Quantitative stability attitude tracking control method, device and equipment for flexible spacecraft

Abstract

The invention discloses a quantitative stability attitude tracking control method, device and equipment of a flexible spacecraft, belongs to the technical field of flexible spacecrafts, and particularly relates to quantitative stability attitude tracking control of the flexible spacecraft. The problem that an existing flexible spacecraft attitude control method cannot give consideration to the convergence speed and the quantitative stability of precision is solved. The method comprises the following steps: representing the attitude of the spacecraft by using a modified Rodrigues parameter, and obtaining an attitude dynamic model of the flexible spacecraft. The quantitative stability attitude tracking control method, device and equipment of the flexible spacecraft are suitable for quantitative stability attitude tracking control of the flexible spacecraft.

Description

Technical Field

[0001] This invention relates to the field of flexible spacecraft technology, and more particularly to quantitative stability attitude tracking control of flexible spacecraft. Background Technology

[0002] Modern spacecraft typically incorporate flexible components, such as solar sails and flexible robotic arms. The presence of these flexible components presents the following challenges to spacecraft attitude control: (1) The attitude maneuver of a spacecraft will inevitably excite the vibration of flexible components, thereby generating a rigid-flexible coupling torque that destroys the stability of the attitude control system. (2) The modal coordinates and modal velocities that characterize the vibration of flexible components are usually not measurable in real time by sensors, and it is difficult to construct compensation terms in the control law to cancel the stiff-flexible coupling torque.

[0003] To address this issue, those skilled in the art have proposed designing modal observers to estimate modal coordinates and modal velocities in real time, for example: (Du H, Chen MZQ, Wen G. Leader-Following Attitude Consensus for Spacecraft Formation with Rigid and Flexible Spacecraft[J]. Journal of Guidance Control Dynamics, 2016, 39(4):1-8.) and (Xiao Y, Wang Y, YeD, Sun Z. Predefined-Time Robust Attitude Tracking Control of Flexible Spacecraft with Continuous and Nonsingular Performance[J]. Aerospace Science Technology, 2025, 159: 110000.).

[0004] However, these modal observers are asymptotically convergent and lack quantitative stability characteristics.

[0005] Based on the proposed modal observer, the literature (Du H, Chen MZQ, Wen G. Leader-Following Attitude Consensus for Spacecraft Formation with Rigid and FlexibleSpacecraft[J]. Journal of Guidance Control Dynamics, 2016, 39(4):1-8.) proposes an attitude controller, which is also asymptotically stable and does not possess quantitative stability characteristics.

[0006] In addition, the paper (Xiao Y, Wang Y, Ye D, Sun Z. Predefined-Time RobustAttitude Tracking Control of Flexible Spacecraft with Continuous and Nonsingular Performance[J]. Aerospace Science Technology, 2025, 159: 110000.) proposes a controller that is time-stable and has quantitative stability in terms of convergence speed, but it still does not have quantitative stability in terms of convergence accuracy.

[0007] Currently, there are no reported methods for flexible spacecraft attitude control that balance quantitative stability with convergence speed and accuracy. Summary of the Invention

[0008] This invention proposes a quantitative stability attitude tracking control method, device, and equipment for flexible spacecraft, which solves the problem of quantitative stability in existing flexible spacecraft attitude control methods that cannot simultaneously take into account convergence speed and accuracy.

[0009] The quantitative stability attitude tracking control method for flexible spacecraft of the present invention includes: Step S1: Use the modified Rodriguez parameters to represent the spacecraft's attitude and obtain the attitude dynamics model of the flexible spacecraft; Step S2: Based on the attitude dynamics model of the flexible spacecraft, obtain the attitude tracking error and angular velocity tracking error to construct an error attitude dynamics model; Step S3: Design the terminal sliding surface for the error attitude dynamics model of the flexible spacecraft; when the modulus of this terminal sliding surface is kept in a specified neighborhood near zero, the attitude tracking error will converge to the specified accuracy within a specified time. Step S4: Construct a performance function for the error attitude dynamics model of the flexible spacecraft; construct intermediate variables, diagonal matrices, and column vectors based on the performance function; Step S5: Construct an attitude controller based on the terminal sliding surface, performance function, intermediate variables, diagonal matrix, and column vector; the attitude controller is an adaptive quantitative stability attitude tracking controller; the attitude controller is used to complete the quantitative stability attitude tracking control of the flexible spacecraft.

