Spacecraft attitude preset time control method based on adjustable preset performance

Abstract

The application discloses a spacecraft attitude preset time control method based on adjustable preset performance, first, a kinematics and dynamics model is established for spacecraft attitude control to obtain a spacecraft attitude control system model. Then, an adjustable preset performance function and a new error conversion function are designed to convert the original system into a new second-order system. Finally, a non-singular sliding mode controller is designed for the converted second-order system to realize accurate control of system error, so that the system still has the ability to keep stable and the controller can take effect under certain sudden disturbance. The method introduces an adjustable preset performance boundary, designs a new error conversion function, and combines the non-singular sliding mode control to realize accurate control of system error, improve the robustness and anti-disturbance ability of the system, and provide solid technical support for spacecraft attitude control.

Description

Technical Field

[0001] This invention belongs to the field of spacecraft attitude control and relates to a spacecraft attitude control method, specifically a spacecraft attitude control method based on adjustable preset performance control with preset time stability. Background Technology

[0002] Spacecraft often require high precision in attitude control during missions. Preset performance control methods, compared to traditional control methods, offer advantages such as speed, high precision, and controllable error, making them suitable for spacecraft attitude control. However, basic preset performance control methods suffer from control vulnerability; when the controlled target is subjected to sudden disturbances, the error exceeds the preset performance boundary, leading to singularities and control system failure. This issue limits the practical application of preset performance control methods. To address this challenge, researchers and engineers have continuously explored and improved control strategies and methods, proposing adjustable preset performance control methods. By dynamically adjusting the preset performance boundary, this new control method balances the control precision and speed of traditional preset performance control methods while enhancing robustness. Therefore, how to utilize adjustable preset performance control methods to achieve precise attitude control of spacecraft is a problem worthy of in-depth research. Summary of the Invention

[0003] To overcome the limitations of traditional preset performance control methods and address the inherent vulnerabilities of preset performance control in practical applications, this invention provides a spacecraft attitude preset time control method based on adjustable preset performance. This method introduces adjustable preset performance boundaries, designs a new error transformation function, and combines it with non-singular sliding mode control to achieve precise control of system errors while improving system robustness and disturbance rejection capabilities, thus providing solid technical support for spacecraft attitude control.

[0004] The objective of this invention is achieved through the following technical solution:

[0005] A spacecraft attitude preset time control method 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 11: Describe the spacecraft's attitude using the corrected Rodriguez parameters:

[0008] Assuming the principal rotation vector of the spacecraft's attitude is e and the rotation angle is φ, the spacecraft's attitude, expressed using the modified Rodriguez parameters, is as follows:

[0009]

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

[0011]

[0012] 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 experienced by the spacecraft. × Let σ be the skew-symmetric matrix of ω. × I represents the skew-symmetric matrix of σ, and I3 represents the 3rd order identity matrix;

[0013] Steps 1 and 2: Determine how to describe the relative error between the spacecraft's attitude and the reference attitude:

[0014] Given the reference attitude σ r Reference attitude angular velocity ω r And there are:

[0015]

[0016] The error of the spacecraft's attitude relative to a reference attitude is defined as:

[0017]

[0018] The relative error of angular velocity is:

[0019] ω e =ω-C(σ e )ω r

[0020] In the formula, C(σ) e ) is the rotation matrix, σ e With ω e These are the attitude and angular velocity of the spacecraft relative to the reference frame, with the reference attitude as the reference coordinate system. From this, we can obtain the attitude error and angular velocity error of the spacecraft relative to the reference attitude.

[0021] Step 13: Establish kinematic and dynamic models for spacecraft attitude errors:

[0022] Differentiating the spacecraft attitude error and angular velocity error, we get:

[0023]

[0024] right Differentiating again, we get:

[0025]

[0026] This leads to the kinematic and dynamic model of the spacecraft's attitude error:

[0027]

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

[0029] Step 2.1: Design the initial preset performance function:

[0030] The upper and lower boundaries of the preset performance are known to be ρ. ui ρ li The sign of the initial attitude error, sign(σ) ei After (0)), the attitude error needs to be controlled to meet the following:

[0031] ρ li <sign(σ ei (0))σ ei <ρ ui

[0032] In the formula, i = 1, 2, 3 represent the three components of the vector;

[0033] In adjustable preset performance control, the performance boundary consists of an initial preset performance function and a performance adjustment term, i.e., the upper and lower constraints are ρ and ρ, respectively. ui ρ li Then we have:

[0034]

[0035] In the formula, ρ u0i ρ l0i The initial upper and lower constraints are pre-designed and include:

