Spacecraft attitude preset time control method based on adjustable preset performance

Abstract

The invention discloses a spacecraft attitude preset time control method based on adjustable preset performance, and the method comprises the steps: building a kinematics and dynamics model for spacecraft attitude control, and obtaining a spacecraft attitude control system model; thirdly, designing an adjustable preset performance function and a new error conversion function, and converting the original system into a new second-order system; and finally, designing a non-singular sliding mode controller for the converted second-order system to realize accurate control of system errors, so that the system still has the capabilities of keeping the system stable and enabling the controller to take effect under the condition that the system is subjected to certain sudden change disturbance. According to the method, by introducing an adjustable preset performance boundary, designing a new error conversion function and combining nonsingular sliding mode control, accurate control over system errors is achieved, meanwhile, the robustness and the disturbance rejection capacity of the system are improved, and solid technical support is provided for spacecraft attitude control.

Description

Technical Field

[0001] The present invention belongs to the field of spacecraft attitude control, and relates to a spacecraft attitude control method, specifically to a preset-time stable spacecraft attitude control method based on adjustable preset performance control. Background Technique

[0002] When a spacecraft executes tasks, it often has very high requirements for its own attitude control accuracy. Compared with traditional control methods, the preset performance control method has the advantages of fast speed, high accuracy, and controllable error, and is suitable for spacecraft attitude control. However, in the basic preset performance control method, there is a problem of control vulnerability, that is, after the control target is subjected to a sudden disturbance, the error exceeds the preset performance boundary, resulting in singularity of the system and the failure of the control system. This problem restricts the application of the preset performance control method in reality. To address this challenge, researchers and engineers have continuously explored improved control strategies and methods, and proposed an adjustable preset performance control method. By dynamically adjusting the preset performance boundary, the new control method takes into account both the control accuracy and speed of the preset performance control method, while enhancing the robustness of the control method. Therefore, how to use the adjustable preset performance control method to achieve precise control of the spacecraft attitude is a problem worthy of in-depth study. Summary of the Invention

[0003] In order to overcome the limitations of the traditional preset performance control method, solve the problems in its actual control application caused by the vulnerability of the preset performance control itself, and provide support for the precise control of the spacecraft attitude, the present invention provides a preset-time control method for spacecraft attitude based on adjustable preset performance. This method realizes precise control of the system error by introducing an adjustable preset performance boundary, designing a new error transformation function, and combining non-singular sliding mode control, while improving the robustness and anti-disturbance ability of the system, providing solid technical support for spacecraft attitude control.

[0004] The object of the present invention is achieved by the following technical solutions:

[0005] A preset-time control method for spacecraft attitude based on adjustable preset performance includes the following steps:

[0006] Step 1: Establish a kinematic and dynamic model for the relative error between the spacecraft and the reference attitude:

[0007] Step 1.1: Describe the spacecraft attitude using the modified Rodriguez parameters:

[0008] Assume that the main rotation vector of the spacecraft attitude is e and the rotation angle is φ, then the spacecraft attitude is expressed using the modified Rodriguez parameters as:

[0009]

[0010] Under the modified Rodriguez parameter description, the kinematic and dynamic models of the spacecraft attitude are as follows:

[0011]

[0012] where ω represents the angular velocity of the spacecraft, J represents the moment of inertia of the spacecraft, τ represents the control torque of the spacecraft, d represents the disturbance acting on the spacecraft, ω × represents the skew-symmetric matrix of ω, σ × represents the skew-symmetric matrix of σ, and I3 represents the 3-order identity matrix;

[0013] Step 1: Determine the description method of the relative error between the spacecraft attitude and the reference attitude:

[0014] Given the reference attitude σ r , the reference attitude angular velocity ω r , and there are:

[0015]

[0016] Define the error of the spacecraft attitude relative to the reference attitude as:

[0017]

[0018] The relative angular velocity error is:

[0019] ω e = ω - C(σ e )ω r

[0020] where C(σ e ) is the rotation matrix, σ e and ω e are respectively the attitude and angular velocity of the spacecraft relative to the reference frame in the reference coordinate system with the reference attitude as the reference, thus obtaining the attitude error and angular velocity error of the spacecraft relative to the reference attitude;

[0021] Step 2: Establish the kinematic and dynamic models for the spacecraft attitude error:

[0022] Differentiate the spacecraft attitude error and angular velocity error to obtain:

[0023]

[0024] Differentiate again to obtain:

[0025]

[0026] Thus, the kinematic and dynamic models of the spacecraft attitude error are obtained:

[0027]

[0028] Step 2: Design a preset performance function:

[0029] Step 2-1: Design an initial preset performance function:

[0030] Given that the upper and lower bounds of the preset performance are ρ ui and ρ li , after the sign of the initial value of the attitude error sign(σ ei (0)), it is necessary to control the attitude error to satisfy:

[0031] ρ li < sign(σ ei (0))σ ei < ρ ui

[0032] where i = 1, 2, 3 represents the three components of the vector;

[0033] In adjustable preset performance control, the performance boundary consists of the initial preset performance function and the performance adjustment term, that is, the upper and lower constraints are ρ ui and ρ li , respectively, then:

[0034]

[0035] where ρ u0i and ρ l0i are the designed initial upper and lower constraints, and:

[0036]

[0037] where T > 0 is the designed convergence time, α > 1 is the designed constant, is the constraint adjustment term; at the same time, define ρ i = ρ ui - ρ li , ρ 0i = ρ u0i - ρ l0i , ρ ui0 and ρ lio are the initial values of the upper and lower boundaries of the initial preset performance function design, and ρ uiT and ρ liT are the final values of the upper and lower boundaries of the initial preset performance function design;

[0038] Step 2-2: Design the constraint adjustment term:

[0039] Design is a constraint adjustment term against the preset performance vulnerability, taking the variable

[0040]

[0041] When ε 0i satisfies the following conditions:

[0042]

[0043] where, Δ > 0, 0 < L < 0.5 are set constants; the moment satisfying this condition is denoted as t1, then the designed adjustment term is:

[0044]

[0045] where, is the gain coefficient of the designed adjustment term, and T1, T2 are time coefficients related to the adjustment term;

[0046] Step Three: Convert the attitude error according to the designed preset performance function and conversion function to obtain a new control model for the converted error:

[0047] Step 3-1: Design the conversion error:

[0048] Take the intermediate variable:

[0049]

[0050] To map the bounded error to the unbounded error, take the conversion error:

[0051]

[0052] where, q i (t) is a designed function that varies with time and is designed as follows: Take ε di (t) ∈ (0, 1) as the desired error convergence curve, that is, the desired intermediate variable ε i converges along ε di (t), and is designed as:

[0053]

[0054] where, ε di0 is the initial value of the desired error convergence curve ε di (t), ε diT is its final value, and ε diT (ρ u0iT - ρ l0iT ) + ρ l0iT = 0, that is, after time T, the attitude error σ di corresponding to ε diIs 0. Considering the influence of the preset performance boundary adjustment term, take:

[0055]

[0056] Among them, ε Di Is the expected error convergence curve considering the preset performance adjustment term, and its relationship with ε di Is: At When, ε Di = ε di ; At When, that is, when the preset performance function changes, the expected error corresponding to ε Di Is equal to the expected error corresponding to ε di When the preset performance function does not change;

[0057] Take again:

[0058]

[0059] That is, when ε i = ε Di When:

[0060]

[0061] Thereby controlling the zero position of the conversion error mapping;

[0062] Step Three Two. According to the conversion error, obtain the dynamic model of the conversion error:

[0063] Derive the intermediate variable ε i , there is:

[0064]

[0065] Take Then there is:

[0066]

