Control method, device, equipment and medium for single flexible solar wing spacecraft

Abstract

The present disclosure relates to the field of spacecraft control technology, and discloses a control method, device, equipment and medium for a single flexible solar wing spacecraft, which is used to solve the problem of low control accuracy of the spacecraft. The control method for a single flexible solar wing spacecraft may include: establishing a spacecraft model according to the geometric parameters of the spacecraft; determining the external force acting on the spacecraft, and determining the dynamic model of the spacecraft according to the external force; determining the piezoelectric driver model corresponding to the piezoelectric driver in the spacecraft model, and updating the dynamic model based on the piezoelectric driver model; discretizing the updated dynamic model to obtain a discretized dynamic model; designing a nonlinear control algorithm according to the discretized dynamic model to control the spacecraft. The control accuracy of the spacecraft can be improved.

Description

Technical Field

[0001] The embodiments of the present disclosure relate to the field of spacecraft control technology, and in particular to a control method, device, equipment and medium for a single flexible solar wing spacecraft. Background Art

[0002] With the rapid development of space technology, the control accuracy and reliability of spacecraft are increasingly required. In particular, as a key component of spacecraft, the control technology of flexible solar panels is crucial to ensure the stability of spacecraft in orbit and the accuracy of mission execution. Traditional spacecraft control methods are usually based on rigid body dynamics models. However, these methods are not fully applicable to spacecraft with flexible attachments, because flexible attachments will introduce additional complexity and uncertainty in spacecraft motion.

[0003] In the existing technology, the dynamic models of spacecraft often fail to fully consider the dynamic characteristics of flexible solar wings. The inaccuracy of the dynamic models, the limitations of the control methods, the lack of real-time and adaptability, as well as energy efficiency and control accuracy issues all limit the further improvement of spacecraft control performance. Summary of the invention

[0004] In view of this, the embodiments of the present disclosure hope to provide a control method, device, equipment and medium for a single flexible solar wing spacecraft, which can improve the control accuracy of the single flexible solar wing spacecraft.

[0005] The technical solution of the embodiment of the present disclosure is implemented as follows:

[0006] In a first aspect, an embodiment of the present disclosure provides a control method for a single flexible solar wing spacecraft, comprising:

[0007] Establishing a spacecraft model according to geometric parameters of the spacecraft;

[0008] determining an external force acting on the spacecraft, and determining a dynamic model of the spacecraft based on the external force;

[0009] Determining a piezoelectric actuator model corresponding to the piezoelectric actuator in the spacecraft model, and updating the dynamic model based on the piezoelectric actuator model;

[0010] Discretizing the updated dynamic model to obtain a discretized dynamic model;

[0011] A nonlinear control algorithm is designed based on the discretized dynamic model to control the spacecraft.

[0012] In some examples, determining the external force acting on the spacecraft and determining the dynamic model of the spacecraft based on the external force includes:

[0013] Determining the kinematic equations of the spacecraft based on the spacecraft model and the small deformation assumption;

[0014] According to the external force, a dynamic model of the spacecraft is determined based on the kinematic equation using Hamilton's principle.

[0015] In some examples, determining the kinematic equations of the spacecraft based on the spacecraft model and a small deformation assumption includes:

[0016] The kinematic equations of the spacecraft are determined in a spacecraft body fixed coordinate system according to the spacecraft model based on the small deformation assumption.

[0017] In some examples, determining a piezoelectric actuator model based on the dynamic model, and updating the dynamic model based on the piezoelectric actuator model includes:

[0018] Determining a piezoelectric actuator model in the spacecraft model based on the piezoelectric effect principle;

[0019] The dynamic model is updated according to the piezoelectric actuator model.

[0020] In some examples, updating the dynamic model according to the piezoelectric actuator model includes:

[0021] According to the installation position of the piezoelectric actuator on the solar sail panel, the neutral axis position and the bending stiffness are recalculated to update the dynamic model.

[0022] In some examples, the dynamic model includes an ordinary differential system equation and a partial differential system equation, the ordinary differential system equation is used to describe the uniaxial rigid rotation of the spacecraft, and the partial differential system equation is used to describe the planar continuous flexible dynamics of the solar wing in the spacecraft;

[0023] The step of discretizing the updated dynamic model to obtain a discretized dynamic model includes:

[0024] The Galerkin method is used to obtain the discretized dynamic model for numerical simulation.

[0025] In some examples, designing a nonlinear control algorithm based on a discretized dynamics model to control the spacecraft includes:

[0026] A nonlinear control algorithm is designed based on the discretized dynamic model to determine the input voltage of the piezoelectric actuator.