[0036]

[0037] In the formula, T>0 is the designed convergence time, and α>1 is the designed constant. This is a constraint adjustment term; ρ is also defined. i =ρ ui -ρ li , ρ 0i =ρ u0i -ρ l0i , ρ ui0 ρ lio ρ represents the initial value designed for the upper and lower boundaries of the initial preset performance function. uiT ρ liT These are the final values ​​designed for the upper and lower boundaries of the initial preset performance function, respectively;

[0038] Step 22: Design Constraint Adjustment Items:

[0039] design is a constraint adjustment term for resisting 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 time when this condition is met 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 3. Convert the attitude error according to the designed preset performance function and conversion function to obtain a new control model of 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 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 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 diThe value is 0. Considering the impact of the preset performance boundary adjustment term, the value is set to:

[0055]

[0056] Where, ε Di To consider the expected error convergence curve of the preset performance adjustment term, its relationship with ε di The relationship is: in At that time, ε Di =ε di ;exist When, i.e., when the preset performance function changes, ε Di When the expected error and the preset performance function remain unchanged, ε di The corresponding expected errors are equal;

[0057] Take again:

[0058]

[0059] That is, when ε i =ε Di hour:

[0060]

[0061] This controls the zero-point position of the conversion error mapping;

[0062] Step 3.2: Based on the conversion error, obtain the dynamic model of the conversion error:

[0063] For the intermediate variable ε i Differentiating, we have:

[0064]

[0065] Pick Then we have:

[0066]

[0067] Then consider the conversion error e 1i Differentiating, we have:

[0068]

[0069] make:

[0070]

[0071] Simplifying, we get:

[0072]

[0073] To simplify, let's take another variable:

[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, which simplifies to:

[0080]

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

[0082]

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

[0084]

[0085] Step 4: Design the sliding surface:

[0086] The sliding surface is designed as follows:

[0087] s=ΦΞe2+θ+ζ

[0088] Where ζ = [ζ1 ζ2 ζ3] T ∈R 3 ,have:

[0089]

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

[0091] When the sliding surface s converges to 0, the conversion error e1 will occur within a preset time. Converging inward to the domain:

[0092]

[0093] in:

[0094]

[0095] Step 5: Design the control torque:

[0096] Differentiating with respect to s, we get:

[0097]

[0098] Spacecraft attitude error models include:

[0099]

[0100] Take the extended state observer:

[0101]

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

[0103] Pick:

[0104]

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

[0106] The control torque is taken as:

[0107]

[0108] Where k1,k2>0,0<δ2<1 are design constants, and T c2 This is the preset convergence time parameter; when there is no sudden disturbance, d=0, the sliding surface s will converge within the preset time T. c2 Internal convergence; if there is a sudden disturbance and d≠0, the system will avoid singularity and failure due to the presence of the disturbance observer and the preset performance adjustment terms, thus keeping the system stable.

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

[0110] 1. By utilizing adjustable preset performance control, not only is the system's control performance guaranteed, but its ability to withstand sudden disturbances is also improved. This method helps overcome the vulnerability issues of traditional preset performance control methods and is more suitable for practical applications.

[0111] 2. Designing a new conversion function for preset performance control can provide an ideal error convergence curve for system control, which facilitates adjusting the error convergence speed as needed during the control process, while avoiding the influence of preset performance boundary changes on the zero point of conversion error.

[0112] 3. A non-singular preset time sliding mode control is used in the control torque design. This allows the system to converge within a preset time while avoiding the control torque chattering problem that occurs in ordinary sliding mode control, making it more suitable for practical applications. Attached Figure Description

[0113] Figure 1 This is a block diagram of the spacecraft attitude control system.

[0114] Figure 2 The convergence curve for the conversion error e1;

[0115] Figure 3 The spacecraft attitude error σ e1 Convergence curve;

[0116] Figure 4 The spacecraft attitude error σ e2 Convergence curve;

[0117] Figure 5 The spacecraft attitude error σ e3 Convergence curve;

[0118] Figure 6 spacecraft angular velocity error ω e Convergence curve. Detailed Implementation

[0119] The technical solution of the present invention will be further described below with reference to the accompanying drawings, but it is not limited thereto. Any modifications or equivalent substitutions to the technical solution of the present invention that do not depart from the spirit and scope of the technical solution of the present invention should be covered within the protection scope of the present invention.

