A spacecraft preset time preset accuracy attitude tracking control method and system based on a performance function

Abstract

The application discloses a spacecraft preset time preset accuracy attitude tracking control method and system based on a performance function and relates to the field of spaceflight. The method solves the problems that the existing preset time preset accuracy attitude control method requires the upper limit of a disturbance torque to be known, has singularity or requires the attitude error at the initial moment to be within a certain range. The method comprises the following steps: establishing an attitude dynamics model of a spacecraft according to modified Rodrigues parameters; designing a performance function and performing mathematical conversion on an attitude tracking error of the attitude dynamics model of the spacecraft; constructing a continuous non-singular adaptive attitude tracking controller; and realizing preset time preset accuracy attitude tracking control of the spacecraft according to the continuous non-singular adaptive attitude tracking controller. The application is applied to the field of spacecraft attitude control.

Description

Technical Field

[0001] This invention relates to the aerospace field, and more particularly to a spacecraft attitude tracking control method based on a performance function with preset time and preset accuracy. Background Technology

[0002] Spacecraft attitude control is a crucial research area in aerospace, directly impacting the successful execution of various space missions. Based on the rate at which attitude error approaches zero, existing attitude control methods can be categorized into asymptotic control, finite-time control, fixed-time control, and preset-time control. Compared to asymptotic control, finite-time and fixed-time control guarantee that the attitude error converges to zero or near zero within a finite time; however, the upper bound of their convergence time typically exhibits a complex functional relationship with controller parameters or initial system conditions. In contrast, preset-time control, under arbitrary initial conditions, can converge the attitude error to the required accuracy within a defined time upper bound, which can be easily adjusted according to mission requirements.

[0003] Traditional preset-time control methods can only guarantee that the attitude error converges to near zero within a preset time, but cannot determine the specific convergence accuracy. To address this, preset-time preset-accuracy control has emerged. It can converge the attitude error to a known neighborhood of zero within a preset time, effectively solving the problem of uncertain convergence accuracy. Wang Yunteng, Xiao Yan, Ye Dong, and others disclosed a terminal sliding mode control method in their 2023 publication, "Preset-Time Preset-Accuracy Attitude Tracking Control for Rigid Body Spacecraft." This method can be used to design preset-time preset-accuracy control, but it requires that the upper bound of the disturbance to the system be known, which constitutes a limitation. On the other hand, performance functions provide another effective tool for achieving preset-time preset-accuracy control because they do not require the upper bound of the disturbance to be known. However, existing performance function-based preset time precision control methods have some problems in practical applications. For example, they may exhibit singularities, as seen in the 2022 paper "Adaptive Sliding Mode Attitude-Tracking Control of Spacecraft with Prescribed Time Performance" by Runze Chen, Zhenling Wang, and Weiwei Che et al., or they may only be effective when the initial attitude error does not exceed a certain range, as seen in the 2021 paper "Novel Finite-Time Adaptive Neural Control of Flexible Spacecraft with Actuator Constraints and Prescribed Attitude Tracking Performance" by Jiawei Tao, Tao Zhang, and Qirui Liu et al. Therefore, although preset time precision control shows promising potential, further research and optimization are needed to overcome these limitations. Summary of the Invention

[0004] This invention addresses the shortcomings of existing preset time and preset accuracy attitude control methods, which either require a known upper bound on the disturbance torque, suffer from singularity issues, or require the initial attitude error to be within a certain range. It proposes a spacecraft preset time and preset accuracy attitude tracking control method based on a performance function, the method comprising:

[0005] S1: Establish the attitude dynamics model of the spacecraft based on the modified Rodriguez parameters (MRPs);

[0006] S2: Design the performance function and perform mathematical transformation on the attitude tracking error in the spacecraft's attitude dynamics model;

[0007] S3: Construct a continuous non-singular adaptive attitude tracking controller;

[0008] S4: Implement preset time and preset accuracy attitude tracking control for the spacecraft based on the continuous non-singular adaptive attitude tracking controller.

[0009] Furthermore, a preferred embodiment is proposed, wherein step S1 includes:

[0010]

[0011] Where, σ∈R 3 Let the spacecraft attitude be expressed in MRPs, ω∈R 3 Let J be the angular velocity of the spacecraft, J∈R 3×3 Let R be the rotational inertia matrix of the spacecraft relative to its center of mass, τ∈R 3 The control input applied to the actuator, d∈R 3 This is the disturbance torque.