[0010] Furthermore, in a preferred embodiment, step S1 includes: Using the modified Rodriguez parameters to represent the spacecraft's attitude, the attitude dynamics model of the flexible spacecraft is obtained as follows:

[0011]

[0012] In the formula: The spacecraft attitude is expressed in terms of the modified Rodriguez parameters; The angular velocity of the spacecraft; Let be the rotational inertia matrix of the rigid body at the center of the spacecraft relative to its center of mass. The control input applied to the actuator; External disturbance torque; and These represent the modal coordinates and modal velocities, respectively, indicating the deformation and vibration of the flexible attachment. It is a rigid-flexible coupling matrix; and These are the damping matrix and the stiffness matrix, respectively. and The first of each of the flexible attachments j The first natural frequency and the corresponding damping ratio.

[0013] Furthermore, in a preferred embodiment, step S2 includes: Let the target attitude be The corresponding target angular velocity is Then the attitude tracking error and angular velocity tracking error are respectively: (4) (5) in:

[0014] Represents the rotation matrix from the target volume coordinate system to the actual volume coordinate system; The error attitude dynamics model is as follows: (6) (7) Furthermore, in a preferred embodiment, step S3 includes: Constructing the terminal sliding surface (8) Among them, intermediate variables The specific form is (9) in , , and All are positive numbers and ,function and The definition is as follows: (10) (11) in , , It is a symbolic function, defined as follows: (12) Furthermore, in a preferred embodiment, step S4 includes: Define performance function (13) And based on this, construct intermediate variables.

[0015] (14) Further construct a diagonal matrix (15) (16) and column vectors (17) in, It is a performance function Time derivative, , , They are The three components, , , They are The three components, , , They are The three components.

[0016] Furthermore, in a preferred embodiment, step S5 includes: Design the following attitude controller: (18) in: It is a positive number. , and It is an adaptive variable that satisfies the following adaptive law: (19) (20) in , , It is a normal number.

[0017] This invention also proposes a quantitative stability attitude tracking and control device for flexible spacecraft, the device comprising: Step S1: Use the modified Rodriguez parameters to represent the spacecraft's attitude and obtain the attitude dynamics model of the flexible spacecraft; Step S2: Based on the attitude dynamics model of the flexible spacecraft, obtain the attitude tracking error and angular velocity tracking error to construct an error attitude dynamics model; Step S3: Design the terminal sliding surface for the error attitude dynamics model of the flexible spacecraft; when the modulus of this terminal sliding surface is kept in a specified neighborhood near zero, the attitude tracking error will converge to the specified accuracy within a specified time. Step S4: Construct a performance function for the error attitude dynamics model of the flexible spacecraft; construct intermediate variables, diagonal matrices, and column vectors based on the performance function; Step S5: Construct an attitude controller based on the terminal sliding surface, performance function, intermediate variables, diagonal matrix, and column vector; the attitude controller is an adaptive quantitative stability attitude tracking controller; the attitude controller is used to complete the quantitative stability attitude tracking control of the flexible spacecraft.

[0018] The present invention also proposes a computer device comprising: a processor and a memory, the memory for storing executable instructions of the processor, the processor being configured to execute the quantitative stability attitude tracking control method for a flexible spacecraft as described above by executing the executable instructions.

[0019] The present invention also proposes a computer storage medium storing a computer program, wherein when the computer program is executed, it performs the quantitative stability attitude tracking control method for flexible spacecraft described in any of the above-mentioned embodiments.

[0020] The present invention also proposes a computer program product, including a computer program / instruction, which, when executed by a processor, implements the steps of the quantitative stability attitude tracking control method for flexible spacecraft described in any of the above-mentioned claims.

[0021] The present invention has the following beneficial effects: The quantitative stability attitude tracking control method for flexible spacecraft described in this invention is a novel quantitative stability attitude tracking control method for flexible spacecraft that takes into account both convergence speed and convergence accuracy. It ensures that after receiving the attitude tracking control command, the attitude value of the flexible spacecraft converges to the desired attitude value within a specified time and with a specified accuracy; wherein, the convergence time and convergence accuracy can be specified by the space mission.

[0022] The quantitative stability attitude tracking control method for flexible spacecraft described in this invention achieves a control effect that balances convergence speed and accuracy by combining the terminal sliding mode method with the performance function method.