[0027] In a second aspect, the disclosed embodiment provides a control device for a single flexible solar wing spacecraft, including:

[0028] A building module, used for building a spacecraft model according to the geometric parameters of the spacecraft;

[0029] a determination module, configured to determine an external force acting on the spacecraft, and determine a dynamic model of the spacecraft according to the external force;

[0030] An updating module, configured to determine a piezoelectric actuator model corresponding to the piezoelectric actuator in the spacecraft model, and update the dynamics model based on the piezoelectric actuator model;

[0031] A processing module, used for discretizing the updated dynamic model to obtain a discretized dynamic model;

[0032] The control module is used to design a nonlinear control algorithm according to the discretized dynamic model to control the spacecraft.

[0033] In a third aspect, an embodiment of the present disclosure provides an electronic device, comprising: a processor and a memory; the processor is used to execute instructions stored in the memory to implement the control method of the single flexible solar wing spacecraft described in the first aspect.

[0034] In a fourth aspect, an embodiment of the present disclosure provides a computer storage medium, wherein the storage medium stores at least one instruction, and the at least one instruction is used to be executed by a processor to implement the control method of a single flexible solar wing spacecraft as described in the first aspect.

[0035] The disclosed embodiment provides a control method, device, equipment and medium for a single flexible solar wing spacecraft; through precise geometric modeling and external force and torque analysis, a comprehensive dynamic model is constructed, which can carefully capture the complex dynamic behavior of the flexible solar wing in the space environment. Further, by integrating the piezoelectric actuator model and updating the dynamic model, the method optimizes the control input, making the attitude adjustment of the spacecraft more accurate and efficient. Discretization processing not only enhances the practicality of the model, but also provides a basis for designing advanced nonlinear control algorithms, which can adaptively respond to the dynamic changes of the spacecraft and achieve fast and precise attitude control. In addition, the method significantly improves the robustness of the system, and can maintain the stability and control accuracy of the spacecraft even in the face of uncertainty in the external environment and changes in internal parameters. Through the integration of these technologies, the method not only improves the energy efficiency of the spacecraft, prolongs its life in orbit, but also enhances the flexibility and adaptability of mission execution, thereby bringing breakthrough technological progress to the field of spacecraft control. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1A flow chart of a control method for a single flexible solar wing spacecraft provided in an embodiment of the present disclosure.

[0037] Figure 2 A schematic diagram of a rectangular plate and a flexible beam model with one degree of freedom provided in an embodiment of the present disclosure.

[0038] Figure 3 A schematic diagram of the position of a piezoelectric driver provided in an embodiment of the present disclosure.

[0039] Figure 4 A flowchart of another control method for a single flexible solar wing spacecraft provided in an embodiment of the present disclosure.

[0040] Figure 5 A schematic structural diagram of a control device for a single flexible solar wing spacecraft provided in an embodiment of the present disclosure.

[0041] Figure 6 A schematic diagram of the structure of an electronic device provided in an embodiment of the present disclosure.

[0042] The above drawings show clear embodiments of the present disclosure, which will be described in more detail below. These drawings and text descriptions are not intended to limit the scope of the present disclosure in any way, but to illustrate the concepts of the present disclosure to those skilled in the art by referring to specific embodiments. DETAILED DESCRIPTION

[0043] Exemplary embodiments will be described in detail herein, examples of which are shown in the accompanying drawings. When the following description refers to the drawings, the same numbers in different drawings represent the same or similar elements unless otherwise indicated. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with the present disclosure. Instead, they are merely examples of devices and methods consistent with some aspects of the present disclosure as detailed in the appended claims.

[0044] In related technologies, the dynamic models of spacecraft are mostly based on the rigid body assumption, which fails to fully consider the dynamic characteristics of flexible attachments. This simplified method has obvious shortcomings when facing spacecraft with flexible solar panels, especially in application scenarios that require high-precision attitude adjustment and vibration control. In addition, traditional control methods often rely on empirical parameter adjustment and lack the ability to accurately predict and adaptively adjust the dynamic behavior of flexible attachments.

[0045] The deformation of the flexible solar wing has a significant impact on the attitude control of the spacecraft, and the existing models fail to accurately capture these deformation dynamics. Under the complex dynamic behavior caused by the flexible attachment, it is difficult for the existing control methods to achieve high-precision attitude control. Faced with the variability of the space environment, the existing control strategies lack sufficient adaptability and are difficult to cope with sudden external disturbances.

[0046] Based on this, the present disclosure first provides a control method for a single flexible solar wing spacecraft, referring to Figure 1 , wherein the control method of the above-mentioned single flexible solar wing spacecraft may include steps S110 to S150.

[0047] In step S110, a spacecraft model is established according to the geometric parameters of the spacecraft.

[0048] In an example implementation of the present disclosure, design data such as the size, shape, and mass distribution of the solar wing and the spacecraft body can be first collected, and then a three-dimensional geometric model of the spacecraft can be created in computer-aided design (CAD) software. Further, finite element analysis (FEA) is performed to determine the stress and strain of the structure under different loads, and modal analysis is performed to capture the vibration characteristics of the solar wing. At the same time, the mass, center of mass position, and inertia tensor of the spacecraft are calculated, and these key parameters will directly affect the accuracy of the dynamic model. The physical properties of the material, such as the elastic modulus and Poisson's ratio, are integrated to ensure the physical authenticity of the model.