[0012] Furthermore, a preferred embodiment is proposed, wherein step S2 includes:

[0013] The error attitude dynamics model is as follows:

[0014]

[0015] in, T(σ) is the time rate of change of attitude tracking error. e ) is the error attitude kinematics matrix, ω e For angular velocity tracking error, σ e For attitude tracking error, is the time rate of change of angular velocity tracking error, and f is an intermediate variable;

[0016] Design performance function:

[0017]

[0018] Where β(t) is the performance function, T p ε is the preset time constant, t is the time variable, and ε is a positive constant.

[0019] Furthermore, a preferred embodiment is proposed, wherein the attitude tracking error is specifically:

[0020]

[0021] Where, σ d For the target posture, To match the target attitude σ d The cross product matrix corresponding to (t).

[0022] Furthermore, a preferred embodiment is proposed, wherein the angular velocity tracking error is specifically:

[0023] ω e =ω-C qe ω d

[0024] Among them, C qe To represent the rotation matrix from the target volume coordinate system to the actual volume coordinate system, ω d The target angular velocity.

[0025] Furthermore, a preferred embodiment is proposed, wherein step S3 includes:

[0026]

[0027] Where τ is the control torque, S T (σ e ) is the intermediate variable matrix S(σ e The transpose of ) and Θ is an intermediate variable. As an intermediate variable, For adaptive parameters, K0 is an adaptive parameter and a symmetric positive definite matrix.

[0028] Furthermore, a preferred embodiment is proposed, wherein step S4 includes:

[0029]

[0030] Where h is an intermediate variable, s is an intermediate variable, K1 is a symmetric positive definite matrix, and c, g1 and g2 are positive constants.

[0031] Based on the same inventive concept, this invention also proposes a spacecraft preset time preset accuracy attitude tracking and control system based on a performance function. The system includes: an onboard computer, an actuator, a spacecraft body, an onboard attitude sensor, and an onboard angular velocity sensor; the onboard computer stores the tracking and control method described above.

[0032] The onboard computer generates control signals based on the spacecraft's expected attitude and current attitude;

[0033] Control signals are used to drive actuators and generate control torque;

[0034] The actuators apply torque to the spacecraft body, thereby changing the spacecraft's attitude and angular velocity;

[0035] The onboard attitude sensor and onboard angular velocity sensor capture the spacecraft's attitude and angular velocity information and feed the data back to the onboard computer;

[0036] After receiving the feedback signal, the onboard computer compares it with the desired attitude and adjusts the control signal again based on the deviation to ensure that the spacecraft can reach or maintain the desired attitude.

[0037] Based on the same inventive concept, the present invention also proposes a computer device, including a memory and a processor, wherein the memory stores a computer program, and when the processor runs the computer program stored in the memory, the processor executes a spacecraft preset time preset accuracy attitude tracking control method according to any one of the above-mentioned methods.

[0038] Based on the same inventive concept, the present invention also proposes a computer-readable storage medium storing a computer program, which, when executed by a processor, performs the steps of a spacecraft preset time preset accuracy attitude tracking control method based on a performance function as described in any of the preceding claims.

[0039] The advantages of this invention are:

[0040] Existing methods typically require a known upper bound on the disturbance torque, but in practical applications, this constraint is often difficult to obtain accurately, leading to unsatisfactory control performance. The method proposed in this invention, through the design of performance functions and adaptive laws, eliminates the requirement for a known upper bound on the disturbance torque.

[0041] Singularities sometimes occur in spacecraft attitude control, especially under certain specific attitudes, where the controller may fail or become unstable. The method proposed in this invention designs a continuous non-singular attitude tracking controller, which can effectively avoid the impact of singularities on the control performance.

[0042] Traditional performance function-based control methods typically require the initial attitude error to be within a certain range, limiting the flexibility of practical applications. The method proposed in this invention, through an improved mathematical model and control strategy, reduces the requirements for initial conditions, enabling effective control under a wider range of conditions.