[0023] The quantitative stability attitude tracking control method, apparatus, and equipment for flexible spacecraft described in this invention are applicable to the quantitative stability attitude tracking control of flexible spacecraft. Attached Figure Description

[0024] To more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0025] Figure 1 This is a flowchart illustrating a quantitative stability attitude tracking control method for a flexible spacecraft, as described in one embodiment of the present invention. Figure 2 In one embodiment of the present invention, the terminal sliding surface A schematic diagram of the response curve; Figure 3 In one embodiment of the present invention, attitude tracking error A schematic diagram of the response curve; Figure 4 In one embodiment of the present invention, angular velocity tracking error A schematic diagram of the response curve; Figure 5 In one embodiment of the present invention, the control torque A schematic diagram; Figure 6 In one embodiment of the present invention, modal coordinates A schematic diagram of the response curve; Figure 7 In one embodiment of the present invention, modal velocity A schematic diagram of the response curve. Detailed Implementation

[0026] To make the technical solutions and advantages of the present invention clearer, the specific embodiments of the present invention will be described in further detail and completely below with reference to the accompanying drawings. The various embodiments described below are only some preferred embodiments of the present invention, and not all of them; the various embodiments described below are intended to explain the present invention and should not be construed as limiting the present invention; reasonable combinations of the technical features defined in the various embodiments of the present invention, as well as all other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort, are all within the scope of protection of the present invention.

[0027] Implementation Method 1: A quantitative stability attitude tracking control method for flexible spacecraft, the method comprising: Step S1: Use the modified Rodriguez parameters to represent the spacecraft's attitude and obtain the attitude dynamics model of the flexible spacecraft; Step S2: Based on the attitude dynamics model of the flexible spacecraft, obtain the attitude tracking error and angular velocity tracking error to construct an error attitude dynamics model; Step S3: Design the terminal sliding surface for the error attitude dynamics model of the flexible spacecraft; when the modulus of this terminal sliding surface is kept in a specified neighborhood near zero, the attitude tracking error will converge to the specified accuracy within a specified time. Step S4: Construct a performance function for the error attitude dynamics model of the flexible spacecraft; construct intermediate variables, diagonal matrices, and column vectors based on the performance function; Step S5: Construct an attitude controller based on the terminal sliding surface, performance function, intermediate variables, diagonal matrix, and column vector; the attitude controller is an adaptive quantitative stability attitude tracking controller; the attitude controller is used to complete the quantitative stability attitude tracking control of the flexible spacecraft.

[0028] In this implementation, the Rodriguez parameter, abbreviated as "MRPs", is modified.

[0029] It should be noted that the quantitative stability of the control algorithm includes two aspects: the quantitative stability of the convergence speed and the quantitative stability of the convergence accuracy.

[0030] (1) In terms of convergence speed: Fixed-time control and preset-time control can provide an upper bound on the convergence time that can be analytically expressed. This upper bound is only related to the controller parameters, thereby achieving quantitative stability of the convergence speed.

[0031] The upper bound of the convergence time provided by fixed-time control usually has a complex functional relationship with the controller parameters, which is not conducive to the selection of controller parameters.

[0032] In contrast, preset time control can provide an upper bound on the convergence time that is explicitly present in the controller parameters, greatly reducing the difficulty of selecting controller parameters.

[0033] (2) In terms of convergence accuracy: Precision-preserving control and preset precision control can provide an upper bound for the steady-state error that can be analytically expressed, thus achieving quantitative stability of convergence accuracy.

[0034] Similar to fixed-time control, the upper bound of steady-state error provided by precision control usually has a complex functional relationship with the controller parameters.

[0035] Similar to preset time control, preset precision control can provide an upper bound on the steady-state error that is explicitly present in the controller parameters, thus having a wider range of application prospects.

[0036] In this embodiment, the method is a novel quantitative stability attitude tracking control method for flexible spacecraft that balances convergence speed and accuracy.

