Attitude tracking control method for deep space exploration mission of electric sail based on voltage regulation

Abstract

The application discloses a kind of electric sail deep space exploration task attitude tracking control methods based on voltage regulation, belong to spacecraft technical field.Method includes using Lagrange model to construct electric sail orbit motion model;Electric sail attitude dynamics model is constructed using Euler model;According to electric sail orbit motion model and electric sail attitude dynamics model, electric sail attitude coupling dynamic model is constructed;Based on electric sail attitude coupling dynamic model, sliding surface and control torque are obtained;Sliding surface and control torque are converted into executable voltage command, and electric sail is controlled according to executable voltage command.This method is based on the modeling of electric sail attitude coupling dynamics, designs a predetermined time sliding film controller to realize attitude tracking control, and uses rope voltage regulation to generate the required control torque, avoids frequent and substantial switching of rope voltage, and ensures the stability of the electric sail configuration itself.

Description

Technical Field

[0001] This invention relates to the field of spacecraft technology, specifically to a voltage-regulated electric sail attitude tracking control method, system, device, medium, and program for deep space exploration missions. Background Technology

[0002] In recent years, with the continuous advancement of space missions such as asteroid exploration and outer solar system exploration, deep space exploration faces increasingly severe challenges. One of the core challenges is enabling spacecraft to maintain precise attitude control for years or even decades while carrying sufficient propellant. However, due to the fixed payload capacity of launch rockets, carrying large amounts of propellant inevitably reduces the spacecraft's payload capacity, severely limiting the efficiency of deep space exploration missions. Furthermore, traditional chemical propulsion requires multiple gravity slingshot maneuvers, which not only prolongs the mission cycle but also increases the complexity of trajectory design, clearly failing to meet the requirements. To address these challenges, propellantless propulsion technologies such as solar sails and electric sails have emerged, providing new ideas and more possibilities for future deep space exploration missions.

[0003] Compared to solar sails, electric sails offer advantages such as slower thrust decay, higher thrust-to-weight ratio, and the ability to achieve attitude control simply by adjusting the cable voltage, eliminating the need for additional control mechanisms. Consequently, several attitude tracking control methods for electric sails based on cable voltage modulation have been proposed. References (M. Bassetto, G. Mengali, AA Quarta, “E-sail attitude control with tether voltage modulation”, Acta Astronautica. 166(2020) 350–357) and (G. Li, ZH Zhu, C. Du, “Flight dynamics and controlstrategy of electric solar wind sails”, Journal of Guidance, Control, and Dynamics. 43 (2020) 462–474) present two methods for attitude tracking control using cable voltage modulation, one based on a rigid body dynamics model and the other on a flexible dynamics model of the electric sail, respectively. However, both of these methods affect the original electric sail's trajectory, causing its actual trajectory to deviate from the preset path. Meanwhile, implementing these methods to achieve attitude tracking control requires frequent and significant switching of the rope voltage between 0 and 40kV, which not only increases the difficulty of engineering implementation but also affects the stability of the electric sail's own configuration. Summary of the Invention

[0004] To address the problems of existing electric sail attitude tracking control methods based on cable voltage regulation, which cause the actual trajectory to deviate from the preset route and require frequent and significant cable voltage switching, increasing engineering implementation difficulty and affecting the stability of the electric sail's own configuration, this invention provides a voltage-regulated electric sail attitude tracking control method for deep space exploration missions. Based on the dynamic modeling of the electric sail's attitude-orbit coupling, a predetermined-time sliding membrane controller is designed to achieve attitude tracking control. The required control torque is generated by cable voltage regulation, avoiding frequent and significant cable voltage switching and ensuring the stability of the electric sail's own configuration.

[0005] To achieve the above objectives, the present invention provides the following technical solution.

