A method, system, device, medium, and product for determining the degree of instability of an electrodynamic rope system

Abstract

The application discloses a method, system, device, medium and product for judging the instability degree of an electric power rope system, and relates to the technical field of spacecraft attitude control. The method comprises the following steps: acquiring the orbit inclination of the deployment orbit of a main star in the electric power rope system; determining the instantaneous equilibrium point distribution area of the electric power rope system based on the orbit inclination; positioning the optimal balance area of the electric power rope system in the instantaneous equilibrium point distribution area of the electric power rope system; acquiring the attitude angle of the electric power rope system at the current moment, and determining the instability degree of the electric power rope system at the current moment based on the attitude angle of the electric power rope system at the current moment, the instantaneous equilibrium point distribution area and the optimal balance area. The application improves the efficiency and reliability of the instability evaluation of the electric power rope system.

Description

Technical Field

[0001] This application relates to the field of spacecraft attitude control technology, and in particular to a method, system, device, medium and product for determining the degree of instability of an electro-powered rope system. Background Technology

[0002] Electro-dynamic tethers are considered one of the primary applications of tethered systems in space transportation. An electro-dynamic tether consists of two satellites, the tether itself, and an electron collection and transmission device. The two satellites are located at either end of the tether and carry the electron transmission device. The electron collection device can be carried by the satellites or replaced by the conductive tether. Through the interaction between the electron collection and transmission device and space plasma, the tether generates an electric current, which interacts with the Earth's magnetic field during motion, producing a Lorentz force that can be used for electro-dynamic tether orbital maneuvers. Due to its advantages such as light weight, no propellant required, simple design, and wide applicable orbital altitude range, electro-dynamic tethers are the optimal orbital control system for most low Earth orbit missions, including space debris removal, deorbiting of end-of-life spacecraft, and payload delivery.

[0003] Previous research has indicated that electrodynamic tether systems are inherently unstable, a situation that space missions must avoid. To maintain stability, researchers have dedicated themselves to in-depth analysis of their dynamic characteristics. J. Pelaez has completed a series of landmark works in the analysis of electrodynamic tether dynamic characteristics. For electrodynamic tethers running on circular orbits, Pelaez used perturbation methods and Flokai theory to analyze the periodic motion starting from the system's zero point. He found that due to the continuous energy pumping in by the Lorentz force, the periodic motion is unstable, and eventually the in-plane motion evolves into rotation. This instability is universal, exhibiting this characteristic regardless of whether the tether is described using a rigid or flexible model. Simultaneously, Pelaez used a similar method to analyze electrodynamic tether (EDT) systems on elliptical orbits, pointing out that eccentricity is also a factor affecting system stability, and providing the boundary between strong and weak stability regions under parameters such as eccentricity and orbital inclination. Liu constructed a coupled multiphysics field and studied the dynamic characteristics of the electrodynamic tether in this field. Through numerical simulation, he demonstrated that the electro-hydroelectric rope system on a small-angle track can remain stable during the ascent process. Cui primarily studied the dynamic characteristics of the electro-hydroelectric rope deployment phase, designed indices to evaluate system stability and entanglement risk, and, through numerical simulation, provided the safe range of initial in-plane / out-of-plane angles during deployment. Li, by analyzing the necessary conditions for the existence of instantaneous equilibrium points, provided the range of out-of-plane angles and system parameters leading to rapid system instability. While existing research has made progress in understanding the instability mechanism of EDT systems, quantitative studies on the degree of instability remain insufficient.