[0067] Derive the conversion error e 1i again, there is:

[0068]

[0069] Let:

[0070]

[0071] Simplify to get:

[0072]

[0073] For simplification, take the variable again:

[0074] Φ = diag([Φ1 Φ2 Φ3])

[0075] Ξ = diag([sign(σ e1 (0)) sign(σ e2 (0)) sign(σ e3 (0))])

[0076] θ = [θ1 θ2 θ3] T

[0077] e1 = [e 11 e 12 e 13 T

[0078] e2 = [e 21 e 22 e 23 T

[0079] where Φ and Ξ are third-order matrices, and θ, e1, and e2 are vectors with three components. After simplification, we get:

[0080]

[0081] Then take Ω = diag([Ω1 Ω2 Ω3]), and we have:

[0082]

[0083] Thus, the dynamic model of the conversion error is obtained as:

[0084]

[0085] Step 4: Design the sliding surface:

[0086] Design the sliding surface as follows:

[0087] s = ΦΞe2 + θ + ζ

[0088] where ζ = [ζ1 ζ2 ζ3] T ∈R 3 , and we have:

[0089]

[0090] where b1, b2 > 0, 0 < δ1 < 1, and Δ > 0 are designed constants, and T c1 is the preset convergence time parameter;

[0091] When the sliding surface s converges to 0, the conversion error e1 will converge to the domain within the preset time :​​

[0092]

[0093] Among them:

[0094]

[0095] Step Five: Design the control moment:

[0096] Derive s with respect to s, and get:

[0097]

[0098] The spacecraft attitude error model is:

[0099]

[0100] Take the extended state observer:

[0101]

[0102] Among them, 0 < α < 1, α1 = (α + 1) / 2, β1 = 2 - α1, β2 = 2 - α, γ1, γ2 are constants greater than zero;

[0103] Take:

[0104]

[0105] That is the estimated value of the disturbance;

[0106] Take the control moment as:

[0107]

[0108] Among them, k1, k2 > 0, 0 < δ2 < 1 are designed constants, and T c2 is the preset convergence time parameter; when there is no sudden disturbance and d = 0, the sliding mode surface s will converge within the preset time T c2 ; if there is a sudden disturbance and d ≠ 0, due to the existence of the disturbance observer and the preset performance adjustment term, the system will avoid singularity and failure, and keep the system stable.

[0109] Compared with the prior art, the present invention has the following advantages:

[0110] 1. By using the adjustable preset performance control, not only the control performance of the system is guaranteed, but also the ability of the system to resist sudden disturbances is improved. This method helps to overcome the vulnerability problem in the traditional preset performance control method and is more suitable for practical applications.

[0111] 2. Designing a new conversion function applied to preset performance control can provide an ideal error convergence curve for system control, facilitating the adjustment of the error convergence speed as needed during the control process and avoiding the influence of changes in the preset performance boundary on the zero point of the conversion error.

[0112] 3. A non - singular preset - time sliding - mode control is used in the control - torque design. While enabling the system to converge within the preset time, it avoids the control - torque chattering problem that occurs in ordinary sliding - mode control and is more suitable for practical applications. Brief Description of the Drawings

[0113] Figure 1 is the structural block diagram of the spacecraft attitude control system;

[0114] Figure 2 is the convergence curve of the conversion error e1;

[0115] Figure 3 is the spacecraft attitude error σ e1 convergence curve;

[0116] Figure 4 is the spacecraft attitude error σ e2 convergence curve;

[0117] Figure 5 is the spacecraft attitude error σ e3 convergence curve;

[0118] Figure 6 is the spacecraft angular - velocity error ω e convergence curve. Detailed Implementation Manner

[0119] The technical solutions of the present invention will be further described below in conjunction with the accompanying drawings, but are not limited thereto. Any modification or equivalent replacement of the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention shall be covered by the protection scope of the present invention.