[0006] In a first aspect, the present invention provides a voltage-regulated electric sail attitude tracking control method for deep space exploration missions, comprising: A Lagrange model was used to construct an orbital motion model for the electric sail; an Euler model was used to construct an attitude dynamics model for the electric sail. Based on the electric sail orbital motion model and the electric sail attitude dynamics model, an electric sail attitude-orbit coupled dynamic model is constructed. The sliding surface and control torque are obtained based on the electric sail attitude-track coupled dynamic model; The sliding surface and control torque are converted into executable voltage commands, and the electric sail is controlled according to the executable voltage commands.

[0007] As a further improvement of the present invention, the method of constructing an electric sail orbital motion model using a Lagrange model and constructing an electric sail attitude dynamics model using an Euler model includes:

[0008]

[0009] in, For the selected generalized coordinates, It is the radius of the electric sail track. and Its latitude and longitude, It is the total kinetic energy of the electric sail. It is the total potential energy. It is the total mass of the electric sail. The thrust is generated by the voltage across the rope.

[0010] As a further improvement of the present invention, the method of constructing the electric sail attitude dynamics model using the Euler model includes:

[0011] in, Represents control torque. and These are the moment of inertia and spin angular velocity of the electric sail.

[0012] As a further improvement of the present invention, the step of constructing an electric sail attitude-track coupled dynamic model based on the electric sail orbital motion model and the electric sail attitude dynamic model includes:

[0013] in, The mass matrix represents the variables. , , This represents the coupling mass matrix between attitude variables and orbital variables. and The Coriolis force and centrifugal force terms represent the orbital and attitude variables, respectively. This represents the control matrix.

[0014] As a further improvement of the present invention, the step of obtaining the sliding surface and control torque based on the electric sail attitude-rail coupled dynamic model includes: The control torque is obtained based on the electric sail-rail coupled dynamic model:

[0015] Sliding surface is

[0016] in, Represents the gamma function, in The time function has convergence property, for any Therefore, the total convergence time can be determined by a predefined... and If the decision is made, the system stability and convergence within the predetermined time are proven.

[0017] As a further improvement of the present invention, the step of converting the sliding surface and control torque into executable voltage commands, and controlling the electric sail according to the executable voltage commands, includes: The sliding surface and control torque are calculated in real time using numerical calculations to obtain executable voltage commands. The electric sail is controlled according to executable voltage commands.

[0018] Secondly, the present invention provides a voltage-regulated electric sail attitude tracking control system for deep space exploration missions, comprising: Basic model building module: used to build an electric sail orbital motion model using the Lagrange model; and to build an electric sail attitude dynamics model using the Eulerian model; Attitude-track coupled dynamic model module: used to construct the electric sail attitude-track coupled dynamic model based on the electric sail orbital motion model and the electric sail attitude dynamic model; The control torque acquisition module is used to acquire the sliding surface and control torque based on the electric sail attitude-rail coupled dynamic model. Command execution module: used to convert the sliding surface and control torque into executable voltage commands, and control the electric sail according to the executable voltage commands.

[0019] Thirdly, the present invention provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the voltage-regulated electric sail deep space exploration mission attitude tracking control method.

[0020] Fourthly, the present invention provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the voltage-regulated electric sail deep space exploration mission attitude tracking control method.

[0021] Fifthly, the present invention provides a computer program product, including computer instructions that, when executed by a processor, implement the steps of the voltage-regulated electric sail deep space exploration mission attitude tracking control method as described above.