[0037] Implementation Method 2: Step S1 includes: Using the modified Rodriguez parameters to represent the spacecraft's attitude, the attitude dynamics model of the flexible spacecraft is obtained as follows:

[0038] (2) (3) In the formula: The spacecraft attitude is expressed in terms of the modified Rodriguez parameters; The angular velocity of the spacecraft; Let be the rotational inertia matrix of the rigid body at the center of the spacecraft relative to its center of mass. The control input applied to the actuator; External disturbance torque; and These represent the modal coordinates and modal velocities, respectively, indicating the deformation and vibration of the flexible attachment. It is a rigid-flexible coupling matrix; and These are the damping matrix and the stiffness matrix, respectively. and The first of each of the flexible attachments j The first natural frequency and the corresponding damping ratio.

[0039] Implementation method 3: Step S2 includes: Let the target attitude be The corresponding target angular velocity is Then the attitude tracking error and angular velocity tracking error are respectively: (4) (5) in:

[0040] Represents the rotation matrix from the target volume coordinate system to the actual volume coordinate system; The error attitude dynamics model is as follows: (6) (7) Implementation method 4: Step S3 includes: Constructing the terminal sliding surface (8) Among them, intermediate variables The specific form is (9) in , , and All are positive numbers and ,function and The definition is as follows: (10) (11) in , , It is a symbolic function, defined as follows: (12) In this embodiment, the terminal sliding surface is used to ensure the quantitative stability of the attitude tracking error. When the magnitude of this terminal sliding surface remains within a specified neighborhood of zero, the attitude tracking error will converge to a specified accuracy within a specified time.

[0041] Implementation method 5: Step S4 includes: Define performance function (13) And based on this, construct intermediate variables.

[0042] (14) Further construct a diagonal matrix (15) (16) and column vectors (17) in It is a performance function Time derivative, , , They are The three components, , , They are The three components, , , They are The three components.

[0043] In this embodiment, the performance function is used to ensure the quantitative stability of the terminal sliding surface, so that the modulus of the terminal sliding surface converges to a specified neighborhood near zero within a specified time.

[0044] In this embodiment, the intermediate variables, diagonal matrix, and column vectors are used for the construction of the subsequent attitude controller.

[0045] Implementation method 6: Step S5 includes: Design the following attitude controller: (18) in: It is a positive number. , and It is an adaptive variable that satisfies the following adaptive law: (19) (20) in , , It is a normal number.

[0046] In this embodiment, under any external disturbance, the attitude controller (18) can achieve quantitative stability attitude tracking control of the flexible spacecraft, that is, the attitude tracking error. The three components will be Stay in the range Within.

[0047] In this embodiment, the attitude controller (18) is an adaptive attitude tracking controller designed to take into account the external disturbances experienced by the flexible spacecraft, ensuring that the magnitude of the sliding mode converges to a specified neighborhood near the zero within a specified time and remains in this neighborhood.

[0048] Implementation Method 7: A quantitative stability attitude tracking and control device for a flexible spacecraft, the device comprising: Step S1: Use the modified Rodriguez parameters to represent the spacecraft's attitude and obtain the attitude dynamics model of the flexible spacecraft; Step S2: Based on the attitude dynamics model of the flexible spacecraft, obtain the attitude tracking error and angular velocity tracking error to construct an error attitude dynamics model; Step S3: Design the terminal sliding surface for the error attitude dynamics model of the flexible spacecraft; when the modulus of this terminal sliding surface is kept in a specified neighborhood near zero, the attitude tracking error will converge to the specified accuracy within a specified time. Step S4: Construct a performance function for the error attitude dynamics model of the flexible spacecraft; construct intermediate variables, diagonal matrices, and column vectors based on the performance function; Step S5: Construct an attitude controller based on the terminal sliding surface, performance function, intermediate variables, diagonal matrix, and column vector; the attitude controller is an adaptive quantitative stability attitude tracking controller; the attitude controller is used to complete the quantitative stability attitude tracking control of the flexible spacecraft.

[0049] Implementation Method 8: A computer device comprising: a processor and a memory, the memory for storing executable instructions of the processor, the processor being configured to execute the quantitative stability attitude tracking control method for a flexible spacecraft as described above by executing the executable instructions.

[0050] Implementation Method 9: A computer storage medium storing a computer program, wherein when the computer program is executed, the quantitative stability attitude tracking control method for flexible spacecraft described in any one of the above embodiments is executed.

[0051] Implementation Method 10: A computer program product, comprising a computer program / instructions, which, when executed by a processor, implement the steps of the quantitative stability attitude tracking control method for a flexible spacecraft as described in any one of the above embodiments.