[0049] In addition, when building a spacecraft model, space environmental factors such as temperature changes and radiation effects can also be considered and incorporated into the spacecraft model. The accuracy and reliability of the model can be verified by comparing it with ground tests and flight data. Finally, the model is parameterized to facilitate rapid adaptation to design changes and multidisciplinary comprehensive analysis.

[0050] In step S120, the external force acting on the spacecraft is determined, and the dynamic model of the spacecraft is determined according to the external force;

[0051] In some example embodiments of the present disclosure, after obtaining the above-mentioned spacecraft model, the external forces acting on the spacecraft can be identified and quantified. These external forces may come from a variety of factors, including but not limited to solar wind, interference from the Earth's magnetic field, solar light pressure, collision risk of space debris, and torques generated by the spacecraft's own operations, such as attitude adjustment and orbital maneuvers. Through environmental models and physical laws, we can determine the impact of these external forces on the motion state of the spacecraft.

[0052] Specifically, a small deformation assumption is used to simplify the dynamic analysis of the flexible solar wing. This assumption allows us to regard the deformation of the flexible solar wing as a small change relative to its total size, thereby accurately capturing the impact of the flexible attachment on the spacecraft dynamics while maintaining computational efficiency.

[0053] Based on the spacecraft model and kinematic equations, the dynamic model of the spacecraft can be determined using the Hamiltonian principle, which describes the motion of a physical system through the Lagrangian (kinetic energy minus potential energy). In other words, the Hamiltonian principle can take into account the control input and external force torque to derive a dynamic model that describes the rotation of the spacecraft and the vibration of the flexible solar wing.

[0054] In step S130, a piezoelectric driver model corresponding to the piezoelectric driver in the spacecraft model is determined, and the dynamics model is updated based on the piezoelectric driver model.

[0055] In some example embodiments of the present disclosure, a spacecraft model includes a piezoelectric driver, which is arranged on the surface of the solar wing of the above-mentioned spacecraft. First, the physical characteristics of the piezoelectric driver can be analyzed in detail, including its size, material properties, piezoelectric coefficient, permittivity, and strain response under different voltage inputs. Then, a mathematical model of the piezoelectric driver can be established based on the principle of piezoelectric effect. The model describes the mechanical behavior of the driver under the action of an electric field, including the relationship between the torque it generates and the input voltage.

[0056] Next, the interaction mechanism between the piezoelectric actuator and the flexible solar wing can be analyzed. How the torque generated by the piezoelectric actuator is transmitted through the structure of the solar wing, affecting its deformation and vibration. The piezoelectric actuator model is integrated into the dynamic model of the spacecraft as a control input to update the above dynamic model.

[0057] In step S140, the updated dynamic model is discretized to obtain a discretized dynamic model.

[0058] In some examples, the updated dynamic model can be discretized. Specifically, it can be discretized by methods such as direct numerical integration and Galerkin method to facilitate control. Specifically, determine the appropriate time step, which is a key parameter in the discretization process. The time step should be small enough to ensure that the discrete model can accurately capture the dynamic behavior of the system while taking into account computational efficiency. Replace the differential terms in the dynamic model with difference terms. For example, use numerical integration methods such as backward Euler method or forward Euler method to convert continuous ordinary differential equations into discrete time series models. The boundary conditions and initial conditions of the dynamic model are also converted into discrete forms to ensure that the discrete model can correctly reflect the initial state and boundary behavior of the system at all time steps.

[0059] In step S150, a nonlinear control algorithm is designed according to the discretized dynamics model to control the spacecraft.

[0060] In some example implementations, the specific requirements for spacecraft control may be first clarified, which may include attitude stabilization, orbit adjustment, target tracking, etc., and the requirements for control accuracy and response time may be determined, which are not elaborated in this example implementation.

[0061] In some examples, a suitable nonlinear control strategy may be selected according to the characteristics of the above-mentioned discretized dynamic model. Specifically, the control strategy may include adaptive control, robust control, sliding mode control or neural network control.

[0062] Then, a nonlinear control algorithm is designed based on control theory, wherein the control theory may include Lyapunov stability theory, optimal control theory, etc., which are not described in detail in this example.