[0022] Compared with the prior art, the present invention has the following beneficial effects: This invention constructs an electric sail orbital motion model using a Lagrange model, an electric sail attitude dynamics model using an Eulerian model, and an electric sail attitude-orbit coupled dynamic model, accurately describing the electric sail's motion state in the deep space environment. Based on the sliding surface and control torque obtained from this model, the electric sail can be guided more precisely along a preset route, greatly improving the accuracy of attitude tracking control and providing a solid guarantee for the successful implementation of deep space exploration missions. Secondly, this invention converts the sliding surface and control torque into executable voltage commands, controlling the electric sail according to these commands, avoiding frequent and large-scale switching of cable voltage. This optimized voltage regulation method simplifies the system operation process, reduces the performance requirements of hardware equipment, and thus significantly reduces the difficulty and cost of engineering implementation, making the electric sail attitude tracking control technology more practically valuable. Finally, this invention achieves attitude tracking control by designing a time-determined sliding surface controller and uses cable voltage regulation to generate the required control torque. While achieving accurate attitude tracking, it ensures that the electric sail experiences uniform force and structural stability during flight, effectively avoiding configuration changes caused by voltage issues, extending the electric sail's service life, and improving the sustainability of deep space exploration missions. Attached Figure Description

[0023] The accompanying drawings described herein are for illustrative purposes only and are not intended to limit the scope of the invention in any way. In the drawings: Figure 1 This is a flowchart illustrating the attitude tracking and control method for a voltage-regulated electric sail deep space exploration mission according to the present invention. Figure 2 This is a schematic diagram of voltage regulation generating control torque and a specific voltage distribution diagram in this invention, wherein (a) is a schematic diagram of control torque; and (b) is a schematic diagram of voltage distribution. Figure 3 This is a flowchart of the attitude control proposed in this invention; Figure 4 The following are the trajectory change diagrams and orbit radius tracking error diagrams for Example 1: (a) is the Earth-Mars transfer trajectory change diagram; (b) is the Earth-Mars transfer trajectory tracking error diagram. Figure 5 This shows the tracking changes of the attitude angle and its error in Example 1; Figure 6 The differential voltage required for Example 1 and Changes; Figure 7 This is a schematic diagram of the attitude tracking control system for a voltage-regulated electric sail deep space exploration mission according to the present invention. Figure 8 This is a schematic diagram of an electronic device in an embodiment of the present invention. Detailed Implementation

[0024] To enable those skilled in the art to better understand the technical solutions of this invention, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings. The described embodiments are merely some embodiments of this invention, and not all embodiments. Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of this invention.

[0025] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. The terminology used herein in the description of the invention is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. The term "and / or" as used herein includes any and all combinations of one or more of the associated listed items.

[0026] To address the problems in existing technologies where electric sail attitude tracking control methods based on cable voltage regulation cause the actual trajectory to deviate from the preset path, and require frequent and significant switching of cable voltage, increasing engineering implementation difficulty and affecting the stability of the electric sail's own configuration, this invention provides a voltage-regulated electric sail attitude tracking control method for deep space exploration missions, such as... Figure 1 As shown, it includes: S100: Construct an electric sail orbital motion model using the Lagrange model; construct an electric sail attitude dynamics model using the Euler model; S200: Construct an electric sail attitude-track coupled dynamic model based on the electric sail track motion model and the electric sail attitude dynamic model; S300: Obtaining sliding surface and control torque based on electric sail attitude-track coupled dynamic model; S400: Converts the sliding surface and control torque into executable voltage commands, and controls the electric sail according to the executable voltage commands.

[0027] Based on the attitude-track coupling dynamics modeling of the electric sail, this method designs a sliding film controller with a predetermined time to achieve attitude tracking control, and uses rope voltage regulation to generate the required control torque, avoiding frequent and large-scale switching of rope voltage, thus ensuring the structural stability of the electric sail itself.

[0028] The present invention will be further explained and described below with reference to the accompanying drawings.

[0029] This invention provides a voltage-regulated electric sail attitude tracking control method for deep space exploration missions, comprising the following: S1: Establishment of the coupled dynamic model of electric sail attitude and track Using the Lagrange equations as shown in formula (1), the equations of motion for the electric sail are established as follows: (1) (2) in, For the selected generalized coordinates, It is the radius of the electric sail track. It is the longitude angle; It is a latitude angle; It is the total kinetic energy of the electric sail. It is the total potential energy. It is the total mass of the electric sail. The thrust generated by the voltage across the rope. for exist The components on; for exist The components on; for exist The components on the coordinate system; their representation in the generalized coordinate system: (3) in, It refers to the number of ropes. , It is the length of the rope. It is the voltage value of the i-th rope. It is the amplitude of the solar wind speed. Solar wind electron density; The mass of solar wind protons. It is the vacuum permittivity. Represents attitude variables, One standard astronomical unit (AU); , , It is a three-axis Euler angle.