[0043] The proposed spacecraft attitude tracking control method based on performance functions uses modified Rodriguez parameters to establish a spacecraft attitude dynamics model, effectively describing the spacecraft's three-dimensional rotation and avoiding the singularity problem of traditional Euler angle methods. By constructing a performance function and combining it with attitude tracking errors for mathematical transformation, the control objective becomes more explicit, and the control strategy can be flexibly adjusted to adapt to different needs. The controller is designed to ensure non-singularity at all times, guaranteeing stability and reliability during attitude tracking.

[0044] Through adaptive design, the controller can dynamically adjust parameters according to the actual operating status, improving the flexibility and accuracy of control.

[0045] This invention proposes a spacecraft pre-set time and pre-set accuracy attitude tracking control method based on performance functions. This method maintains high control performance without relying on known disturbance torques and enhances robustness against external disturbances. It reduces the limitation on initial attitude error, making the method applicable to more real-world scenarios and improving the operational flexibility of the spacecraft. The continuous non-singular attitude tracking controller design ensures stable control under various attitudes, avoiding control failures due to singularities. The inclusion of adaptive rules allows the control system to adjust in real time, better responding to dynamic environmental changes and improving attitude tracking accuracy and response speed.

[0046] This invention proposes a spacecraft attitude tracking and control system based on performance functions, which receives attitude and angular velocity information in real time via an onboard computer. This allows for rapid evaluation of the current state, comparison with the expected attitude, and generation of adjusted control signals. This rapid feedback mechanism ensures timely response to attitude changes, enhancing system stability and reliability. Utilizing high-precision data from onboard attitude and angular velocity sensors, the system accurately calculates attitude errors, thereby more effectively adjusting control signals to ensure the spacecraft reaches or maintains the target attitude within a preset time. The system can adjust control strategies in real time based on environmental changes and external disturbances, adapting to different flight states and mission requirements, improving the spacecraft's operational flexibility under complex missions. The system tightly integrates computers, sensors, and actuators into a comprehensive attitude control solution, improving overall system performance and maintenance efficiency. The introduction of a performance function-based control method allows for a trade-off between response speed and steady-state error during system design, ensuring optimal tracking performance during mission execution. Because the system can automatically process and adjust control signals, it reduces reliance on manual intervention, improving mission automation and operational safety.

[0047] This invention is applied to the field of spacecraft attitude control. Attached Figure Description

[0048] Figure 1 This is a flowchart of a spacecraft preset time preset accuracy attitude tracking control method based on performance function as described in Implementation Method 1.

[0049] Figure 2 This is a schematic diagram of a spacecraft preset time preset accuracy attitude tracking control system based on a performance function, as described in Embodiment 8.

[0050] Figure 3This is a schematic diagram of the attitude tracking error described in Implementation Method Eleven;

[0051] Figure 4 This is a schematic diagram of the angular velocity tracking error described in Implementation Method Eleven;

[0052] Figure 5 This is a schematic diagram of the control torque described in Implementation Method Eleven. Detailed Implementation

[0053] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments.

[0054] Implementation Method 1, see Figure 1 This embodiment describes a spacecraft attitude tracking control method based on a performance function with preset time and preset accuracy. The method includes:

[0055] S1: Establish the attitude dynamics model of the spacecraft based on the modified Rodriguez parameters (MRPs);

[0056] S2: Design the performance function and perform mathematical transformation on the attitude tracking error of the spacecraft's attitude dynamics model;

[0057] S3: Construct a continuous non-singular adaptive attitude tracking controller;

[0058] S4: Implement preset time and preset accuracy attitude tracking control for the spacecraft based on the continuous non-singular adaptive attitude tracking controller.

[0059] Existing methods typically require that the upper bound of the disturbance torque be known, but in practical applications, this constraint is often difficult to obtain accurately, leading to unsatisfactory control performance. This embodiment, through the design of the performance function, eliminates the requirement that the upper bound of the disturbance torque be known.

[0060] Singularities sometimes occur in spacecraft attitude control, especially under certain specific attitudes, where the controller may fail or become unstable. This method designs a continuous non-singular attitude tracking controller, which can effectively avoid the impact of singularities on control performance.

[0061] Traditional performance function-based control methods typically require the initial attitude error to be within a certain range, limiting the flexibility of practical applications. This implementation, through an improved mathematical model and control strategy, reduces the requirements for initial conditions, enabling effective control under a wider range of conditions.