[0052] Implementation Method 11: A specific embodiment is provided to verify the technical effects of the present invention through numerical simulation.

[0053] (1) Numerical simulation problem description (numerical simulation setting conditions): The moment of inertia of the rigid body at the center of the flexible spacecraft is taken as

[0054] The rigid-flexible coupling matrix is

[0055] The natural frequencies and corresponding damping ratios of the first four modes are as follows: , , , , , , , The target attitude trajectory is taken as... .

[0056] External disturbance torque set as .

[0057] The preset time constant is selected as The preset precision constant is selected as .

[0058] Other controller parameter selections are as follows: , , , , , , .

[0059] Adaptive variables , and The initial values ​​are respectively taken as , and .

[0060] Initial attitude set to Angular velocity set to The modal coordinates and modal velocities are respectively , .

[0061] (2) Based on the above-mentioned conditions, numerical simulation was performed, and the simulation results are as follows: Figures 2-7 As shown.

[0062] like Figure 2 As shown, these are the terminal sliding surfaces between 0 and 200 s. The response curve shows that all three components are within the preset time. Within the specified range, it converged. .

[0063] like Figure 3 , Figure 4 As shown, the response curves of attitude tracking error and angular velocity tracking error are respectively between 0 and 200 s. It can be seen that the tracking error of the flexible spacecraft attitude to the desired trajectory converges to within the preset accuracy within the preset time.

[0064] like Figure 5 , Figure 6 , Figure 7 The figures show the response curves of the control torque, modal coordinates, and modal velocities applied to the flexible spacecraft body during the simulation process.

[0065] This embodiment provides a computer device or system. The hardware device in this part is a general model and is not shown in the figure. The system includes a processor and a memory, wherein the processor and the memory can be connected by a bus or other means. The memory, as a non-transitory computer-readable storage medium, can be used to store non-transitory software programs, non-transitory computer-executable programs and modules, as well as corresponding program instructions / modules. The processor executes various functional applications and data processing by running the non-transitory software programs, instructions and modules stored in the memory, so as to realize the data quality enhancement method for data space entity parsing in the above method embodiment.

[0066] The memory may include a program storage area and a data storage area, wherein the program storage area may store the operating system and applications required for at least one function; the data storage area may store data created by the processor, etc. Furthermore, the memory may include high-speed random access memory and may also include non-transitory memory, such as at least one disk storage device, flash memory device, or other non-transitory solid-state storage device. In some embodiments, the memory may optionally include memory remotely located relative to the processor, which can be connected to the processor via a network. Examples of such networks include, but are not limited to, the Internet, corporate intranets, mobile communication networks, and combinations thereof.

[0067] One or more modules are stored in the memory. When the processor executes, it performs the method steps in the embodiments. In this way, the invention objective can be achieved through the method, apparatus and process of the present invention. The specific details of the computer device described above can be understood by referring to the relevant descriptions and effects in the embodiments, and will not be repeated here.

[0068] Those skilled in the art will understand that implementing all or part of the processes in the above embodiments can be accomplished by a computer program instructing related hardware. The program can be stored in a computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. The storage medium can be a magnetic disk, optical disk, read-only memory (ROM), random access memory (RAM), flash memory, hard disk drive (HDD), or solid-state drive (SSD), etc.; the storage medium can also include combinations of the above types of memory.

[0069] The above description of several specific embodiments further details the technical solution provided by the present invention in order to highlight the advantages and benefits of the technical solution provided by the present invention. However, the above-described specific embodiments are not intended to limit the present invention. Any reasonable modifications and improvements to the present invention, reasonable combinations of embodiments, and equivalent substitutions based on the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A quantitative stability attitude tracking control method for flexible spacecraft, characterized in that, The method includes: Step S1: Use the modified Rodriguez parameters to represent the spacecraft's attitude and obtain the attitude dynamics model of the flexible spacecraft; Step S2: Based on the attitude dynamics model of the flexible spacecraft, obtain the attitude tracking error and angular velocity tracking error to construct an error attitude dynamics model; Step S3: Design the terminal sliding surface for the error attitude dynamics model of the flexible spacecraft; when the modulus of this terminal sliding surface is kept in a specified neighborhood near zero, the attitude tracking error will converge to the specified accuracy within a specified time. Step S4: Construct a performance function for the error attitude dynamics model of the flexible spacecraft; construct intermediate variables, diagonal matrices, and column vectors based on the performance function; Step S5: Construct an attitude controller based on the terminal sliding surface, performance function, intermediate variables, diagonal matrix, and column vector; the attitude controller is an adaptive quantitative stability attitude tracking controller; the attitude controller is used to complete the quantitative stability attitude tracking control of the flexible spacecraft.