[0063] Through precise geometric modeling and external force and torque analysis, a comprehensive dynamic model is constructed, which can carefully capture the complex dynamic behavior of the flexible solar wing in the space environment. Furthermore, by integrating the piezoelectric actuator model and updating the dynamic model, this method optimizes the control input, making the attitude adjustment of the spacecraft more accurate and efficient. Discretization not only enhances the practicality of the model, but also provides a basis for the design of advanced nonlinear control algorithms, which can adaptively respond to the dynamic changes of the spacecraft and achieve fast and precise attitude control. In addition, this method significantly improves the robustness of the system, and can maintain the stability and control accuracy of the spacecraft even in the face of external environmental uncertainties and changes in internal parameters. Through the integration of these technologies, this method not only improves the energy efficiency of the spacecraft and extends its life in orbit, but also enhances the flexibility and adaptability of mission execution, thus bringing breakthrough technological progress to the field of spacecraft control.

[0064] In some examples, reference Figure 2 When building a spacecraft model, the spacecraft can include the spacecraft body and the solar wing. The spacecraft body can be modeled as a length of The solar panel, i.e. the solar wing, is modeled as a rectangular flat plate with a length of , width is The solar wing has a flexible beam with two piezoelectric actuators attached to the upper and lower surfaces.

[0065] In some examples, the deformation and vibration of the flexible beam along the axial direction are ignored, considering the small deformation assumption. The kinematic equations of the system are derived in the fixed coordinate system of the spacecraft body, whose origin is located at the center of mass of the spacecraft body. The axis direction points to the undeformed axis direction of the flexible beam. represents the reference inertial coordinate system, represents the body-fixed coordinate system. In the coordinate system, the particle In Liang Weiyuan The position vector on ,in The bending of the beam causes Deformation in direction. The satellite body is about the origin The rotation angle is ,in . The position and velocity of a point relative to the origin of the spacecraft are expressed by the kinematic equations, where the kinematic equations are:

[0066]

[0067]

[0068] in, is a function used to map the position and time on the flexible beam to the displacement in the y direction. This function describes the bending deformation of the flexible beam at different positions and times; the rotation of the satellite body about the origin O is determined by the angle Description: This angle changes with time, reflecting the change in the attitude of the spacecraft body relative to the fixed coordinate system. represents the time derivative of the rotation angle, represents the time derivative of the deflection, Representing coordinates The time derivative, Representing coordinates The derivative with respect to time.

[0069] It should be noted that a particle is an idealized model that represents a point with mass but occupies an infinitesimal volume in space. It is possible to focus on the local behavior of the flexible beam while ignoring its size and shape. In the analysis of the flexible beam, the flexible beam is divided into many tiny parts, namely microelements. Each microelement can be regarded as a small part of the flexible beam, and the particle P is a point located on these microelements dx. The spacecraft body fixed coordinate system is a coordinate system with the center of mass of the spacecraft body as the origin, and the x-axis points to the axis direction of the flexible beam when it is not deformed. This coordinate system is used to describe the position and motion of the particle P.

[0070] By applying the calculation formula of the particle velocity given by the kinematic equation, the spacecraft dynamics model can be further established. The dynamics of the spacecraft includes the elastic bending of the flexible beam and the rotation of the planar rigid spacecraft, which can be described as a coupled ordinary differential-partial differential (ODE-PDE) equation with boundary condition constraints of fixed roots and free terminals. Specifically, the dynamic model of the system can be established by the Hamiltonian principle.

[0071] Lagrangian function of the spacecraft It consists of several components, including the rotational kinetic energy of the spacecraft itself , the kinetic energy of the beam due to the asymmetric strain , the elastic potential energy generated by the centrifugal force of the busbar rotation The Lagrangian function of the spacecraft is expressed as:

[0072]

[0073] According to Hamilton's principle, the movement distance that a system experiences between two time points is such that the integral of the Lagrangian function reaches a maximum or minimum value among all possible paths used.

[0074] definition is the non-conservative force generated by the piezoelectric actuator, i.e., the external force, where

[0075]

[0076] in, Indicates the initial time, Indicates the end time.

[0077] By introducing state variables and boundary conditions, a dynamic model using Lagrangian functions can be derived, where the dynamic model can be:

[0078]

[0079]

[0080] in, represents the horizontal axis coordinate of the particle in the fixed coordinate system of the body, represents the bending moment acting on the flexible beam, and t represents the time.

[0081] In some example embodiments of the present disclosure, reference is made to Figure 3 As shown, the piezoelectric driver is installed on the surface of the solar array of the above-mentioned spacecraft, and the solar array is set on the above-mentioned flexible beam. The piezoelectric driver model corresponding to the above-mentioned piezoelectric sensor can be determined. Specifically, when the potential difference is applied to the electrode of the piezoelectric material, the piezoelectric material will produce uniform strain. The piezoelectric driver patch can be bonded to the surface of the solar array or embedded in the solar array substructure.