[0062] The method proposed in this embodiment uses modified Rodriguez parameters to establish a spacecraft attitude dynamics model, which can effectively describe the spacecraft's three-dimensional rotation and avoid the singularity problem of traditional Euler angle methods. Combining attitude tracking errors with mathematical transformation makes the control objective more explicit and allows for flexible adjustment of the control strategy to adapt to different needs. The controller is designed to ensure non-singularity at all times, ensuring stability and reliability when handling attitude tracking. Through adaptive design, the controller can dynamically adjust parameters according to the actual operating state, improving the flexibility and accuracy of control.

[0063] The method proposed in this embodiment maintains high control performance without relying on known disturbance torques, enhancing robustness to external disturbances. It reduces the limitation on initial attitude error, making the method applicable to more real-world scenarios and improving the operational flexibility of spacecraft. The continuous non-singular attitude tracking controller design ensures stable control under various attitudes, avoiding control failures due to singularities. The inclusion of adaptive laws allows the control system to adjust in real time, better responding to dynamic environmental changes and improving attitude tracking accuracy and response speed.

[0064] Implementation Method Two: This implementation method further defines the preset time and preset accuracy attitude tracking control method described in Implementation Method One. Step S1 includes:

[0065]

[0066] Where, σ∈R 3 Let the spacecraft attitude be expressed in MRPs, ω∈R 3 Let J be the angular velocity of the spacecraft, J∈R 3×3 Let R be the rotational inertia matrix of the spacecraft relative to its center of mass, τ∈R 3 The control input applied to the actuator, d∈R 3 This is the disturbance torque.

[0067] In this implementation, MRPs are used to represent the spacecraft's attitude, effectively avoiding singularity issues and ensuring continuity and operability throughout the attitude space. Explicitly defining the angular velocity and moment of inertia matrices allows for a more precise description of the spacecraft's dynamic characteristics, improving the reliability of control. Clearly defining the role of control inputs enables more effective application of control signals in complex environments, achieving precise attitude tracking. The introduction of adaptive mechanisms allows the control system to better adapt to external disturbances, improving system robustness and stability.

[0068] Implementation Method 3: This implementation method further defines the preset time and preset accuracy attitude tracking control method described in Implementation Method 1. Step S2 includes:

[0069] The error attitude dynamics model is as follows:

[0070]

[0071] in, T(σ) is the time rate of change of attitude tracking error. e ) is the error attitude kinematics matrix, ω e For angular velocity tracking error, σ e For attitude tracking error, is the time rate of change of angular velocity tracking error, and f is an intermediate variable;

[0072] Design performance function:

[0073]

[0074] Where β(t) is the performance function, T p ε is the preset time constant, t is the time variable, and ε is a positive constant.

[0075] This embodiment, by defining the time rate of change of the error attitude and the kinematic matrix, clearly describes the dynamic evolution of the attitude tracking error, making the control algorithm more targeted. The designed performance function considers a preset time constant, effectively balancing the response speed and steady-state error of the control system, ensuring that the required accuracy is achieved within a preset time. By introducing the time variable t, the control system can evaluate the current state in real time and dynamically adjust the control strategy to adapt to actual operating conditions. The constant and variable settings in the design can improve the system's adaptability to external disturbances and uncertainties, enhancing the stability of the overall control performance.

[0076] Implementation Method Four: This implementation method further defines the preset time and preset accuracy attitude tracking control method described in Implementation Method Three. Specifically, the attitude tracking error is:

[0077]

[0078] Where, σ d For the target posture, To match the target attitude σ d The cross product matrix corresponding to (t).

[0079] This implementation introduces a target attitude, making error calculation more intuitive and accurate, clearly reflecting the difference between the current state and the target state. Using a cross product matrix effectively converts the attitude error into control input, simplifying the control algorithm implementation and improving computational efficiency. A clear error definition makes the control system's behavior easier to understand and analyze, facilitating subsequent debugging and optimization. By accurately describing the attitude tracking error, the control strategy can be better optimized, thereby achieving the target attitude more efficiently within a preset time and improving tracking accuracy.

[0080] Implementation Method 5: This implementation method further defines the preset time and preset accuracy attitude tracking control method described in Implementation Method 3. Specifically, the angular velocity tracking error is:

[0081] ω e =ω-C qe ω d

[0082] Among them, C qe To represent the rotation matrix from the target volume coordinate system to the actual volume coordinate system, ω d The target angular velocity.