[0004] However, in fields such as materials mechanics and fluid mechanics, scholars have conducted extensive research on the degree of system instability and further revealed the dynamic characteristics of the system. Xu et al. constructed a dynamic stability evaluation index for tunnels based on the loading / unloading response ratio (LURR) theory. This index is positively correlated with the degree of tunnel instability and can more accurately identify the potential instability region of the structure compared to traditional instability criteria. Abhiram et al., for finite amplitude plane inertial waves, proposed two instability evaluation criteria based on the nonlinear time scale and Rossby number in the inertial waves, respectively, achieving a keen capture of the transformation process from three-dimensional parametric subharmonic instability to two-dimensional shear-aligned instability. It is evident that the study of the degree of instability is crucial for understanding the dynamic characteristics of the system. However, due to the strong nonlinearity, periodic solution instability, and long-term operation requirements of EDT systems, existing methods are difficult to effectively assess their degree of instability: traditional methods based on single-valued matrices can only determine the stability of the periodic solution neighborhood, with limited sensitivity and inability to assess the degree of instability in real time, resulting in low evaluation efficiency; while methods based on IEP are still in the exploratory stage, and their clear relationship with the degree of system instability has not yet been established.

[0005] Therefore, it is necessary to provide a method for determining the degree of instability of an electro-powered rope system in order to solve the above problems. Summary of the Invention

[0006] The purpose of this application is to provide a method, system, device, medium, and product for determining the degree of instability of an electro-powered rope system, thereby improving the efficiency and reliability of instability assessment of the electro-powered rope system.

[0007] To achieve the above objectives, this application provides the following solution:

[0008] Firstly, this application provides a method for determining the degree of instability of an electro-powered rope system, the method comprising:

[0009] Obtain the orbital inclination of the primary satellite's deployment orbit in the electro-tether system;

[0010] Based on the track inclination angle, determine the distribution area of ​​the instantaneous equilibrium point of the electro-powered rope system;

[0011] Locate the optimal equilibrium zone of the electric power rope system within the instantaneous equilibrium point distribution area of ​​the electric power rope system;

[0012] The attitude angles of the electro-dynamic rope system at the current moment are obtained, and the degree of instability of the electro-dynamic rope system at the current moment is determined based on the attitude angles, the distribution area of ​​the instantaneous equilibrium point, and the optimal equilibrium zone. The attitude angles include in-plane angles and out-of-plane angles. The degree of instability is classified as low, medium, or high.

[0013] In one embodiment, determining the instantaneous equilibrium point distribution area of ​​the electro-dynamic rope system based on the track inclination angle specifically includes:

[0014] The interior angles and exterior angles of the face are traversed within the range of 0°-180° with a preset step size to obtain the list of interior angles and the list of exterior angles.

[0015] Based on the track inclination angle, in-plane angle list, and out-of-plane angle list, calculate multiple characteristic parameters of the electro-powered rope system;

[0016] Based on the aforementioned characteristic parameters, the instantaneous equilibrium point at the corresponding orbital inclination angle is determined;

[0017] Based on the instantaneous equilibrium points at the corresponding track inclination angle, the distribution area of ​​the instantaneous equilibrium points of the electro-dynamic rope system is obtained by plotting them as scattered points on the plane corresponding to the characteristic parameters and the exterior angle.

[0018] In one embodiment, the formula for calculating the characteristic parameter is:

[0019]

[0020] Where ε is a characteristic parameter of the electro-dynamic rope system; θ is an in-plane angle; is the exterior angle; i is the orbital inclination angle; A, B, and C are all intermediate parameters.

[0021] In one embodiment, the instantaneous equilibrium point at the corresponding orbital inclination angle is determined based on multiple characteristic parameters. Specifically, it includes:

[0022] When the track inclination angle satisfies sini≠0, and intermediate parameters A, B, and C are not all 0, q=1, and the instantaneous equilibrium point corresponding to the track inclination angle is... Wherein, θ1 is the in-plane angle corresponding to the first instantaneous equilibrium point; i1 is the exterior angle corresponding to the first instantaneous equilibrium point; i1 is the orbital inclination angle corresponding to the first instantaneous equilibrium point; ε1 is the characteristic parameter corresponding to the first instantaneous equilibrium point; v1 is the latitudinal argument corresponding to the first instantaneous equilibrium point.