[0120] Aiming at the spacecraft attitude control problem under possible sudden disturbance interference, the present invention provides a spacecraft attitude preset - time control method based on adjustable preset performance. First, establish the kinematic and dynamic models for spacecraft attitude control to obtain the spacecraft attitude control system model. Then, design an adjustable preset - performance function and a new error - conversion function to convert the original system into a new second - order system. Finally, design a non - singular sliding - mode controller for the converted second - order system to achieve precise control of the system error, enabling the system to remain stable and the controller to be effective under certain sudden disturbances. The specific steps are as follows:

[0121] Step 1. Establish the kinematic and dynamic models for the relative error between the spacecraft attitude and the reference attitude. The specific steps are as follows:

[0122] Step 1-1. Describe the spacecraft attitude using the modified Rodriguez parameters:

[0123] Assume that the principal rotation vector of the spacecraft attitude is e and the rotation angle is φ. Then the spacecraft attitude can be expressed using the modified Rodriguez parameters as:

[0124]

[0125] Under the description of the modified Rodriguez parameters, the kinematic and dynamic models of the spacecraft attitude are:

[0126]

[0127] Where:

[0128]

[0129] Among them, I3 represents the 3-order identity matrix, and G(σ) has the following properties:

[0130]

[0131] In the formula, ω represents the angular velocity of the spacecraft, J represents the moment of inertia of the spacecraft, τ represents the control torque of the spacecraft, and d represents the disturbance acting on the spacecraft. For the vector x = [x1 x2 x3] T ∈R 3 , x × represents the skew-symmetric matrix of this vector, that is:

[0132]

[0133] Step 1-2. Determine the description method of the relative error between the spacecraft attitude and the reference attitude:

[0134] Given the reference attitude σ r , the reference attitude angular velocity ω r , and there are:

[0135]

[0136] The relative error of the spacecraft attitude with respect to the reference attitude can be defined as:

[0137]

[0138] The relative angular velocity error is:

[0139] ω e = ω - C(σ e )ωr

[0140] In the formula, C(σ e ) is the rotation matrix:

[0141]

[0142] In the formula, σ e and ω e are respectively the attitude and angular velocity of the spacecraft relative to the reference frame in the reference attitude as the reference coordinate system. From this, the attitude error and angular velocity error of the spacecraft relative to the reference attitude can be obtained.

[0143] Step 13: Establish the kinematic and dynamic models for the spacecraft attitude error:

[0144] Taking the derivatives of the spacecraft attitude error and angular velocity error, we can obtain:

[0145]

[0146] Among them,

[0147] Taking the derivative again, we can obtain:

[0148]

[0149] From this, the kinematic and dynamic models of the spacecraft attitude error can be obtained:

[0150]

[0151] Step 2: Design the preset performance function, and the specific steps are as follows:

[0152] Step 21: Design the initial preset performance function:

[0153] According to the idea of preset performance control, it is necessary to control the error within the preset performance boundary. Given that the upper and lower boundaries of the preset performance are ρ ui , ρ li , after the positive or negative value sign(σ ei (0)) of the initial value of the attitude error, it is necessary to control the attitude error to satisfy:

[0154] ρ li < sign(σ ei (0))σ ei < ρ ui

[0155] Among them, i = 1, 2, 3 represent the three components of the vector.

[0156] In the adjustable preset performance control, the performance boundary consists of the initial preset performance function and the performance adjustment term, that is, the upper and lower constraints are ρ ui and ρ li , respectively. Then, we have:

[0157]

[0158] where ρ u0i and ρ l0i are the designed initial upper and lower constraints, and we have:

[0159]

[0160] where T > 0 is the designed convergence time, α > 1 is the designed constant, is the constraint adjustment term. At the same time, define ρ i = ρ ui - ρ li , ρ 0i = ρ u0i - ρ l0i . It can be seen from the design of the initial preset performance function that the initial values of the upper and lower boundaries of the initial preset performance function are ρ ui0 and ρ lio , respectively, and the final values are ρ uiT and ρ liT , respectively. And it should satisfy:

[0161] ρ lio < σ ei (0) < ρ ui0

[0162] where σ ei (0) represents the initial value of the ith component of the attitude error vector σ e at time 0.