[0083] Implementation Method Six: This implementation method further defines the preset time and preset accuracy attitude tracking control method described in Implementation Method Three. Step S3 includes:

[0084]

[0085] Where τ is the control torque, S T (σ e ) is the intermediate variable matrix S(σ e The transpose of ) and Θ is an intermediate variable. As an intermediate variable, For adaptive parameters, K0 is an adaptive parameter and a symmetric positive definite matrix.

[0086] Implementation Method Seven: This implementation method further defines the preset time and preset accuracy attitude tracking control method described in Implementation Method One. Step S4 includes:

[0087]

[0088] Where h is an intermediate variable, s is an intermediate variable, K1 is a symmetric positive definite matrix, and c, g1 and g2 are positive constants.

[0089] Implementation Method 8, see below Figure 2This embodiment describes a spacecraft preset time and preset accuracy attitude tracking control system based on a performance function. The system includes: an onboard computer, an actuator, a spacecraft body, an onboard attitude sensor, and an onboard angular velocity sensor; the onboard computer stores the tracking control method described in Embodiment 1.

[0090] The onboard computer generates control signals based on the spacecraft's expected attitude and current attitude;

[0091] Control signals are used to drive actuators and generate control torque;

[0092] The actuators apply torque to the spacecraft body, thereby changing the spacecraft's attitude and angular velocity;

[0093] The onboard attitude sensor and onboard angular velocity sensor capture the spacecraft's attitude and angular velocity information and feed the data back to the onboard computer;

[0094] After receiving the feedback signal, the onboard computer compares it with the desired attitude and adjusts the control signal again based on the deviation to ensure that the spacecraft can reach or maintain the desired attitude.

[0095] The system described in this embodiment receives attitude and angular velocity information in real time via an onboard computer, enabling rapid assessment of the current state, comparison with the expected attitude, and generation of adjusted control signals. This rapid feedback mechanism ensures the spacecraft can respond promptly to attitude changes, enhancing system stability and reliability. Utilizing high-precision data from onboard attitude and angular velocity sensors, the system can accurately calculate attitude errors, thereby more effectively adjusting control signals to ensure the spacecraft reaches or maintains the target attitude within a preset time. The system can adjust control strategies in real time according to environmental changes and external disturbances, adapting to different flight states and mission requirements, improving the spacecraft's operational flexibility under complex missions. This system tightly integrates computers, sensors, and actuators to form a comprehensive attitude control solution, improving overall system performance and maintenance efficiency. The introduction of a performance function-based control method allows the system design to balance response speed and steady-state error, ensuring optimal tracking performance during mission execution. Because the system can automatically process and adjust control signals, it reduces reliance on manual intervention, improving mission automation and operational safety.

[0096] Implementation Method Nine: A computer device according to this implementation method includes a memory and a processor. The memory stores a computer program. When the processor runs the computer program stored in the memory, the processor executes a spacecraft preset time preset accuracy attitude tracking control method based on a performance function according to any one of Implementation Methods One to Seven.

[0097] Implementation Method 10: A computer-readable storage medium according to this implementation method stores a computer program, which, when executed by a processor, performs the steps of a spacecraft preset time preset accuracy attitude tracking control method based on a performance function as described in any one of Implementation Methods 1 to 7.

[0098] Implementation Method 11, see below Figures 3 to 5 This embodiment describes a specific example of the spacecraft preset time and preset accuracy attitude tracking control method based on a performance function as described in Embodiment 1. It also serves to explain Embodiments 2 through 7. Specifically:

[0099] This implementation proposes a preset-time, preset-accuracy attitude tracking control method for spacecraft. Modified Rodrigues parameters (MRPs) are chosen to describe the spacecraft's attitude. First, a novel performance function is designed, and the attitude tracking error represented by the MRPs is mathematically transformed to ensure that the initial conditions of the attitude tracking error are within the region defined by the performance function. Then, based on this performance function and considering the disturbances experienced by the spacecraft, an adaptive preset-time, preset-accuracy attitude tracking control algorithm is designed.

[0100] Using MRPs to represent the attitude of a spacecraft, the attitude dynamics model of the spacecraft is as follows:

[0101]

[0102] Where, σ∈R 3 Let the spacecraft attitude be expressed in MRPs, ω∈R 3 Let J be the angular velocity of the spacecraft, J∈R 3×3 Let R be the rotational inertia matrix of the spacecraft relative to its center of mass, τ∈R 3 The control input applied to the actuator, d∈R 3 This is the disturbance torque.