[0023] θ1 is obtained through traversal. The calculation process of v1 includes: i1 is a preset value obtained through iteration, ε1 is calculated using the formula for characteristic parameters; the calculation process of v1 includes:

[0024] Using formula Based on the in-plane angle corresponding to the first instantaneous equilibrium point, calculate the value of the corresponding intermediate parameter; where ξ is the intermediate parameter, ξ∈(0,π);

[0025] Using formula and Based on the in-plane angle corresponding to the first instantaneous equilibrium point, the out-of-plane angle corresponding to the first instantaneous equilibrium point, the first characteristic parameter of the electro-dynamic rope system, and the corresponding intermediate parameter, calculate the latitudinal argument corresponding to the first instantaneous equilibrium point;

[0026] When the track inclination angle satisfies sini = 0, q = 2 and 3, the instantaneous equilibrium points under the corresponding track inclination angle include: the second instantaneous equilibrium point. and the third instantaneous equilibrium point Where θ2 is the in-plane angle corresponding to the second instantaneous equilibrium point; θ1 is the exterior angle corresponding to the second instantaneous equilibrium point; i2 is the orbital inclination angle corresponding to the second instantaneous equilibrium point; ε2 is the characteristic parameter corresponding to the second instantaneous equilibrium point; v2 is the latitudinal argument corresponding to the second instantaneous equilibrium point; θ3 is the interior angle corresponding to the third instantaneous equilibrium point. i3 is the exterior angle corresponding to the third instantaneous equilibrium point; i3 is the orbital inclination angle corresponding to the third instantaneous equilibrium point; ε3 is the characteristic parameter corresponding to the third instantaneous equilibrium point; v3 is the latitudinal argument corresponding to the third instantaneous equilibrium point.

[0027] Where v2 and v3 are arbitrary values, the calculation formulas for the in-plane angle, out-of-plane angle, orbital inclination angle, and characteristic parameters corresponding to the second instantaneous equilibrium point are as follows:

[0028]

[0029] i2 = 0;

[0030] ε2=0;

[0031] Where, μ m The dipole moment of the dipole model is denoted by I; I is the current in the conducting tether; m t The mass of the conductive tether; m s The mass of the sub-star; μ g It is the gravitational constant;

[0032] The formulas for calculating the interior angle, exterior angle, orbital inclination, and characteristic parameters corresponding to the third instantaneous equilibrium point are as follows:

[0033]

[0034] i3 = π;

[0035] ε3 = 0;

[0036] When intermediate parameters A, B, and C are all 0, q = 4, and the instantaneous equilibrium point at the corresponding track inclination angle is: the fourth instantaneous equilibrium point. Wherein, θ4 is the in-plane angle corresponding to the fourth instantaneous equilibrium point; i4 is the out-of-plane angle corresponding to the fourth instantaneous equilibrium point; i4 is the orbital inclination angle corresponding to the fourth instantaneous equilibrium point; ε4 is the characteristic parameter corresponding to the fourth instantaneous equilibrium point; v4 is the latitudinal argument corresponding to the fourth instantaneous equilibrium point.

[0037] Where ε4 and v4 are arbitrary values, the formulas for calculating the in-plane angle, out-of-plane angle, and orbital inclination angle corresponding to the fourth instantaneous equilibrium point are as follows:

[0038] θ4 = 0;

[0039]

[0040] In one embodiment, locating the optimal equilibrium zone of the electro-powered rope system within the instantaneous equilibrium point distribution area of ​​the system specifically includes:

[0041] When the track inclination angle is less than At that time, the optimal balance zone of the electric power rope system is located within the first preset zone of the instantaneous balance point distribution area;

[0042] When the track inclination angle is greater than At that time, the optimal balance zone of the electric power rope system is located in the second preset zone within the instantaneous balance point distribution area.

[0043] In one embodiment, the degree of instability of the electro-dynamic rope system at the current moment is determined based on the attitude angle, instantaneous equilibrium point distribution area, and optimal equilibrium zone of the electro-dynamic rope system at the current moment, specifically including:

[0044] Determine whether the attitude angle of the electro-powered rope system at the current moment is within the distribution area of ​​the instantaneous equilibrium point, and obtain the first determination result;

[0045] If the first judgment result is negative, then the instability level of the electric rope system at the current moment is determined to be high.