[0163] Step 2. Design the constraint adjustment term:

[0164] To solve the vulnerability problem existing in the preset performance control, the preset performance adjustment term can be used to expand the performance boundary when the error approaches the performance boundary under the interference of sudden disturbances, so as to solve the system singularity problem. Design is the constraint adjustment term to resist the vulnerability of the preset performance. Take the variable

[0165]

[0166] When ε 0i satisfies the following conditions:

[0167]

[0168] Among them, Δ > 0, 0 < L < 0.5 are set constants. Denote the moment satisfying this condition as t1, then the design adjustment term is:

[0169]

[0170] Among them, is the gain coefficient of the designed adjustment term. It can be seen that no matter what value t takes, there is always T1 and T2 are time coefficients related to the adjustment term, controlling the time for the increase and decrease of the adjustment term.

[0171] It can be seen from the design of the adjustment term that at the initial moment t1 and the end moment t1 + T1 + T2 of the adjustment, the adjustment term has a value of 0. Within the time T1 after t1, the value gradually increases from 0 and reaches the maximum value at t1 + T1; within the time T2 after t1 + T1, the value gradually decreases from the maximum value and returns to 0 at t1 + T1 + T2.

[0172] Step 3: According to the designed preset performance function and conversion function, convert the attitude error to obtain a new control model for the converted error. The specific steps are as follows:

[0173] Step 3-1: Design the conversion error:

[0174] Take the intermediate variable

[0175]

[0176] To control σ ei in the preset performance function, it is necessary to keep ε i within (0, 1). To map the bounded error to the unbounded error, take the conversion error:

[0177]

[0178] As long as e 1i is bounded, ε i can be kept within (0, 1). Among them, q i (t) is a designed function that changes with time, which can control the zero-point mapping position of the conversion error. Its design is as follows: Take ε di (t) ∈ (0, 1) as the desired error convergence curve, that is, the desired intermediate variable ε i converges along ε di (t), and the design is:

[0179]

[0180] Among them, ε di0is the desired error convergence curve ε di (t) initial value, ε diT is its final value, and ε diT (ρ u0iT -ρ l0iT ) + ρ l0iT = 0, that is, after time T, ε di corresponding attitude error σ di is 0. Considering the influence of the preset performance boundary adjustment term, take:

[0181]

[0182] where ε Di is the desired error convergence curve considering the preset performance adjustment term, and its relationship with ε di is: at , ε Di = ε di . At , that is, when the preset performance function changes, the desired error corresponding to ε Di is equal to the desired error corresponding to ε di when the preset performance function does not change. Then take

[0183]

[0184] That is, when ε i = ε Di :

[0185]

[0186] Thus, the zero position of the conversion error mapping can be controlled.

[0187] Step Three Two. According to the conversion error, obtain the dynamic model of the conversion error:

[0188] Differentiate the intermediate variable ε i , and there is:

[0189]

[0190] Take Then there is:

[0191]

[0192] Differentiate the conversion error e 1i again, and there is:

[0193]

[0194] Let:

[0195]

[0196] It can be simplified to:

[0197]

[0198] For simplification, take variables again:

[0199] Φ = diag([Φ1 Φ2 Φ3])

[0200] Ξ = diag([sign(σ e1 (0)) sign(σ e2 (0)) sign(σ e3 (0))])

[0201] θ = [θ1 θ2 θ3] T

[0202] e1 = [e 11 e 12 e 13 T

[0203] e2 = [e 21 e 22 e 23 T

[0204] Among them, Φ and Ξ are third-order matrices, and θ, e1, and e2 are vectors with three components. It can be simplified to:

[0205]

[0206] Take Ω = diag([Ω1 Ω2 Ω3]) again, There is:

[0207]

[0208] Then the dynamic model of the conversion error can be obtained as:

[0209]

[0210] Step 4. Design the sliding surface: To make the control system converge within the preset time, design a non-singular sliding surface that is stable in the preset time. The specific steps are as follows:

[0211] Design the sliding surface as follows:

[0212] s = ΦΞe2 + θ + ζ

[0213] Among them, ζ = [ζ1 ζ2 ζ3] T ∈R 3 There is: ​​

[0214]

[0215] where \(b_1,b_2\gt0\), \(0\lt\delta_1\lt1\), \(\Delta\gt0\) are designed constants, and \(T\) c1 is a preset convergence time parameter. The meaning of the sig(·) function is that for variable \(x\in R\) and constant \(\gamma\in R\), there is:

[0216] sig γ (x) = sign(x)|x| γ

[0217] For vector \(x = [x_1 x_2 \cdots x\) n \(\in R\) n , and constant \(\gamma\in R\), there is:

[0218] sig γ (x) = [sign(x_1)|x_1| γ sign(x_2)|x_2| γ \(\cdots\) sign(x n )|x n | \(\gamma]\) T

[0219] When the sliding mode surface \(s\) converges to 0, the conversion error \(e_1\) will converge to the domain within the preset time :

[0220]

[0221] where:

[0222]

[0223] Step 5. Design the control torque: According to the designed sliding mode surface, design the control torque so that the sliding mode surface can converge within the preset time. The specific steps are as follows:

[0224] Take the derivative of \(s\), and we can get:

[0225]

[0226] where:

[0227]

[0228] By introducing a disturbance observer to cancel the external disturbance. The spacecraft attitude error model is:

[0229]

[0230] Take the extended state observer:

[0231]

[0232] Among them, 0 < α < 1, α1 = (α + 1) / 2, β1 = 2 - α1, β2 = 2 - α, γ1 and γ2 are constants greater than zero. Take:

[0233]

[0234] That is the estimated value of the perturbation.

[0235] Take the control torque as:

[0236]

[0237] Among them, η has:

[0238]

[0239] Among them, k1, k2 > 0, 0 < δ2 < 1 are designed constants, and T c2 is the preset convergence time parameter. When there is no sudden perturbation and d = 0, the sliding surface s will converge within the preset time T c2 ; if there is a sudden perturbation and d ≠ 0, due to the existence of the disturbance observer and the preset performance adjustment term, the system can avoid singularity and failure, and keep the system stable.

[0240] Embodiment:

[0241] According to the proposed controller, a simulation experiment was carried out, and the simulation results are as Figures 2 to 6 shown. Among them, the set sudden perturbation is d = [d1 d2 d3] T , and there is:

[0242]

[0243] d2 = d3 = 0

[0244] Through Figure 2 it can be seen that when there is no interference, the conversion error e1 can converge rapidly; after being subjected to a sudden perturbation, e1 increases rapidly but still remains bounded and finally converges. Through Figures 3 to 5 it can be seen that the system error can always be kept within the preset performance boundary. When the sudden perturbation causes the system error to increase rapidly, the preset performance can be expanded accordingly to keep the system from failing and make the error converge again. Through Figure 6 it can be seen that the system angular velocity error can also be kept stable and finally converge. Overall Figures 2 to 6According to the simulation results, the spacecraft state preset-time control method based on adjustable preset performance proposed by the present invention can still ensure the stable control of the system under the interference of sudden disturbances, improve the control accuracy and robustness of the system, and verify the effectiveness of the method proposed by the present invention in controlling the attitude of the spacecraft.