[0120] To address the spacecraft attitude control problem under potential sudden disturbances, this invention provides a spacecraft attitude preset time control method based on adjustable preset performance. First, a kinematic and dynamic model of the spacecraft attitude control is established, resulting in a spacecraft attitude control system model. Next, an adjustable preset performance function and a new error transformation function are designed to transform the original system into a new second-order system. Finally, a non-singular sliding mode controller is designed for the transformed second-order system to achieve precise control of the system error, ensuring that the system remains stable and the controller remains effective even under certain sudden disturbances. Specifically, the method includes the following steps:

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

[0122] Step 11: Describe the spacecraft's attitude using the corrected Rodriguez parameters:

[0123] Assuming the principal rotation vector of the spacecraft's attitude is e and the rotation angle is φ, the spacecraft's attitude using the corrected Rodriguez parameters can be expressed as:

[0124]

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

[0126]

[0127] in:

[0128]

[0129] Where I3 represents the 3rd 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 experienced by the spacecraft. For the vector x = [x1 x2 x3] T ∈R 3 x × The skew-symmetric matrix representing this vector is:

[0132]

[0133] Steps 1 and 2: Determine how to describe the relative error between the spacecraft's attitude and the reference attitude:

[0134] Given the reference attitude σ r Reference attitude angular velocity ω r And there are:

[0135]

[0136] The error of the spacecraft's attitude relative to a reference attitude can be defined as:

[0137]

[0138] The relative error of angular velocity 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 With ω e These represent the spacecraft's attitude and angular velocity relative to the reference frame, with the reference attitude as the reference coordinate system. From this, the spacecraft's attitude error and angular velocity error relative to the reference attitude can be obtained.

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

[0144] Taking the derivatives of the spacecraft's attitude error and angular velocity error, we get:

[0145]

[0146] in,

[0147] right Taking the derivative again, we get:

[0148]

[0149] From this, we can obtain the kinematic and dynamic model of the spacecraft's attitude error:

[0150]

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

[0152] Step 2.1: Design the initial preset performance function:

[0153] Based on the concept of preset performance control, the error needs to be controlled within the preset performance boundaries. The upper and lower boundaries of the preset performance are known to be ρ. ui , ρ li The sign of the initial attitude error, sign(σ) ei After (0)), the attitude error needs to be controlled to meet the following:

[0154] ρ li <sign(σ ei (0))σ ei <ρ ui

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

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

[0157]

[0158] Where, ρ u0i ρ l0i The initial upper and lower constraints are pre-designed and include:

[0159]

[0160] Where T>0 is the designed convergence time, and α>1 is the designed constant. This is a constraint adjustment term. ρ is also defined. i =ρ ui -ρ li , ρ 0i =ρ u0i -ρ l0i From the design of the initial preset performance function, it can be seen that the initial values ​​of the upper and lower boundaries of the initial preset performance function are ρ, respectively. ui0 ρ lio The final values ​​are ρ uiT ρ liT And it should satisfy:

[0161] ρ lio <σ ei (0)<ρ ui0

[0162] Where, σ ei (0) represents the attitude error vector σ e The initial value of the i-th component at time 0.

[0163] Step 22: Design Constraint Adjustment Items:

[0164] To address the vulnerability inherent in preset performance control, preset performance adjustment terms can be used. When the error approaches the performance boundary under sudden disturbances, the performance boundary is widened to resolve system singularity issues. It is a constraint adjustment term to resist pre-defined performance vulnerabilities, taking variables.

[0165]

[0166] When ε 0i When the following conditions are met:

[0167]

[0168] where, Δ > 0, 0 < L < 0.5 are set constants. Denote the time satisfying this condition as t1, then the designed adjustment term is:

[0169]

[0170] where, is the gain coefficient of the designed adjustment term. It can be seen that for any value of t, there is T1 and T2 are time coefficients related to the adjustment term, controlling the time for the increase and decrease of the adjustment term.

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

[0172] Step Three: 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 Three - One: 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] where, ε di0The desired error convergence curve ε di The initial value of (t), ε diT Let it be its final value, and ε diT (ρ u0iT -ρ l0iT )+ρ l0iT =0, meaning that ε = 0 after time T. di The corresponding attitude error σ di The value is 0. Considering the impact of the preset performance boundary adjustment term, we take:

[0181]

[0182] Where, ε Di To consider the expected error convergence curve of the preset performance adjustment term, its relationship with ε di The relationship is: in At that time, ε Di =ε di .exist When, i.e., when the preset performance function changes, ε Di When the expected error and the preset performance function remain unchanged, ε di The corresponding expected errors are equal. Then take...

[0183]

[0184] That is, when ε i =ε Di hour:

[0185]

[0186] This allows control over the zero-point position of the transformation error mapping.