[0082] In deriving the piezoelectric actuator model, it is assumed that the piezoelectric actuator and the beam fit perfectly and that the width of the flexible beam is is a constant. Therefore, the strain distribution of the flexible beam is linear along the cross section:

[0083]

[0084] in, represents the strain distribution of the flexible beam, is the slope of the strain distribution due to bending, represents the elongation of the beam due to the shift of the neutral axis, In the process of deriving the model, it can be assumed that the deflection caused by bending is a small amount and the vibration of the beam in the axial direction is ignored, that is, The influence of can be ignored. The resulting uniform piezoelectric actuator strain causes the bending moment of the beam, so the piezoelectric actuator model can be established based on this:

[0085]

[0086] in,

[0087]

[0088] in, and denote the elastic moduli of the beam and the piezoelectric actuator, respectively, and denote the thickness of the beam and the piezoelectric actuator, respectively, represents the cross-sectional modulus of inertia of the beam.

[0089] The bending moment of the flexible beam is proportional to the voltage on the piezoelectric actuator. The above piezoelectric actuator model is extended to a scenario with multiple piezoelectric actuators, such as Figure 3 As shown, the first piezoelectric driver 31 is attached to the upper surface of the flexible beam, and the second piezoelectric driver 32 is attached to the lower surface of the flexible beam. Indicates that the The voltage across the piezoelectric actuator, represents the unit step amplitude function. Defined as The length of the piezoelectric actuator, Figure 3 middle Used to define The length of the first piezoelectric actuator 31 is equal to 1, The bending moment of the beam due to the piezoelectric actuator is , that is, the piezoelectric actuator model is:

[0090]

[0091] In some example implementations, after the piezoelectric driver model is obtained, the external force may be updated using the piezoelectric driver model. Specifically, the moment acting on the flexible beam may be updated to obtain an updated dynamic model.

[0092] After obtaining the above kinetic model, the above kinetic model can be discretized, wherein the kinetic model can be expressed as an ordinary differential-partial differential equation. Specifically, the Galerkin method can be used to discretize the ODE-PDE equation for numerical simulation.

[0093] The deflection equation of the flexible beam established using the Galerkin method is:

[0094]

[0095] in and are the Galerkin function and amplitude, respectively, both of which are continuous differentiable functions. Since the frequency of the target attitude maneuvering trajectory is much lower than the first-order natural frequency of the flexible beam, the first four-order Galerkin functions are used to describe the vibration of the beam and the desired attitude trajectory, that is, .

[0096]

[0097] in, represents the order of modal cutoff, Table Length of the flexible beam.

[0098] The above dynamic model is replaced by the Galerkin function in the deflection equation to obtain a discretized dynamic model, which can be:

[0099]

[0100]

[0101]

[0102]

[0103] Among them, the matrix , , , To represent the mass matrix and matrix The cross-coupling terms in represents the second-order derivative of the bending moment with respect to time, represents the Poisson’s ratio of the flexible beam, represents the mass per unit length of the beam, represents the stiffness of the flexible beam, represents the modal amplitude, represents the inverse of the modal amplitude with respect to time, Represents the moment of inertia of the spacecraft body.

[0104] After obtaining the above discretized dynamic model, a nonlinear algorithm may be designed according to the above discretized dynamic model. Specifically, a nonlinear control algorithm may be designed based on the discretized dynamic model to determine the input voltage of the piezoelectric driver.

[0105] In some examples, the control target can be determined first, and then the input voltage of the piezoelectric ceramic of the piezoelectric actuator can be determined using nonlinear control. The control target can be to ensure that the spacecraft body rotates at a certain angle. Tracking the desired pose trajectory In order to track the desired rotation trajectory , refer to the angular velocity signal, and calculate by superimposing the rotation angular velocity and the angle error, as follows:

[0106]

[0107]

[0108] in, Indicates the posture trajectory The time derivative, represents the proportional coefficient in the control law, represents the time derivative of the reference rotation angle, represents the second-order derivative of the reference rotation angle with respect to time, It indicates that it is second-order differentiable within the range of values.

[0109] Reference deflection This can be done by using the Galerkin function estimate, Indicates the reference amplitude corresponding to each mode. The formula that needs to be satisfied is the dynamic model before discretization, that is:

[0110]

[0111] Total control torque generated by the bending of the piezoelectric actuator It can be expressed as:

[0112]

[0113] The voltage signal is used as the input signal of the piezoelectric actuator and is calculated by the Galerkin form of the control signal. The voltage of the two piezoelectric actuators calculated using the least squares method for:

[0114]

[0115] in, Represent the modal matrix:

[0116]

[0117] in, denote the time derivatives of the first to fourth order modes, respectively. represents the abscissa of the initial position of the first piezoelectric actuator, The horizontal coordinate representing the end position of the first piezoelectric actuator, represents the abscissa of the initial position of the second piezoelectric actuator, The horizontal coordinate representing the end position of the second piezoelectric actuator.

[0118] Refer to the following Figure 4 The control method of the above-mentioned single flexible solar wing spacecraft is described in detail. The control method of the single flexible solar wing spacecraft may include steps S410 to S470.

[0119] In step S410, a spacecraft model is established according to the geometric parameters of the spacecraft.