Claims

1. A spacecraft attitude preset time control method based on adjustable preset performance, characterized in that The method includes the following steps: Step 1: Establish kinematic and dynamic models for the relative error between the spacecraft and the reference attitude: Step 1.1: Describe the spacecraft attitude using modified Rodriguez parameters: Assume that the principal rotation vector of the spacecraft attitude is e and the rotation angle is φ. Then the spacecraft attitude is expressed using modified Rodriguez parameters as: Under the description of modified Rodriguez parameters, the kinematic and dynamic models of the spacecraft attitude are: where ω represents the angular velocity of the spacecraft, J represents the moment of inertia of the spacecraft, τ represents the control torque of the spacecraft, d represents the disturbance acting on the spacecraft, ω × represents the skew-symmetric matrix of ω, σ × represents the skew-symmetric matrix of σ, and I3 represents the 3-order identity matrix; Step 1.2: Determine the description method for the relative error between the spacecraft attitude and the reference attitude: At a known reference attitude σ r , a reference attitude angular velocity ω r , and there is: Define the error of the spacecraft attitude relative to the reference attitude as: The relative angular velocity error is: ω e = ω-C(σ e )ω r where \(C(\sigma e )\) is the rotation matrix, \(\sigma e \) and \(\omega e \) are respectively the attitude and angular velocity of the spacecraft relative to the reference frame in the reference attitude as the reference coordinate system, and thus the attitude error and angular velocity error of the spacecraft relative to the reference attitude are obtained; Step 1.3: Establish kinematic and dynamic models for the spacecraft attitude error: Take the derivatives of the spacecraft attitude error and the angular velocity error to obtain: For Derive again to obtain: Thus, the kinematic and dynamic models of the spacecraft attitude error are obtained: Step 2: Design a preset performance function: Step 2.1: Design an initial preset performance function: The upper and lower bounds of the known preset performance are ρ ui and ρ li . After the positive and negative values sign(σ ei (0)) of the initial attitude error, it is necessary to control the attitude error to satisfy: ρ li <sign(σ ei (0))σ ei <ρ ui where i = 1, 2, 3 represents the three components of the vector; In adjustable preset performance control, the performance boundary consists of an initial preset performance function and a performance adjustment term, that is, the upper and lower constraints are ρ ui and ρ li respectively. Then, we have: where ρ u0i , ρ l0i are the designed initial upper and lower constraints, and we have: where \(T>0\) is the designed convergence time, \(\alpha>1\) is the designed constant, is the constraint adjustment term; at the same time, \(\rho\) is defined i =\(\rho\) ui -\(\rho\) i , \(\rho\) 0i =\(\rho\) u0i -\(\rho\) l0i , \(\rho\) uo0 and \(\rho\) lio are respectively the initial values designed for the upper and lower boundaries of the initial preset performance function, and \(\rho\) uiT and \(\rho\) liT are respectively the final values designed for the upper and lower boundaries of the initial preset performance function; Step 2.2: Design a constraint adjustment term: Design is a constraint adjustment item for resisting preset performance vulnerabilities and takes variables When ε 0i satisfies the following conditions: where Δ>0, 0<L<0.5 are set constants; Denote the time satisfying this condition as t1, then the designed adjustment term is: Among them, is the gain coefficient of the design adjustment item, and T1 and T2 are time coefficients related to the adjustment item; Step 3: Transform the attitude error according to the designed preset performance function and transformation function to obtain a new control model for the transformed error: Step 3.1: Design a transformed error: Take an intermediate variable: To map the bounded error to an unbounded error, take the transformed error: where q i (t) is a designed time-varying function, which is designed as follows: Take ε di (t) ∈ (0, 1) as the desired error convergence curve, that is, the desired intermediate variable ε i converges along ε di (t), and is designed as: where ε di0 is the initial value of the desired error convergence curve ε di (t), and ε diT is its final value. Considering the influence of the preset performance boundary adjustment term, take: Among them, ε Di is the expected error convergence curve considering the preset performance adjustment items; Then take: That is, when ε i = ε Di : Thereby controlling the zero position of the transformed error mapping; Step 3.2: According to the transformed error, obtain the dynamic model of the transformed error: Derive the intermediate variable ε i We get: Take Then there is: Derive the conversion error e 1i again, we get: Let: After simplification: For simplification, take another variable: Φ = diag([Φ1 Φ2 Φ3]) Ξ = diag([sign(σ e1 (0)) sign(σ e2 (0)) sign(σ e3 (0))]) θ = [θ1 θ2 θ3] T e1 = [e 11 e 12 e 13 T ​ e2 = [e 21 e 22 e 23 T ​ where Φ and Ξ are third-order matrices, and θ, e1, e2 are vectors with three components. After simplification: Take Ω = diag([Ω1 Ω2 Ω3]) again, We have: Thus, the dynamic model of the transformed error is obtained as: Step 4: Design a sliding surface: Design the sliding surface as follows: s = ΦΞe2 + θ + ζ where ζ = [ζ1 ζ2 ζ3] T ∈R 3 , there is: where \(b_1, b_2>0\), \(0 < \delta_1 < 1\), \(\Delta>0\) are designed constants, and \(T\) c1 is a preset convergence time parameter; When the sliding surface s converges to 0, the conversion error e1 will converge to the domain within a preset time where: Step 5: Design a control torque: Take the derivative of s to obtain: The spacecraft attitude error model is: Take an extended state observer: wherein, 0 < α < 1, α1 = (α + 1) / 2, β1 = 2 - α1, β2 = 2 - α, θ, γ1, γ2 are constants greater than zero; Take: That is, the estimated value of the disturbance; Take the control torque as: where \(k_1,k_2>0\), \(0 < \delta_2 < 1\) are designed constants, and \(T\) c2 is a preset convergence time parameter; when there is no mutation disturbance, \(d = 0\), the sliding surface \(s\) will converge within the preset time \(T\) c2 ; if there is a mutation disturbance, \(d\neq0\), due to the existence of the disturbance observer and the preset performance adjustment term, the system will avoid singularity and failure, and keep the system stable.