[0187] Step 3.2: Based on the conversion error, obtain the dynamic model of the conversion error:

[0188] For the intermediate variable ε i Differentiating, we have:

[0189]

[0190] Pick Then we have:

[0191]

[0192] Then consider the conversion error e 1i Differentiating, we have:

[0193]

[0194] make:

[0195]

[0196] Simplifying, we get:

[0197]

[0198] To simplify, let's take another variable:

[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] Where Φ and Ξ are third-order matrices, and θ, e1, and e2 are vectors with three components. Simplifying, we get:

[0205]

[0206] Then take Ω=diag([Ω1 Ω2 Ω3]), have:

[0207]

[0208] Therefore, the dynamic model of the conversion error can be obtained as follows:

[0209]

[0210] Step 4: Design the sliding surface: In order for the control system to converge within a preset time, a non-singular sliding surface that is stable within the preset time is designed. The specific steps are as follows:

[0211] The sliding surface is designed as follows:

[0212] s=ΦΞe2+θ+ζ

[0213] Where ζ = [ζ1 ζ2 ζ3] T ∈R 3 ,have:

[0214]

[0215] Where b1, b2>0, 0<δ1<1, Δ>0 are design constants, and T c1 This is the preset convergence time parameter. The meaning of the sig(·) function is that for variables x∈R and constant γ∈R, we have:

[0216] sig γ (x) = sign(x)|x| γ

[0217] For a vector x = [x1 x2 … x… n ]∈R n For a constant γ∈R, we have:

[0218] sig γ (x)=[sign(x1)|x1| γ sign(x2)|x2| γ … sign(x n )|x n | γ] T

[0219] When the sliding surface s converges to 0, the conversion error e1 will occur within a preset time. Converging inward to the domain:

[0220]

[0221] in:

[0222]

[0223] Step 5: Design Control Torque: Based on the designed sliding surface, design the control torque so that the sliding surface can converge within a preset time. The specific steps are as follows:

[0224] Differentiating with respect to s, we get:

[0225]

[0226] in:

[0227]

[0228] External disturbances are counteracted by introducing a disturbance observer. Spacecraft attitude error models include:

[0229]

[0230] Take the extended state observer:

[0231]

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

[0233]

[0234] This is the estimated value of the disturbance.

[0235] The control torque is taken as:

[0236]

[0237] Among them, η has:

[0238]

[0239] Where k1,k2>0,0<δ2<1 are design constants, and T c2 This is the preset convergence time parameter. When there is no sudden disturbance, d=0, the sliding surface s will converge within the preset time T. c2 Internal convergence; if there is a sudden disturbance and d≠0, the system will avoid singularity and failure due to the presence of the disturbance observer and the preset performance adjustment terms, thus keeping the system stable.

[0240] Example:

[0241] A simulation experiment was conducted based on the proposed controller, and the simulation results are as follows: Figures 2-6 As shown in the figure. The mutation perturbation is set to d = [d1 d2 d3]. T ,have:

[0242]