[0046] If the first judgment result is yes, then continue to judge whether the attitude angle of the electric power rope system at the current moment is within the optimal balance zone, and obtain the second judgment result;

[0047] If the second judgment result is negative, then the instability level of the electric rope system at the current moment is determined to be medium.

[0048] If the second judgment result is yes, then the instability level of the electric rope system at the current moment is determined to be low.

[0049] Secondly, this application provides a system for determining the degree of instability of an electro-powered rope system. This system is used to implement the method for determining the degree of instability of the electro-powered rope system. The system includes:

[0050] The data acquisition unit is used to acquire the orbital inclination of the primary satellite's deployment orbit in the electro-hydrodynamic tether system;

[0051] The instantaneous equilibrium point distribution area determination unit is used to determine the instantaneous equilibrium point distribution area of ​​the electro-powered rope system based on the track inclination angle.

[0052] The optimal equilibrium zone determination unit is used to locate the optimal equilibrium zone of the electric power rope system in the instantaneous equilibrium point distribution area of ​​the electric power rope system;

[0053] The instability degree determination unit is used to obtain the attitude angle of the electro-dynamic rope system at the current moment, and determine the instability degree of the electro-dynamic rope system at the current moment based on the attitude angle, instantaneous equilibrium point distribution area and optimal equilibrium area of ​​the electro-dynamic rope system at the current moment; the attitude angle includes: in-plane angle and out-of-plane angle; the instability degree is low level, medium level or high level.

[0054] Thirdly, this application provides a computer 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 method for determining the degree of instability of the electro-powered rope system described above.

[0055] Fourthly, this application provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the method for determining the degree of instability of the electro-powered rope system described above.

[0056] Fifthly, this application provides a computer program product, including a computer program that, when executed by a processor, implements the method for determining the degree of instability of the electro-powered rope system described above.

[0057] According to the specific embodiments provided in this application, this application has the following technical effects:

[0058] This application discloses a method, system, device, medium, and product for determining the degree of instability of an electro-dynamic rope system. It can generate the instantaneous equilibrium point distribution area and optimal equilibrium zone offline using the track inclination angle. In the online stage, the instability level can be output by a single table lookup, eliminating the need for numerical integration and reducing the time spent traversing the entire parameter domain from hours to seconds, improving the evaluation speed by ≥3 orders of magnitude. The offline stage uses a precise analytical-numerical hybrid model to generate the region, and the online stage directly compares whether the current attitude angle falls within the optimal equilibrium zone. This avoids the blind spot of traditional attitude dynamics simulation methods that can only determine "neighborhood stability / instability," improving the reliability of the evaluation. Attached Figure Description

[0059] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0060] Figure 1 A schematic flowchart illustrating a method for determining the degree of instability of an electro-powered rope system provided in an embodiment of this application;

[0061] Figure 2 A schematic diagram illustrating the running of a dumbbell model on a circular track according to an embodiment of this application;

[0062] Figure 3 Different orbital inclination angles provided in one embodiment of this application Image illustration;

[0063] Figure 4 The track inclination angle provided in one embodiment of this application is less than A schematic diagram of the optimal equilibrium region corresponding to the time;

[0064] Figure 5 The track inclination angle provided in one embodiment of this application is greater than A schematic diagram of the optimal equilibrium region corresponding to the time;

[0065] Figure 6 This is a schematic diagram of the structure of a computer device provided in an embodiment of this application. Detailed Implementation

[0066] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0067] To make the above-mentioned objectives, features and advantages of this application more apparent and understandable, this application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0068] In one exemplary embodiment, such as Figure 1 As shown, a method for determining the degree of instability of an electro-dynamic rope system is provided, including the following steps: Wherein:

[0069] Step S1: Obtain the orbital inclination of the primary star's deployment orbit in the electrodynamic tether system.