[0120] In step S420, the kinematic equations of the spacecraft are determined in the spacecraft body fixed coordinate system according to the spacecraft model based on the small deformation assumption.

[0121] In step S430, the dynamic model of the spacecraft is determined according to the external force and based on the Hamiltonian principle of the kinematic equation.

[0122] In step S440, a piezoelectric actuator model in the spacecraft model is determined based on the piezoelectric effect principle.

[0123] In step S450, the external force is updated according to the piezoelectric actuator model to update the dynamic model.

[0124] In step S460, the Galerkin method is used to obtain a discretized dynamic model for numerical simulation.

[0125] In step S470 , a nonlinear control algorithm is designed based on the discretized dynamic model to determine the input voltage of the piezoelectric actuator.

[0126] It should be noted that the specific details of step S410 to step S470 have been described in detail above, and therefore, they will not be repeated here.

[0127] Furthermore, the present disclosure also provides a control device for a single flexible solar wing spacecraft, referring to Figure 5As shown, the control device 500 of a single flexible solar wing spacecraft may include a building module 510, a determining module 520, an updating module 530, a processing module 540 and a control module 550. Among them:

[0128] The building module 510 may be used to build a spacecraft model according to geometric parameters of the spacecraft;

[0129] The determination module 520 may be used to determine the external forces acting on the spacecraft, and determine the dynamic model of the spacecraft according to the external forces;

[0130] The updating module 530 may be used to determine a piezoelectric actuator model corresponding to a piezoelectric actuator in the spacecraft model, and update the dynamics model based on the piezoelectric actuator model;

[0131] The processing module 540 may be used to discretize the updated dynamic model to obtain a discretized dynamic model;

[0132] The control module 550 may be used to design a nonlinear control algorithm based on the discretized dynamics model to control the spacecraft.

[0133] In some examples, the determination module 520 can also be used to determine the kinematic equation of the spacecraft according to the spacecraft model and the small deformation assumption; and determine the dynamic model of the spacecraft based on the kinematic equation using Hamilton's principle according to the external force.

[0134] In some examples, the determination module 520 may also be used to determine the kinematic equations of the spacecraft in the spacecraft body fixed coordinate system based on the small deformation assumption according to the spacecraft model.

[0135] In some examples, the updating module 530 may also be used to determine a piezoelectric driver model in the spacecraft model based on the piezoelectric effect principle; and update the spacecraft model according to the piezoelectric driver model.

[0136] In some examples, the update module 530 can also be used to update the external force according to the piezoelectric actuator model to update the dynamic model.

[0137] In some examples, the dynamic model includes ordinary differential system equations and partial differential system equations, the ordinary differential system equations are used to describe the uniaxial rigid rotation of the spacecraft, and the partial differential system equations are used to describe the planar continuous flexible dynamics of the solar wing in the spacecraft; the processing module 540 can also be used to adopt the Galerkin method to obtain a discretized dynamic model for numerical simulation.

[0138] In some examples, the control module 550 may also be used to design a nonlinear control algorithm based on the discretized dynamic model to determine an input voltage of the piezoelectric driver.

[0139] It should be understood that the above-mentioned device embodiments are only illustrative, and the device of the present disclosure can also be implemented in other ways. For example, the division of units / modules in the above-mentioned embodiments is only a logical function division, and there may be other division methods in actual implementation. For example, multiple units, modules or components can be combined, or can be integrated into another system, or some features can be ignored or not executed.

[0140] In addition, unless otherwise specified, each functional unit / module in each embodiment of the present disclosure may be integrated into one unit / module, or each unit / module may exist physically separately, or two or more units / modules may be integrated together. The above-mentioned integrated unit / module may be implemented in the form of hardware or in the form of a software program module.

[0141] If the integrated unit / module is implemented in the form of hardware, the hardware may be a digital circuit, an analog circuit, etc. The physical implementation of the hardware structure includes but is not limited to transistors, memristors, etc. Unless otherwise specified, the processor may be any appropriate hardware processor, such as a CPU, a GPU, an FPGA, a DSP, an ASIC, etc. Unless otherwise specified, the storage unit may be any appropriate magnetic storage medium or magneto-optical storage medium, such as a resistive random access memory (RRAM), a dynamic random access memory (DRAM), a static random access memory (SRAM), an enhanced dynamic random access memory (EDRAM), a high-bandwidth memory (HBM), a hybrid memory cube (HMC), etc.

[0142] If the integrated unit / module is implemented in the form of a software program module and sold or used as an independent product, it can be stored in a computer-readable memory. Based on this understanding, the technical solution of the present disclosure, or the part that contributes to the prior art, or all or part of the technical solution can be embodied in the form of a software product, which is stored in a memory and includes several instructions for a computer device (which can be a personal computer, server or network device, etc.) to perform all or part of the steps of the various embodiments of the present disclosure. The aforementioned memory includes: U disk, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), mobile hard disk, disk or optical disk, etc. Various media that can store program codes.

