figure 4As shown, the time history diagrams of the disturbing torque and its estimation error are presented. Since the brush experiences large deformation motions during each despin, it perturbs the attitude of the servicing spacecraft through the rigid-flexible coupling effect. It can be seen that during each despin, the disturbing torque / force exhibits strong time-varying characteristics, 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 the fixed-time disturbance observer, the estimation error is limited to |d rx | ≤ 1×10 -3 (N) and |d ry | ≤ 4=10 -4 (N), and the desired estimation accuracy can be achieved. The above results indicate that the designed observer can effectively estimate the disturbance and compensate for it through the feedforward method, thereby enhancing the anti-disturbance performance of the system.

[0210] As Figure 5 and Figure 6 shown, the time history diagrams of the Euler angles and angular velocities are given. From the local enlarged diagrams, it can be seen that during the despin, the Euler angles are strictly constrained within the performance function μ 1 and the angular velocities are strictly constrained within the performance function μ 2 . As Figure 7 shown, the time history diagram of the position tracking error is plotted. From the local enlarged diagram, it can be seen that during the despin, the position tracking error is strictly constrained within the performance function μ 1 . These results illustrate that the control strategy can achieve the preset performance control objectives of the servicing spacecraft while considering the full-state constraints, ensuring the stable and reliable operation of the servicing spacecraft and safely performing the despin task.

[0211] As Figure 8 shown, the time history diagram of the anti-saturation compensator state variables is given. It can be seen that the state variables are bounded, and during each despin, the state variables quickly converge to the equilibrium position, indicating that after a short saturation, the control input always remains within the saturation constraint, demonstrating that the compensator can reduce the adverse effects brought by the control input saturation.

[0212] As Figure 9 shown, the time history diagram of the control input is presented. During each despin, the control torque / force changes rapidly to achieve rapid attitude stabilization and position tracking control, and always satisfies the input saturation constraint. In addition, due to the existence of the feedforward compensation term of the disturbance estimation value, the control torque / force exhibits a non-smooth jitter phenomenon.

[0213] From the above simulation results, it can be concluded that the control strategy proposed in this embodiment can achieve the full-state constraint control performance of the service spacecraft during the despin operation, effectively compensate for the adverse effects caused by control input saturation on the system, and at the same time estimate the unknown time-varying disturbance through a fixed-time disturbance observer, effectively suppressing the influence of the disturbance on the system, and having strong anti-disturbance performance.

[0214] The present invention also provides an anti-saturation preset performance despin control system for a failed satellite, as Figure 10 shown. The system includes an acquisition module, a modeling module, and a control module.

[0215] The acquisition module is used to acquire the attitudes of the service spacecraft and the failed satellite and establish the dynamic models of the service spacecraft and the failed satellite.

[0216] The modeling module is used to establish the dynamic model of the flexible operating rod of the service spacecraft according to the dynamic models of the service spacecraft and the failed satellite, obtain the large deformation dynamic characteristics of the despin brush, and establish the rigid-flexible coupling dynamic model of the service spacecraft by the Lagrange multiplier method under the framework of the dynamic model of the service spacecraft and the large deformation dynamic characteristics of the despin brush.

[0217] The control module is used to design an anti-saturation preset performance controller based on the rigid-flexible coupling dynamic model of the service spacecraft and perform despin control using the anti-saturation full-state constraint control strategy.

[0218] It can be understood that the anti-saturation preset performance despin control system for a failed satellite provided by the present invention corresponds to the anti-saturation preset performance despin control method for a failed satellite provided in the foregoing embodiments. The relevant technical features of the anti-saturation preset performance despin control system for a failed satellite can refer to the relevant technical features of the anti-saturation preset performance despin control method for a failed satellite, and will not be elaborated here.

[0219] Another object of the present invention is to provide an electronic device, as Figure 11 shown, including a memory, a processor, and a computer program stored in the memory and executable on the processor, and the processor executes the steps of the anti-saturation preset performance despin control method for a failed satellite.