[0103] Let the target attitude be σ. d (t), the corresponding target angular velocity is ω. d (t), then the attitude tracking error and angular velocity tracking error are respectively:

[0104]

[0105] ω e =ω-C qe ω d (4)

[0106] in, ω represents the rotation matrix from the target volume coordinate system to the actual volume coordinate system.d The aforementioned target angular velocity ω d (t); σ d The aforementioned target attitude σ d (t), where σ is the aforementioned spacecraft attitude. To be with σ d The cross product matrix corresponding to (t):

[0107]

[0108] Where, σ d1 σ d2 σ d3 It is a vector σ d The three components;

[0109] The error attitude dynamics model is as follows:

[0110]

[0111] in, T(σ) represents the time rate of change of the attitude tracking error. e ) represents the error attitude kinematics matrix; The angular velocity tracking error represents the rate of change over time; f is an intermediate variable. To be with σ e The corresponding cross product matrix:

[0112]

[0113] Where, σ e1 σ e2 σ e3 It is a vector σ e The three components.

[0114] in:

[0115]

[0116] Define intermediate variables:

[0117]

[0118] Here, arctan(.) is the arctangent function. Clearly, The time derivative is:

[0119]

[0120] Define the performance function:

[0121]

[0122] Where β(t) is the defined performance function, Tp Let t be the preset time constant, ε be the time variable, and ε be a positive constant.

[0123] Further define intermediate variables:

[0124]

[0125] but The time derivative is:

[0126]

[0127] in:

[0128]

[0129] Next, we construct a backstep variable:

[0130]

[0131] Where g0 > 0. Based on this, a continuous nonsingular adaptive attitude tracking controller is constructed as follows:

[0132]

[0133] Where τ is the control torque; S T (σ e ) is the matrix S(σ) in formula (8) e The transpose of () can be called an intermediate variable; Θ is an intermediate variable; For adaptive parameters; a is a positive constant, K0∈R 3×3 It is a symmetric positive definite matrix. The operator L(.) means: for any three-dimensional column vector v = [v1, v2, v3] T ∈R 3 ,have:

[0134]

[0135] and They respectively satisfy the following adaptive laws:

[0136]

[0137] Where c, g1, and g2 are positive constants, and K1∈R 6×6 It is a symmetric positive definite matrix.

[0138] Under any disturbance, the controller (14) can achieve the spacecraft's preset time and preset accuracy attitude tracking control, that is, the attitude tracking error σ e The three components will be in the range of t≥Tp It remains within the interval (-ε, ε).

[0139] The above control method is designed based on the attitude dynamics model of rigid spacecraft. In fact, for flexible spacecraft, the coupling torque generated by the vibration of flexible attachments can be regarded as part of the disturbance, and the control method is still applicable.

[0140] The method described in this embodiment ensures that after receiving an attitude tracking command, the spacecraft's attitude value converges to the vicinity of the desired attitude value within a preset time and with a preset accuracy. This preset time and preset accuracy are specified by the space mission. Compared to existing preset time and preset accuracy attitude control methods, this method does not require prior knowledge of the upper bound of the disturbance torque, does not have singularity issues, and the initial attitude error can be any value, not requiring it to be within a certain range near zero.

[0141] In this embodiment, verification is performed through numerical simulation. The numerical simulation problem, simulation design process, and simulation results are described below as an embodiment and technical evidence of the present invention.

[0142] The moment of inertia of the spacecraft is:

[0143]

[0144] The target attitude trajectory is taken as

[0145] The external disturbance torque is set as d = 0.5[sin(t),cos(t),sin(0.5t)] T Nm.

[0146] The preset time constant is selected as T. p =100s, the preset precision constant is selected as ε=0.0005.

[0147] Other controller parameters are selected as follows: K0 = 2I3, K1 = I6, g1 = g2 = 0.002, a = 0.0001. Variables and The initial values ​​are respectively taken as and The initial attitude is set to σ(0) = [-1, 2, -1.2]. T Let the angular velocity be ω(0) = [-0.06, 0.05, 0.1]. T rad / s.

[0148] Based on the conditions set above, the following simulation was performed.