[0143] Please refer to Figure 6 , which shows a structural block diagram of an electronic device provided by an exemplary embodiment of the present disclosure. In some examples, the electronic device can be at least one of a smart phone, a smart watch, a desktop computer, a laptop, a virtual reality terminal, an augmented reality terminal, a wireless terminal, and a laptop computer. The electronic device has a communication function and can access a wired network or a wireless network. The electronic device can generally refer to one of a plurality of terminals, and those skilled in the art can know that the number of the above terminals can be more or less. It can be understood that the electronic device undertakes the calculation and processing work of the technical solution of the present disclosure, and the embodiments of the present disclosure are not limited to this.

[0144] like Figure 6 As shown, the electronic device 600 may include: at least one processor 610 , a memory 620 , and a communication interface 630 .

[0145] The memory 620 is used to store programs. Specifically, the programs may include program codes, and the program codes include computer operation instructions.

[0146] The memory 620 may include a high-speed RAM memory, and may also include a non-volatile memory (non-volatile memory), such as at least one disk memory.

[0147] The processor 610 is used to execute the computer-executable instructions stored in the memory 620 to implement the control method of the single flexible solar wing spacecraft described in the aforementioned method embodiment. The processor 610 may be a central processing unit (CPU), or an application specific integrated circuit (ASIC), or one or more integrated circuits configured to implement the embodiments of the present disclosure.

[0148] The electronic device 600 may also include a communication interface 630, so that it can communicate and interact with external devices through the communication interface 630. In a specific implementation, if the communication interface 630, the memory 620 and the processor 610 are implemented independently, the communication interface 630, the memory 620 and the processor 610 can be connected to each other through a bus and complete the communication between each other. The bus can be an Industry Standard Architecture (ISA) bus, a Peripheral Component (PCI) bus or an Extended Industry Standard Architecture (EISA) bus, etc. The bus can be divided into an address bus, a data bus, a control bus, etc., but it does not mean that there is only one bus or one type of bus.

[0149] Optionally, in a specific implementation, if the communication interface 630, the memory 620 and the processor 610 are integrated on a chip, the communication interface 630, the memory 620 and the processor 610 can complete communication through an internal interface.

[0150] The present disclosure also provides a computer-readable storage medium, which may include: a U disk, a mobile hard disk, a read-only memory, a random access memory, a disk or an optical disk, and other media that can store program codes. Specifically, the computer-readable storage medium stores program instructions, and the program instructions are used for the control method of the single flexible solar wing spacecraft in the above-mentioned embodiment.

[0151] The embodiments of the present disclosure also provide a computer program product, which includes computer instructions, which are stored in a computer-readable storage medium; a processor of an electronic device reads the computer instructions from the computer-readable storage medium, and the processor executes the computer instructions, so that the electronic device executes to implement the control method of a single flexible solar wing spacecraft of the above-mentioned embodiments.

[0152] Those skilled in the art should be aware that in one or more of the above examples, the functions described in the embodiments of the present disclosure can be implemented using hardware, software, firmware, or any combination thereof. When implemented using software, these functions can be stored in a computer-readable medium or transmitted as one or more instructions or codes on a computer-readable medium. Computer-readable media include computer storage media and communication media, wherein communication media include any media that facilitates the transmission of computer programs from one place to another. Storage media can be any available media that can be accessed by general or special-purpose computers.

[0153] In the above embodiments, the description of each embodiment has its own emphasis. For the part not described in detail in a certain embodiment, please refer to the relevant description of other embodiments. The technical features of the above embodiments can be combined arbitrarily. In order to make the description concise, all possible combinations of the technical features in the above embodiments are not described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0154] Those skilled in the art will readily appreciate other embodiments of the present disclosure after considering the specification and practicing the inventions claimed herein. The present disclosure is intended to cover any variations, uses or adaptations of the present disclosure that follow the general principles of the present disclosure and include common knowledge or customary technical means in the art that are not claimed in the present disclosure.

[0155] It should be understood that the present disclosure is not limited to the exact structures that have been described above and shown in the drawings, and that various modifications and changes may be made without departing from the scope thereof. The scope of the present disclosure is limited only by the appended claims.