[0220] The anti-saturation preset performance despin control method for a failed satellite includes the following steps:

[0221] Acquire the attitudes of the service spacecraft and the failed satellite and establish the dynamic models of the service spacecraft and the failed satellite.

[0222] According to the dynamic models of the servicing spacecraft and the failed satellite, establish the dynamic model of the flexible operating rod of the servicing spacecraft, obtain the large deformation dynamic characteristics of the de-spin brush. Under the framework of the dynamic model of the servicing spacecraft and the large deformation dynamic characteristics of the de-spin brush, establish the rigid-flexible coupling dynamic model of the servicing spacecraft by the Lagrange multiplier method;

[0223] Based on the rigid-flexible coupling dynamic model of the servicing spacecraft, design an anti-saturation preset performance controller and perform de-spin control by using the anti-saturation full state constraint control strategy.

[0224] The fourth object of the present invention is to provide a computer-readable storage medium, which stores a computer program. When the computer program is executed by a processor, the steps of the anti-saturation preset performance de-spin control method for the failed satellite are realized.

[0225] The anti-saturation preset performance de-spin control method for the failed satellite includes the following steps:

[0226] Obtain the attitudes of the servicing spacecraft and the failed satellite, and establish the dynamic models of the servicing spacecraft and the failed satellite;

[0227] According to the dynamic models of the servicing spacecraft and the failed satellite, establish the dynamic model of the flexible operating rod of the servicing spacecraft, obtain the large deformation dynamic characteristics of the de-spin brush. Under the framework of the dynamic model of the servicing spacecraft and the large deformation dynamic characteristics of the de-spin brush, establish the rigid-flexible coupling dynamic model of the servicing spacecraft by the Lagrange multiplier method;

[0228] Based on the rigid-flexible coupling dynamic model of the servicing spacecraft, design an anti-saturation preset performance controller and perform de-spin control by using the anti-saturation full state constraint control strategy.

[0229] Those skilled in the art should understand that the embodiments of the present invention can be provided as a method, a system, or a computer program product. Therefore, the present invention can take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present invention can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0230] The present invention is described with reference to the flowcharts and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the present invention. It should be understood that each flow and / or block in the flowchart and / or block diagram, and combinations of flows and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to the processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing device to produce a machine, such that the instructions executed by the processor of the computer or other programmable data processing device produce means for implementing the functions specified in one flow Figure 1 one flow or multiple flows and / or blocks Figure 1 or means for implementing the functions specified in one block or multiple 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 device to work in a specific manner, such that the instructions stored in the computer-readable memory produce a manufactured article including instruction means that implement the functions specified in one flow Figure 1 one flow or multiple flows and / or blocks Figure 1 or means for implementing the functions specified in one block or multiple blocks.

[0232] These computer program instructions can also be loaded onto a computer or other programmable data processing device, such that a series of operation steps are executed on the computer or other programmable device to produce a computer-implemented process, so that the instructions executed on the computer or other programmable device provide steps for implementing the functions specified in one flow Figure 1 one flow or multiple flows and / or blocks Figure 1 or means for implementing the functions specified in one block or multiple blocks.

[0233] Finally, 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 them. Although the present invention has been described in detail with reference to the above embodiments, those of ordinary skill in the art should understand that: modifications or equivalent substitutions can still be made to the specific embodiments of the present invention. Any modification or equivalent substitution that does not depart from the spirit and scope of the present invention shall be covered by the protection scope of the claims of the present invention.

Claims

1. A method for controlling the anti-saturation preset performance of a failed satellite, characterized in that: include: Obtain the attitude of the service spacecraft and the failed satellite, and establish the dynamic model of the service spacecraft and the failed satellite; According to the dynamic models of the service spacecraft and the failed satellite, the dynamic model of the flexible operating rod of the service spacecraft is established, and the large deformation dynamic characteristics of the de-rotation brush are obtained. Under the framework of the dynamic model of the service spacecraft and the large deformation dynamic characteristics of the de-rotation brush, the rigid-flexible coupling dynamic model of the service spacecraft is established by the Lagrange multiplier method. Based on the rigid-flexible coupling dynamics model of the service spacecraft, an anti-saturation preset performance controller is designed, and the anti-saturation full-state constraint control strategy is used for de-rotation control.