[0030] The attitude dynamics equations of the electric sail are established using Euler's equations as follows: (4) in, Represents control torque. To control the three-axis components of the torque; The moment of inertia of the electric sail; The three-axis components of the moment of inertia; It is the angular velocity of the electric sail's spin. Here are the three-axis components of the spin angular velocity; other variables are defined as follows: (5) (6) (7) Combining formulas (2) and (4), the dynamic equations of the electric sail attitude-track coupling are as follows: (8) in, The mass matrix representing the free variables, , , This represents the coupling quality matrix between the control variables and the free variables. The coupling quality matrix between free variables and control variables; The mass matrix of the control variables; For the Coriolis force of trajectory and attitude variables; The centrifugal force term is the variable relating orbit and attitude. Represents the control matrix; The second derivative of the free variable; The second derivative of the control variable.

[0031] In summary, this model is established within a reference coordinate system comprised of a heliocentric inertial coordinate system, an electric sail orbital coordinate system, a sail body coordinate system, and a body coordinate system. During the dynamic modeling process, the central spacecraft is treated as a point mass, and all cables are considered as rigid rods with uniformly distributed mass and no tension, lying in the same plane of rotation. By selecting appropriate generalized coordinates, the total kinetic energy, potential energy, and external forces of the system are derived, and the coupled dynamic equations of the electric sail attitude and orbit are established based on the Euler-Lagrange equations.

[0032] S2: Design of a sliding mode control strategy with predefined time Define the expected control variables and the sliding surface Represented as: (9) in, This represents the error between the expected control variable and the actual variable. For expected control variables; For actual variables; The first derivative of the error variable; It represents the time constant that guarantees the finite-time convergence of the system and the boundedness of the nonlinear terms on the sliding surface; Indicates making the sliding surface The scheduled time for convergence; It is a diagonal matrix that describes the system's error gain; Represents a symbolic function; This represents an exponential function.

[0033] To obtain the expression for the control torque, a reaching law is defined. for (10) in, Indicates a predefined approach time; It is a synovial surface; This indicates the switching lead time, used to prevent control rate singularities; , as well as Both are diagonal gain matrices, used to ensure the continuity of the two reaching laws; Let represent the diagonal Lupin gain matrix, where Indicates the distractor. This indicates the amplitude of the interference.

[0034] Combining equations (8) to (10), the control torque shown below can be obtained.

[0035] (11) In the formula, To Invert a matrix; To Invert a matrix; for; for Invert a matrix; See the following formula; in, (12) (13) In the formula, To control for the second derivative of the expected variable; for The identity matrix; The Lyapunov stability and convergence time are then proven as follows: Choose the Lyapunov function (hereinafter referred to as the Lyapunov function) as Differentiate the Li function and substitute it into The convergence law yields: (14) because , as well as The above equation can be expressed by the following differential inequality: (15) in, The term is a positive definite function, i.e., a Li's function. The function is negative definite, and the system is asymptotically stable. Furthermore, when... hour, , The system then becomes asymptotically stable over a wide range.

[0036] Formula (15) can be expressed by the following differential inequality: (16) in, Integrating both sides of the inequality, we obtain the approach time. The representation of is (17) Even when We can obtain the time-approaching limit form: (18) Similarly, for The partial reaching law, due to the continuity of its gain setting, defines the Liskov function. Under the condition that, the Lyapunov function is The fact that the ends are also continuous indicates that the approach time of the second segment of the reaching law is also... .