[0070] Specifically, the EDT system consists of a conductive tether and satellites at both ends of the tether. The system's motion in a circular orbit is as follows: Figure 2 As shown. To facilitate analytical solution, this application simplifies the EDT system into a dumbbell model. In this model, the conductive tether is simplified to a single strand with mass m. t A rigid conductive rod of length L (such as...) Figure 2 (The bold black line in the middle); the main star ( Figure 2 (black solid dots) and sub-stars ( Figure 2 The orange solid dot in the image is simplified to two point masses with masses m and m respectively. G and m s (m G >>m s ).

[0071] Assume the EDT system satisfies the following conditions:

[0072] 1. Earth's gravitational field can be approximated as being generated by a uniform spherical celestial body with a gravitational constant of μ. g .

[0073] 2. The Earth's magnetic field can be approximated as a non-tilted dipole model with a dipole moment of μ. m .

[0074] 3. Mass of the primary star m G It is large enough so that the main star always orbits in a circular orbit with radius a and inclination i.

[0075] 4. The current on the tether is uniform, with a value of I. Both satellites carry plasma contactors, therefore the current direction can be along... (Specified as positive direction) or negative direction.

[0076] To describe the motion of the EDT system, the following two coordinate systems are defined:

[0077] 1. Geocentric inertial frame of reference (EXYZ). For example... Figure 2As shown, point E is located at the Earth's center of mass, the EX axis points to the first star in Aries, the EZ axis is in the same direction as the Earth's rotation axis, and the EY axis can be determined according to the right-hand rule.

[0078] 2. Orbital coordinate system (Gxyz). For example... Figure 2 As shown, point G coincides with the primary star, and the Gx axis is parallel to... The velocity vectors of the Gy axis and G are in the same direction, and the Gz axis can be determined according to the right-hand rule.

[0079] The attitude motion of the simplified model that satisfies the above conditions can be described by the dynamic equations (1) and (2):

[0080]

[0081] Where, θ and θ' and θ″ are the interior and exterior angles of the tether relative to Gxyz, respectively, and are the state variables of the system; v is the latitudinal argument; θ′ and θ″ represent the first and second derivatives of θ with respect to v, respectively; Q cθ and For about θ and The generalized control force is the control input of the system; ω is the orbital angular velocity of the main star.

[0082] Step S2: Based on the track inclination angle, determine the instantaneous equilibrium point distribution area of ​​the electro-powered rope system.

[0083] Specifically, the instantaneous equilibrium point of the EDT system in this application needs to satisfy the following relationship: the equations formed by combining equations (3) and (4) are as follows:

[0084]

[0085] Where, θ, The three variables v are the variables to be solved for at the instantaneous equilibrium point, θ, Corresponding state variable x e v = ωt corresponds to the time variable t e Other parameters are constants.

[0086] As an optional implementation method, step S2 specifically includes:

[0087] Step S21, adjust the interior angle θ and exterior angle θ by a preset step size respectively. Traverse the range of 0°-180° to obtain a list of interior angles θ. j (j = 1, 2, ..., N1) and list of exterior angles Where j is the index of the interior angle in the list of interior angles; N1 is the total number of interior angles in the list of interior angles; N2 is the total number of exterior angles in the list of exterior angles; and k is the index of the exterior angle in the list of exterior angles.

[0088] Step S22: Based on the track inclination angle, in-plane angle list, and out-of-plane angle list, calculate multiple characteristic parameters of the electro-dynamic rope system.

[0089] As an optional implementation, in step S22, the formula for calculating the feature parameter is:

[0090]

[0091]

[0092] Where ε is a characteristic parameter of the electro-dynamic rope system; θ is an in-plane angle; is the exterior angle; i is the orbital inclination angle; A, B, and C are all intermediate parameters.

[0093] Step S23: Based on the multiple characteristic parameters, determine the instantaneous equilibrium point at the corresponding track inclination angle.

[0094] Specifically, the above equations (5)-(8) are used to iterate and calculate. The corresponding ε value is denoted as ε jk Build a table to store ε jk The values ​​are recorded in row j and column k of the table, resulting in a table showing the instantaneous equilibrium point distribution at a specified orbital inclination angle.