[0149] Under the above conditions, the simulation results are as follows: Figures 3-5 As shown. Figure 3 , Figure 4 The figures show the response curves for attitude tracking error and angular velocity tracking error between 0 and 200 s. It can be seen that the spacecraft's attitude tracking error for the desired trajectory converges to within the preset accuracy within the preset time, and the actual convergence time is significantly shorter than the preset value T. p =100s, attitude tracking error σ e The actual convergence accuracy of all three components is significantly better than the preset value ε = 0.0005. Figure 5 The figure shows the control torque applied to the spacecraft body during this process. It can be seen that the control torque is continuous, which is in line with expectations.

[0150] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied 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.

[0151] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, as well as combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart. Figure 1 One or more processes and / or boxes Figure 1 The computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0152] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1The steps of the function specified in one or more boxes.

[0153] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit its scope of protection. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that after reading the present invention, they can still make various changes, modifications or equivalent substitutions to the specific implementation of the invention, but these changes, modifications or equivalent substitutions are all within the scope of protection of the pending claims of the invention.

Claims

1. A spacecraft attitude tracking control method based on a performance function with preset time and preset accuracy, characterized in that, The method includes: S1: Construct the attitude dynamics model of the spacecraft based on the modified Rodriguez parameters (MRPs); S2: Design the performance function and perform mathematical transformation on the attitude tracking error in the spacecraft's attitude dynamics model; S3: Construct a continuous non-singular adaptive attitude tracking controller; S4: Implement preset time and preset accuracy attitude tracking control of the spacecraft based on the continuous non-singular adaptive attitude tracking controller; Step S2 includes: The error attitude dynamics model is as follows: in, The time rate of change of attitude tracking error. Here is the error attitude kinematics matrix. For angular velocity tracking error, For attitude tracking error, The time rate of change of angular velocity tracking error. As an intermediate variable; For disturbance torque; Design performance function: in, For performance functions, As a preset time constant, t For time variables, It is a positive number; Step S3 includes: in, To control the torque, intermediate variable matrix transpose, As an intermediate variable, As an intermediate variable, For adaptive parameters, For adaptive parameters, It is a symmetric positive definite matrix. It is an intermediate variable.

2. The attitude tracking control method with preset time and preset accuracy according to claim 1, characterized in that, Step S1 includes: in, The spacecraft attitude is represented by MRPs. The angular velocity of the spacecraft, Let be the rotational inertia matrix of the spacecraft relative to its center of mass. This is the disturbance torque.

3. The attitude tracking control method with preset time and preset accuracy according to claim 1, characterized in that, The attitude tracking error is specifically: in, For the target posture, To achieve the target attitude The corresponding cross product matrix.

4. The attitude tracking control method with preset time and preset accuracy according to claim 2, characterized in that, The angular velocity tracking error is specifically: in, To represent the rotation matrix from the target volume coordinate system to the actual volume coordinate system, The target angular velocity.

5. The attitude tracking control method with preset time and preset accuracy according to claim 1, characterized in that, Step S4 includes: in, As an intermediate variable, As an intermediate variable, It is a symmetric positive definite matrix. , and It is a normal number.

6. A spacecraft preset time and preset accuracy attitude tracking control system based on performance functions, characterized in that, The system includes: an onboard computer, an actuator, a spacecraft body, an onboard attitude sensor, and an onboard angular velocity sensor; the onboard computer stores the tracking control method according to claim 1; The onboard computer generates control signals based on the spacecraft's expected attitude and current attitude; Control signals are used to drive actuators and generate control torque; The actuators apply torque to the spacecraft body, thereby changing the spacecraft's attitude and angular velocity; The onboard attitude sensor and onboard angular velocity sensor capture the spacecraft's attitude and angular velocity information and feed the data back to the onboard computer; After receiving the feedback signal, the onboard computer compares it with the desired attitude and adjusts the control signal again based on the deviation to ensure that the spacecraft can reach or maintain the desired attitude.

7. A computer device, characterized in that: It includes a memory and a processor, wherein the memory stores a computer program, and when the processor runs the computer program stored in the memory, the processor executes a spacecraft preset time preset accuracy attitude tracking control method based on a performance function according to any one of claims 1-5.

8. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, performs the steps of a spacecraft preset time preset accuracy attitude tracking control method as described in any one of claims 1-5.

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