[0037] Make the sliding surface ,get: (19) Define the Li function Following the above procedure, by differentiating and simplifying, we obtain a differential inequality, which, when integrated, gives the convergence time of the sliding surface as: (20) in, Represents the gamma function, in The time function has convergence property, for any Equation (20) has an upper bound. Therefore, the total convergence time can be determined by a predefined... and If the decision is made, the system stability and convergence within the predetermined time are proven.

[0038] S3: Proposal of Rope Voltage Regulation Method This invention proposes a method for regulating rope voltage, such as... Figure 2 As shown. To prevent excessive differential voltage between adjacent main mooring lines, which could compromise the configuration stability of the electric sail, it is assumed that the axisymmetric electric sail is split into two independent sub-electric sails, as follows: Figure 2 As shown in (b).

[0039] The two sub-sails are differential voltages. Type I electric sail and The number of ropes for the Type II electric sail and the Type II electric sail are respectively... .

[0040] Based on the obtained voltage distribution, the Coulomb force is expressed as follows: (twenty one) in, This represents the Coulomb force generated by the reference voltage; This represents the Coulomb force generated by the differential voltage. It is worth noting that since the signs of the differential voltages on the positive and negative half-axis are opposite, summing the Coulomb forces yields... Therefore, the resultant force is the same as when no differential voltage is applied, meaning that this voltage modulation strategy will not affect the orbital motion.

[0041] Based on the voltage distribution pattern and torque formula described above, the resulting torque can be expressed as: (twenty two) (twenty three) In the formula, The voltage generated by the first sub-sail; The voltage generated by the second sub-sail; See formula (23); This refers to the speed of the solar wind (as explained earlier); The differential voltage generated for the first sub-sail; The differential voltage generated for the second sub-sail; in, Let be the initial position of the i-th rope. Substituting the control torque into formula (11), the differential voltage between the two sub-sails can be obtained using the least squares principle.

[0042] In summary, this method aims to achieve high-precision attitude tracking control of an electric sail by generating control torque through adjusting the cable voltage. This process consumes no control fuel and does not affect the sail's orbital motion or the stability of its configuration. This invention establishes a coupled dynamic model of the electric sail's attitude and orbit using the Lagrange and Euler equations by selecting appropriate generalized coordinates. To achieve real-time attitude tracking, a predefined time sliding mode control strategy is designed to ensure the electric sail can accurately control its attitude within a predetermined time. Based on this control strategy, an innovative cable voltage adjustment method is proposed to generate the required control torque. Compared with existing cable voltage adjustment methods at home and abroad, this invention has the advantage of not affecting the original orbital motion and the stability of the electric sail's configuration, providing a reliable guarantee for deep space exploration missions based on electric sails and possessing significant practical application value.

[0043] The present invention will be further explained and illustrated below with reference to specific embodiments.

[0044] Example 1 This invention uses the Earth-Mars transfer mission as a case study to verify the effectiveness of the proposed control strategy. The nominal Earth-Mars transfer trajectory and desired Euler angles are obtained using GPOPS-II software. The desired Euler angles are then... , as well as Substituting the difference between the actual Euler angles and the control input into the above control strategy yields a schematic diagram of the orbital radius tracking error and tracking change curves of the attitude angles and their errors, as shown below. Figure 4 and 4 As shown. Simultaneously, the output yields the differential voltage required to implement the control strategy, as shown. Figure 6 As shown in the figure. The results indicate that the maximum error between the tracked Euler angles and the desired Euler angles is at... The tracked trajectory differed from the desired trajectory by less than 7 km, and the maximum adjustment required during the rope voltage modulation process was only 500V. This further demonstrates that the voltage regulation method proposed in this invention can achieve high-precision attitude tracking control of the electric sail, has only a slight impact on the sail's configuration stability, and does not interfere with its orbital motion.