2. The anti-saturation preset performance de-rotation control method of a failed satellite according to claim 1, characterized in that: The dynamic model of the service spacecraft is: Where ω=[ω φ ω θ ω ψ ] T represents the attitude angular velocity vector of the service spacecraft, σ=[φ θ ψ] T represents the Euler angle vector of the service spacecraft, J represents the moment of inertia of the service spacecraft, r c represents the service spacecraft mass center position vector, m c represents the mass of the service spacecraft, f(t) represents the control force, u(t) represents the control torque, and D c Expressed as 3. The method for controlling the anti-saturation preset performance of a failed satellite according to claim 1, characterized in that: The dynamic model of the failed satellite is: Among them, ω t =[ω tφ ω tθ ω tψ ] T represents the attitude angular velocity vector of the failed satellite, σ t =[φ t θ t ψ t ] T The Euler angle vector of the failed satellite, J t represents the moment of inertia of the failed satellite, r t represents the failed satellite mass center position vector, m t represents the mass of the failed satellite, F c represents the racemic force, T c Denotes the deracination torque, D t Expressed as 4. The method for controlling the anti-saturation preset performance of a failed satellite according to claim 1, characterized in that: The dynamic model of the flexible operating rod of the service spacecraft is: Among them, Q c represents the contact force vector, represents the stiffness matrix associated with the axial deformation, represents the stiffness matrix associated with bending deformation, C = aM e +b(K t +K l ) represents the damping matrix, a and b represent the proportional coefficients, and e(t) represents the node coordinate vector.

5. The method for controlling the anti-saturation preset performance of a failed satellite according to claim 1, characterized in that: The rigid-flexible coupling dynamics model of the service spacecraft is: Among them, M q represents the system mass matrix, q represents the system generalized coordinates, 0 6×6 It is represented as a 6×6 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 generalized force vector of the system, γ represents the Lagrange multiplier vector, β1 and β2 represent feedback control parameters to prevent constraint violations.

6. The method for controlling the anti-saturation preset performance of a failed satellite according to claim 1, characterized in that: The design process of the anti-saturation preset performance controller includes: Define the state tracking error, introduce the finite time preset performance function, consider the barrier Lyapunov function, and impose constraints on the state tracking error; Design virtual control input, define virtual state tracking error, impose constraints on each element of virtual state tracking error, and design an anti-saturation compensator; A fixed-time disturbance observer is used to estimate the disturbance of the anti-saturation compensator to obtain the disturbance estimation value. Considering the Lyapunov function, the disturbance estimation error is made to converge to the origin in a fixed time, and an anti-saturation preset performance controller is obtained.

7. The method for controlling the anti-saturation preset performance of a failed satellite according to claim 1, characterized in that: The anti-saturation full-state constraint control strategy is: Where ζ represents the state variable of the anti-saturation compensator, 0 n×m is an n×m dimensional zero matrix, K2>0 indicates a positive constant, K3>0 indicates a positive constant, α indicates a virtual tracking error, μ2 represents the set performance constraint function, represents the interference estimate, x2 represents the speed level of the service spacecraft, and x d Indicates a desired state.

8. A desaturation control system for a failed satellite with preset performance, characterized in that: include: An acquisition module, the acquisition module is used to acquire the attitudes of the service spacecraft and the failed satellite, and establish a dynamic model of the service spacecraft and the failed satellite; A modeling module, wherein 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 de-rotation brush, and establish a rigid-flexible coupling dynamics model of the service spacecraft by Lagrange multiplier method under the framework of the dynamics model of the service spacecraft and the large deformation dynamics characteristics of the de-rotation brush; A control module is used to design an anti-saturation preset performance controller based on a rigid-flexible coupling dynamic model of a service spacecraft, and to perform de-rotation control using an anti-saturation full-state constraint control strategy.

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

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

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