Claims

1. A control method for a single flexible solar wing spacecraft, characterized in that: include: Establishing a spacecraft model according to geometric parameters of the spacecraft; determining an external force acting on the spacecraft, and determining a dynamic model of the spacecraft based on the external force; Determining a piezoelectric actuator model corresponding to the piezoelectric actuator in the spacecraft model, and updating the dynamic model based on the piezoelectric actuator model; Discretizing the updated dynamic model to obtain a discretized dynamic model; designing a nonlinear control algorithm based on the discretized dynamic model to control the spacecraft; Wherein, the kinetic model is: in, , represents the rotational kinetic energy of the spacecraft body, represents the kinetic energy of the beam due to the asymmetric strain, Represents the elastic potential energy generated by the centrifugal force of the busbar rotation represents the horizontal axis coordinate of the particle in the fixed coordinate system of the body, represents the bending moment acting on the flexible beam, t represents the time, It represents the mapping of the position and time on the flexible beam to the displacement of the vertical axis coordinate in the fixed coordinate system of the body. represents the time derivative of the deflection, It represents the rotation angle of the satellite body about the origin of the body fixed coordinate system. express The time countdown; The piezoelectric actuator model is: in, in, and denote the elastic moduli of the beam and the piezoelectric actuator, respectively, and denote the thickness of the beam and the piezoelectric actuator, respectively, represents the cross-sectional inertia modulus of the beam, V is the applied voltage of the piezoelectric sensor; Using the pressure driver model Replace the kinetic model To update the dynamic model.

2. The method according to claim 1, characterized in that The determining of the external force acting on the spacecraft and determining the dynamic model of the spacecraft according to the external force includes: Determining the kinematic equations of the spacecraft based on the spacecraft model and the small deformation assumption; According to the external force, a dynamic model of the spacecraft is determined based on the kinematic equation using Hamilton's principle.

3. The method according to claim 2, characterized in that Determining the kinematic equation of the spacecraft according to the spacecraft model and the small deformation hypothesis includes: The kinematic equations of the spacecraft are determined in a spacecraft body fixed coordinate system according to the spacecraft model based on the small deformation assumption.

4. The method according to claim 1, characterized in that: The step of determining a piezoelectric driver model based on the dynamic model, and updating the dynamic model based on the piezoelectric driver model, comprises: Determine the mapping relationship between the output bending moment and the input voltage of the piezoelectric driver in the spacecraft model based on the piezoelectric effect principle; The dynamic model is updated according to the piezoelectric actuator model.

5. The method according to claim 4, characterized in that The updating of the dynamic model according to the piezoelectric actuator model comprises: According to the installation position of the piezoelectric actuator on the solar sail panel, the neutral axis position and the bending stiffness are recalculated to update the dynamic model.

6. The method according to claim 1, characterized in that The dynamic model includes ordinary differential system equations and partial differential system equations, wherein the ordinary differential system equations are used to describe the uniaxial rigid rotation of the spacecraft, and the partial differential system equations are used to describe the planar continuous flexible dynamics of the solar wing in the spacecraft; The step of discretizing the updated dynamic model to obtain a discretized dynamic model includes: The Galerkin method is used to obtain the discretized dynamic model for numerical simulation.

7. The method according to claim 1, characterized in that The designing of a nonlinear control algorithm according to the discretized dynamics model to control the spacecraft includes: A nonlinear control algorithm is designed based on the discretized dynamic model to determine the input voltage of the piezoelectric actuator.

8. A control device for a single flexible solar wing spacecraft, characterized in that: include: A building module, used for building a spacecraft model according to the geometric parameters of the spacecraft; a determination module, configured to determine an external force acting on the spacecraft, and determine a dynamic model of the spacecraft according to the external force; An updating module, configured to determine a piezoelectric actuator model corresponding to the piezoelectric actuator in the spacecraft model, and update the dynamics model based on the piezoelectric actuator model; A processing module, used for discretizing the updated dynamic model to obtain a discretized dynamic model; A control module, used for designing a nonlinear control algorithm according to a discretized dynamics model to control the spacecraft; Wherein, the kinetic model is: in, , represents the rotational kinetic energy of the spacecraft body, represents the kinetic energy of the beam due to the asymmetric strain, Represents the elastic potential energy generated by the centrifugal force of the busbar rotation represents the horizontal axis coordinate of the particle in the fixed coordinate system of the body, represents the bending moment acting on the flexible beam, t represents the time, It represents the mapping of the position and time on the flexible beam to the displacement of the vertical axis coordinate in the fixed coordinate system of the body. represents the time derivative of the deflection, It represents the rotation angle of the satellite body about the origin of the body fixed coordinate system. express The time countdown; The piezoelectric actuator model is: in, in, and denote the elastic moduli of the beam and the piezoelectric actuator, respectively, and denote the thickness of the beam and the piezoelectric actuator, respectively, represents the cross-sectional inertia modulus of the beam, V is the applied voltage of the piezoelectric sensor; Using the pressure driver model Replace the kinetic model To update the dynamic model.

9. An electronic device, characterized in that: The electronic device comprises: a processor and a memory; the processor is used to execute instructions stored in the memory to implement the control method of the single flexible solar wing spacecraft as described in any one of claims 1 to 7.

10. A computer storage medium, characterized in that: The storage medium stores at least one instruction, and the at least one instruction is used to be executed by a processor to implement the control method of a single flexible solar wing spacecraft as described in any one of claims 1 to 7.

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