2. The spacecraft attitude preset time control method based on adjustable preset performance according to claim 1, characterized in that In the above Step 1.1, G(σ) has the following properties:

3. The method for presetting the attitude preset time of a spacecraft based on adjustable preset performance according to claim 1, wherein In the first and second steps, the rotation matrix C(σ e ) is as follows:

4. The method for presetting the attitude preset time of a spacecraft based on adjustable preset performance according to claim 1, wherein In the second step 21, the initial values ρ ui0 and ρ lio of the upper and lower boundaries of the initial preset performance function satisfy: ρ lio <σ ei (0)<ρ ui0 Among them, σ ei (0) represents the initial value of the i-th component of the attitude error vector σ e at the 0th moment.

5. The method for presetting the attitude preset time of a spacecraft based on adjustable preset performance according to claim 1, wherein In Step 31, ε diT (ρ u0iT -ρ l0iT )+ρ l0iT = 0, that is, after time T, ε di corresponding attitude error σ di is 0.

6. The method for presetting the attitude preset time of a spacecraft based on adjustable preset performance according to claim 1, characterized in that In step 31, ε Di and ε di are related as follows: When ε Di = ε di ; When , that is, when the preset performance function changes, the expected error corresponding to ε Di is equal to the expected error corresponding to ε di when the preset performance function does not change.

7. The method for presetting the attitude preset time of a spacecraft based on adjustable preset performance according to claim 1, characterized in that In the above Step 4, the meaning of the sig(·) function is: For variable x ∈ R and constant γ ∈ R, there is: sig γ (x) = sign(x)|x| γ For the vector x = [x1 x2…x n ∈ R n , and a constant γ ∈ R, we have: sig γ (x) = [sign(x1)|x1| γ sign(x2)|x2| γ …sign(x n )|x n | γ T .​

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