2. The quantitative stability attitude tracking control method for flexible spacecraft according to claim 1, characterized in that, Step S1 includes: Using the modified Rodriguez parameters to represent the spacecraft's attitude, the attitude dynamics model of the flexible spacecraft is obtained as follows: (2) (3) In the formula: The spacecraft attitude is expressed in terms of the modified Rodriguez parameters; The angular velocity of the spacecraft; Let be the rotational inertia matrix of the rigid body at the center of the spacecraft relative to its center of mass. The control input applied to the actuator; External disturbance torque; and These represent the modal coordinates and modal velocities, respectively, indicating the deformation and vibration of the flexible attachment. It is a rigid-flexible coupling matrix; and These are the damping matrix and the stiffness matrix, respectively. and The first of each of the flexible attachments j The first natural frequency and the corresponding damping ratio.

3. The quantitative stability attitude tracking control method for flexible spacecraft according to claim 2, characterized in that, Step S2 includes: Let the target attitude be The corresponding target angular velocity is Then the attitude tracking error and angular velocity tracking error are respectively: (4) (5) in: Represents the rotation matrix from the target volume coordinate system to the actual volume coordinate system; The error attitude dynamics model is as follows: (6) (7)。 4. The quantitative stability attitude tracking control method for flexible spacecraft according to claim 3, characterized in that, Step S3 includes: Constructing the terminal sliding surface (8) Among them, intermediate variables The specific form is (9) in , , and All are positive numbers and ,function and The definition is as follows: (10) (11) in , , It is a symbolic function, defined as follows: (12)。 5. The quantitative stability attitude tracking control method for flexible spacecraft according to claim 4, characterized in that, Step S4 includes: Define performance function (13) And based on this, construct intermediate variables. (14) Further construct a diagonal matrix (15) (16) and column vectors (17) in, It is a performance function Time derivative, , , They are The three components, , , They are The three components, , , They are The three components.

6. The quantitative stability attitude tracking control method for flexible spacecraft according to claim 5, characterized in that, Step S5 includes: Design the following attitude controller: (18) in: It is a positive number. , and It is an adaptive variable that satisfies the following adaptive law: (19) (20) in , , It is a normal number.

7. A quantitative stability attitude tracking and control device for flexible spacecraft, characterized in that, The device includes: Step S1: Use the modified Rodriguez parameters to represent the spacecraft's attitude and obtain the attitude dynamics model of the flexible spacecraft; Step S2: Based on the attitude dynamics model of the flexible spacecraft, obtain the attitude tracking error and angular velocity tracking error to construct an error attitude dynamics model; Step S3: Design the terminal sliding surface for the error attitude dynamics model of the flexible spacecraft; when the modulus of this terminal sliding surface is kept in a specified neighborhood near zero, the attitude tracking error will converge to the specified accuracy within a specified time. Step S4: Construct a performance function for the error attitude dynamics model of the flexible spacecraft; construct intermediate variables, diagonal matrices, and column vectors based on the performance function; Step S5: Construct an attitude controller based on the terminal sliding surface, performance function, intermediate variables, diagonal matrix, and column vector; the attitude controller is an adaptive quantitative stability attitude tracking controller; the attitude controller is used to complete the quantitative stability attitude tracking control of the flexible spacecraft.

8. A computer device, comprising: A processor and a memory, characterized in that the memory is used to store executable instructions of the processor, the processor being configured to execute the quantitative stability attitude tracking control method for a flexible spacecraft according to any one of claims 1-6 by executing the executable instructions.

9. A computer storage medium, characterized in that, The storage medium stores a computer program, which, when executed, performs the quantitative stability attitude tracking and control method for flexible spacecraft according to any one of claims 1-6.

10. A computer program product comprising a computer program / instructions, characterized in that, When the computer program / instructions are executed by the processor, they implement the steps of the quantitative stability attitude tracking control method for a flexible spacecraft as described in any one of claims 1-6.

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