[0045] The purpose of this invention is to address the problem that existing rope voltage regulation methods affect the original orbital motion and structural stability of electric sails, and to propose a voltage-regulated attitude tracking control method for deep space exploration missions using electric sails. This method, with its advantages of accurate dynamic modeling and easy attitude control implementation, lays a solid foundation for electric sail deep space exploration missions.

[0046] In summary, this application is based on a reference coordinate system comprised of a heliocentric inertial coordinate system, an electric sail orbital coordinate system, a sail body coordinate system, and a body coordinate system. During the dynamic modeling process, the central spacecraft is considered a point mass, and all cables are treated as uniformly distributed, inextensible rigid rods within the same plane of rotation. By selecting appropriate generalized coordinates, the total kinetic energy, potential energy, and external forces of the system are derived, and the electric sail attitude-orbit coupling dynamic equations are established based on the Euler-Lagrange equations.

[0047] To achieve attitude tracking control of an attitude-track coupled electric sail, a sliding mode control strategy with a predefined time is proposed. The error between the desired Euler angle and the actual value is used as the control signal. A sliding mode controller with predefined time convergence is designed, and Lyapunov stability and convergence time are proven. Substituting this into the established attitude-track coupled dynamics model of the electric sail, the control torque required to complete attitude tracking is calculated.

[0048] Similar to existing rope voltage regulation methods, the rope voltage regulation method proposed in this invention also utilizes the asymmetry of rope voltage to generate torque for attitude tracking control. However, to address the problem of existing methods affecting the original orbital motion and structural stability of the electric sail through attitude tracking control, this invention first establishes the electric sail in the body coordinate system. The positive and negative sides of the shaft have different voltage distributions. Specifically, in... The positive half-axis voltage is the reference voltage. With differential voltage The sum of the values, with the negative half-axis representing the reference voltage. With differential voltage The difference is shown. Based on this, it can be proven that the resultant force generated by this voltage regulation distribution is consistent with that before regulation, that is, it will not affect the original orbital motion. Then, the relationship between the control torque and the voltage distribution is established, and the required differential voltage is obtained using the least squares principle. Substituting this into the established electric sail attitude-orbit coupled dynamics model, high-precision attitude tracking control can be achieved.

[0049] This invention proposes a voltage-regulated attitude tracking control method for deep space exploration missions using electric sails. This method utilizes the asymmetry in voltage distribution between the electric sail's tethers to generate control torque, satisfying the control torque required by the sliding membrane controller at a predetermined time. This avoids the use of control fuel, achieving propellant-free attitude tracking control and demonstrating good engineering practicality. Specifically, this invention can achieve high-precision attitude tracking control of the electric sail within a predetermined time using a relatively small control torque, avoiding the implementation difficulties caused by the need for large-range voltage fluctuations between 0 and 40 kV in the tethers. Secondly, the tether voltage regulation method proposed in this invention does not affect the original orbital motion of the electric sail, thereby reducing the additional orbital correction control required for deep space exploration missions. Finally, the tether voltage regulation method proposed in this invention has minimal impact on the stability of the electric sail's own configuration, thus increasing the success rate of deep space exploration missions.

[0050] The second objective of this invention is to propose a voltage-regulated electric sail attitude tracking control system for deep space exploration missions, such as... Figure 7 As shown, it includes: Basic Model Building Module 100: Used to build an electric sail orbital motion model using the Lagrange model; and to build an electric sail attitude dynamics model using the Eulerian model; Attitude-track coupled dynamic model module 200: used to construct the electric sail attitude-track coupled dynamic model based on the electric sail track motion model and the electric sail attitude dynamic model; Module 300 for acquiring control torque: used to acquire sliding surface and control torque based on electric sail attitude-rail coupled dynamic model; Command execution module 400: used to convert the sliding surface and control torque into executable voltage commands, and control the electric sail according to the executable voltage commands.