[0243] d2=d3=0

[0244] pass Figure 2 It can be seen that in the absence of disturbances, the conversion error e1 converges rapidly; after being subjected to a sudden disturbance, e1 increases rapidly but remains bounded, and eventually converges. Figures 3-5 As can be seen, the system error can always be kept within the preset performance boundary. When the system error increases rapidly due to a sudden disturbance, the preset performance can be increased accordingly to prevent system failure and allow the error to converge again. Figure 6 As can be seen, the system's angular velocity error also remains stable and eventually converges. (Summary) Figures 2-6The simulation results show that the spacecraft state preset time control method based on adjustable preset performance proposed in this invention can still ensure stable system control under the interference of sudden disturbances, improve the control accuracy and robustness of the system, and verify the effectiveness of the method proposed in this invention in controlling the attitude of 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 a kinematic and dynamic model for the relative error between the spacecraft and the reference attitude: Step 11: Describe the spacecraft's attitude using the corrected Rodriguez parameters: Assuming the principal rotation vector of the spacecraft's attitude is 𝑒 and the rotation angle is 𝜙, the spacecraft's attitude, expressed using the modified Rodriguez parameters, is as follows: Under the modified Rodriguez parameter description, the kinematic and dynamic models of the spacecraft attitude are as follows: In the formula, Represents the angular velocity of a spacecraft. Represents the moment of inertia of a spacecraft. Indicates the control torque of the spacecraft. This indicates the disturbance experienced by the spacecraft. express A skew-symmetric matrix, express A skew-symmetric matrix, express An identity matrix of order 1; Steps 1 and 2: Determine how to describe the relative error between the spacecraft's attitude and the reference attitude: Given the reference attitude Reference attitude angular velocity And there are: The error of the spacecraft's attitude relative to a reference attitude is defined as: The relative error of angular velocity is: In the formula, For rotation matrix, and These are the attitude and angular velocity of the spacecraft relative to the reference frame, with the reference attitude as the reference coordinate system. From this, we can obtain the attitude error and angular velocity error of the spacecraft relative to the reference attitude. Step 13: Establish kinematic and dynamic models for spacecraft attitude errors: Differentiating the spacecraft attitude error and angular velocity error, we get: right Differentiating again, we get: This leads to the kinematic and dynamic model of the spacecraft's attitude error: Step 2: Design the preset performance function: Step 2.1: Design the initial preset performance function: The upper and lower boundaries of the preset performance are known to be: , The sign of the initial attitude error Then, the attitude error needs to be controlled to meet the following requirements: In the formula, This 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, i.e., the upper and lower constraints are respectively... , Then we have: In the formula, , The initial upper and lower constraints are pre-designed and include: In the formula, For the designed convergence time, For the design constant, As a constraint adjustment term; and simultaneously define , , , These are the initial values ​​designed for the upper and lower boundaries of the initial preset performance function, respectively. , These are the final values ​​designed for the upper and lower boundaries of the initial preset performance function, respectively; Step 22: Design Constraint Adjustment Items: design It is a constraint adjustment term to resist pre-defined performance vulnerabilities, taking variables. when When the following conditions are met: in, , Let be a constant set by the given condition; let be the time when the condition is satisfied. The design adjustment items are as follows: in, The adjustment term gain coefficient is designed. , The time factor associated with 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 31: Design Conversion Error Take intermediate variables: To map bounded errors to unbounded errors, we take the transformation error: in, It is a time-varying function of the design, and its design is as follows: Take The expected error convergence curve, i.e., the expected intermediate variable. along Convergence, designed as follows: in, The desired error convergence curve initial value, For its final value, considering the effect of the preset performance boundary adjustment term, we take: in, To consider the expected error convergence curve of the preset performance adjustment items; Take again: That is, when hour: This controls the zero-point position of the conversion error mapping; Step 3.2: Based on the conversion error, obtain the dynamic model of the conversion error: For intermediate variables Differentiating, we have: Pick , Then we have: Then consider the conversion error Differentiating, we have: make: Simplifying, we get: To simplify, let's take another variable: in , It is a third-order matrix. , , For a vector with three components, simplifying, we get: Take again , ,have: Therefore, the dynamic model of the conversion error is obtained as follows: Step 4: Design the sliding surface: The sliding surface is designed as follows: in, ,have: in, , , It is a design constant. This is the preset convergence time parameter; When the sliding surface convergence to At that time, conversion error It will be at the preset time Converging inward to the domain: in: Step 5: Design the control torque: right Differentiating, we get: Spacecraft attitude error models include: Take the extended state observer: in, , , , , , , , It is a constant greater than zero; Pick: This is the estimated value of the disturbance; The control torque is taken as: in, , It is a design constant. This is the preset convergence time parameter; when there is no sudden disturbance, At that time, sliding surface It will be at the preset time Convergence; if a sudden perturbation exists, At that time, due to the presence of interference observers and preset performance adjustment items, the system will avoid singularity and failure, thus maintaining system stability.

2. The spacecraft attitude preset time control method based on adjustable preset performance according to claim 1, characterized in that... In each of the steps, It has the following properties: 。 3. The spacecraft attitude preset time control method based on adjustable preset performance according to claim 1, characterized in that... In steps one and two, the rotation matrix for: 。 4. The spacecraft attitude preset time control method based on adjustable preset performance according to claim 1, characterized in that... In step two, the initial values ​​of the upper and lower boundaries of the initial preset performance function are designed. , satisfy: in Represents the attitude error vector The Each component in The initial value at time.

5. The spacecraft attitude preset time control method based on adjustable preset performance according to claim 1, characterized in that... In step three, That is, in After a moment Corresponding attitude error for .

6. The spacecraft attitude preset time control method based on adjustable preset performance according to claim 1, characterized in that... In step three, and The relationship is: in hour, ;exist When, that is, when the preset performance function changes, When the corresponding expected error and the preset performance function remain unchanged The corresponding expected errors are equal.

7. The spacecraft attitude preset time control method based on adjustable preset performance according to claim 1, characterized in that... In step four, The meaning of the function is: For variables ,constant ,have: For vectors ,constant ,have: 。

Images