[0051] like Figure 8 As shown, a third objective of this invention is to provide an electronic device comprising a processor 501, a memory 502, and a display screen 503. The memory 502 and the display screen 503 are both connected to the processor 501, such as via a bus 504. Optionally, the electronic device may further include a transceiver 505. It should be noted that in practical applications, the transceiver 505 is not limited to one type, and the structure of this electronic device does not constitute a limitation on the embodiments of this application.

[0052] Processor 501 may be a CPU (Central Processing Unit), a general-purpose processor, a DSP (Digital Signal Processor), an ASIC (Application Specific Integrated Circuit), an FPGA (Field Programmable Gate Array), or other programmable logic devices, transistor logic devices, hardware components, or any combination thereof. It can implement or execute the various exemplary logic blocks, modules, and circuits described in conjunction with the disclosure of this application. Processor 501 may also be a combination that implements computational functions, such as including one or more microprocessor combinations, a combination of a DSP and a microprocessor, etc.

[0053] Bus 504 may include a pathway for transmitting information between the aforementioned components. Bus 504 may be a PCI (Peripheral Component Interconnect) bus or an EISA (Extended Industry Standard Architecture) bus, etc. Bus 504 can be divided into address bus, data bus, control bus, etc.

[0054] The memory 502 may be a ROM (Read Only Memory) or other type of static storage device capable of storing static information and instructions, RAM (Random Access Memory) or other type of dynamic storage device capable of storing information and instructions, or an EEPROM (Electrically Erasable Programmable Read Only Memory), CD-ROM (Compact Disc Read Only Memory) or other optical disc storage, optical disc storage (including compressed optical discs, laser discs, optical discs, digital universal optical discs, Blu-ray discs, etc.), magnetic disk storage media or other magnetic storage devices, or any other medium capable of carrying or storing desired program code in the form of instructions or data structures and accessible by a computer, but not limited thereto.

[0055] The memory 502 is used to store application code that executes the solution of this application, and its execution is controlled by the processor 501. The processor 501 is used to execute the application code stored in the memory 502 to implement the content shown in the foregoing method embodiments.

[0056] Figure 8 The electronic device shown is merely an example and should not impose any limitation on the functionality and scope of use of the embodiments of this application.

[0057] A fourth objective of this invention is to provide a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, performs the aforementioned functions. Figure 1 The illustrated method embodiments include various processes. For example, a memory may include instructions that can be executed by a processor of an electronic device to perform the described method.

[0058] A computer-readable storage medium can be a tangible device that holds and stores instructions used by an instruction execution device. A computer-readable storage medium can be, but is not limited to, an electrical storage device, a magnetic storage device, an optical storage device, an electromagnetic storage device, a semiconductor storage device, or any combination thereof. Specifically, a computer-readable storage medium can be a portable computer disk, a hard disk, a USB flash drive, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), staging random access memory (SRAM), portable compact disc read-only memory (CD-ROM), digital multifunction disc (DVD), memory stick, floppy disk, optical disk, magnetic disk, mechanical encoding device, or any combination thereof.

[0059] A fifth objective of this invention is to provide a computer program product comprising computer instructions that, when executed by a processor, implement the above-described... Figure 1 The various processes of the method embodiments shown can achieve the same technical effect, and will not be described again here to avoid repetition.

[0060] Many embodiments and applications beyond the examples provided will be apparent to those skilled in the art upon reading the foregoing description. Therefore, the scope of this teaching should not be determined by reference to the foregoing description, but rather by reference to the foregoing claims and the full scope of their equivalents. For purposes of completeness, all articles and references, including patent applications and publications, are incorporated herein by reference. The omission of any aspect of the subject matter disclosed herein in the foregoing claims is not intended as a waiver of that subject matter, nor should it be construed as an indication that the applicant has not considered that subject matter as part of the disclosed inventive subject matter.

[0061] The above content provides a further detailed description of the present invention. It should not be construed that the specific embodiments of the present invention are limited to this. For those skilled in the art, several simple deductions or substitutions can be made without departing from the concept of the present invention, and all such deductions or substitutions should be considered to fall within the scope of protection of the present invention as defined by the submitted claims.

Claims

1. A voltage-regulated electric sail attitude tracking control method for deep space exploration missions, characterized in that, include: A Lagrange model was used to construct an orbital motion model for the electric sail; an Euler model was used to construct an attitude dynamics model for the electric sail. Based on the electric sail orbital motion model and the electric sail attitude dynamics model, an electric sail attitude-orbit coupled dynamic model is constructed. The sliding surface and control torque are obtained based on the electric sail attitude-track coupled dynamic model; The sliding surface and control torque are converted into executable voltage commands, and the electric sail is controlled according to the executable voltage commands.

2. The voltage-regulated electric sail attitude tracking control method for deep space exploration missions according to claim 1, characterized in that, The method of constructing an electric sail orbital motion model using the Lagrange model and an electric sail attitude dynamics model using the Euler model includes: in, For the selected generalized coordinates, It is the radius of the electric sail track. and Its latitude and longitude, It is the total kinetic energy of the electric sail. It is the total potential energy. It is the total mass of the electric sail. The thrust is generated by the voltage across the rope.

3. The attitude tracking control method for a voltage-regulated electric sail deep space exploration mission according to claim 1, characterized in that, The process of constructing the electric sail attitude dynamics model using the Euler model includes: in, Represents control torque. and These are the moment of inertia and spin angular velocity of the electric sail.

4. The attitude tracking control method for a voltage-regulated electric sail deep space exploration mission according to claim 1, characterized in that, The process of constructing a coupled dynamic model of the electric sail's attitude and orbit based on the electric sail's orbital motion model and attitude dynamic model includes: in, The mass matrix represents the variables. , , This represents the coupling mass matrix between attitude variables and orbital variables. and The Coriolis force and centrifugal force terms represent the orbital and attitude variables, respectively. This represents the control matrix.

5. The attitude tracking control method for a voltage-regulated electric sail deep space exploration mission according to claim 1, characterized in that, The method for obtaining the sliding surface and control torque based on the electric sail attitude-rail coupled dynamic model includes: The control torque is obtained based on the electric sail-rail coupled dynamic model: Sliding surface is in, Represents the gamma function, in The time function has convergence property, for any Therefore, the total convergence time can be determined by a predefined... and If the decision is made, the system stability and convergence within the predetermined time are proven.

6. The attitude tracking control method for a voltage-regulated electric sail deep space exploration mission according to claim 1, characterized in that, The process of converting the sliding surface and control torque into executable voltage commands, and controlling the electric sail according to the executable voltage commands, includes: The sliding surface and control torque are calculated in real time using numerical calculations to obtain executable voltage commands. The electric sail is controlled according to executable voltage commands.

7. A voltage-regulated electric sail attitude tracking control system for deep space exploration missions, characterized in that, include: Basic model building module: used to build an electric sail orbital motion model using the Lagrange model; and to build an electric sail attitude dynamics model using the Eulerian model; Attitude-track coupled dynamic model module: used to construct the electric sail attitude-track coupled dynamic model based on the electric sail orbital motion model and the electric sail attitude dynamic model; The control torque acquisition module is used to acquire the sliding surface and control torque based on the electric sail attitude-rail coupled dynamic model. Command execution module: used to convert the sliding surface and control torque into executable voltage commands, and control the electric sail according to the executable voltage commands.

8. An electronic device, characterized in that, The method includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the steps of the voltage-regulated electric sail attitude tracking control method for deep space exploration missions according to any one of claims 1-6.

9. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, implements the steps of the voltage-regulated electric sail attitude tracking control method for deep space exploration missions as described in any one of claims 1-6.

10. A computer program product, characterized in that, It includes computer instructions that, when executed by a processor, implement the steps of the voltage-regulated electric sail attitude tracking control method for deep space exploration missions as described in any one of claims 1-6.

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