[0095] As an optional implementation, in step S23, the instantaneous equilibrium point at the corresponding track inclination angle is determined based on multiple characteristic parameters. Specifically, it includes:

[0096] Step S231: When the track inclination angle satisfies sini≠0, and intermediate parameters A, B, and C are not all 0, q=1, and the instantaneous equilibrium point corresponding to the track inclination angle is... Wherein, θ1 is the in-plane angle corresponding to the first instantaneous equilibrium point; i1 is the out-of-plane angle corresponding to the first instantaneous equilibrium point; i1 is the orbital inclination angle corresponding to the first instantaneous equilibrium point; ε1 is the characteristic parameter corresponding to the first instantaneous equilibrium point; v1 is the latitudinal argument corresponding to the first instantaneous equilibrium point.

[0097] θ1 is obtained through traversal. The calculation process of v1 includes: i1 is a preset value obtained through iteration, ε1 is calculated using the formula for characteristic parameters; the calculation process of v1 includes:

[0098] Using formula Based on the in-plane angle corresponding to the first instantaneous equilibrium point, calculate the value of the corresponding intermediate parameter; where ξ is the intermediate parameter, ξ∈(0,π).

[0099] Using formula and Based on the in-plane angle corresponding to the first instantaneous equilibrium point, the out-of-plane angle corresponding to the first instantaneous equilibrium point, the first characteristic parameter of the electro-dynamic rope system, and the corresponding intermediate parameter, the latitudinal argument corresponding to the first instantaneous equilibrium point is calculated.

[0100] Specifically, at this point, the solution for the instantaneous equilibrium point belongs to the general solution for this situation. Solving for the instantaneous equilibrium point means solving for θ, given initial values ​​for other parameters. v, such that the solution simultaneously satisfies equations (3) and (4). Since equations (3) and (4) are actually a system of indeterminate equations containing two equations and three variables, only the relationships satisfied between the variables can be given. Compared to directly using numerical methods to solve nonlinear equation systems, the method proposed in this application can give v and v at the instantaneous equilibrium point. Regarding θ, The analytical expression that i needs to satisfy enables high-precision and efficient calculation of the instantaneous equilibrium point under specific requirements, providing convenience for subsequent analysis.

[0101] Specifically, regarding the periodic characteristics of the instantaneous equilibrium point, this application directly limits the range of each variable in the instantaneous equilibrium point to:

[0102]

[0103] From a physical perspective, the range of values ​​for the orbital parameters and physical parameters at the instantaneous equilibrium point satisfies:

[0104]

[0105] To simplify the form of the equation, when sinini ≠ 0, let Simultaneously, with the help of the auxiliary angle formula, equations (3) and (4) can be rewritten as:

[0106]

[0107] in, ξ∈(0,π).

[0108] Since the above treatments are all identity transformations without introducing additional constraints, the solution will be solved and its accuracy verified according to equations (11) and (12) in the following sections. In addition, for the completeness of the solution, the case of sini = 0 will be analyzed below.

[0109] From equation (12), we can obtain:

[0110]

[0111] Based on the definition of trigonometric functions, an implicit constraint (14) is introduced here:

[0112]

[0113] According to the definitions of ξ and η, we can use the substitution elimination method to substitute equation (13) into equation (11). After rearranging with the characteristic parameter ε as the main variable, we can obtain ε as shown in equations (5)-(8).

[0114] If the solution to equation (5) is non-zero, then equations (10) to (12) are simultaneously satisfied. If the solution also satisfies the constraints of equations (9) and (14), then the solution is the ε corresponding to the instantaneous equilibrium point. Since equation (13) gives the instantaneous equilibrium point as needing to satisfy... Therefore, when the orbital inclination angle i is determined, this application can provide v and ε with respect to θ. The analytical form of i.

[0115] Furthermore, to ensure the completeness of the understanding, we will continue to analyze the special solutions in the two special cases of sini=0 and A=B=C=0, specifically in steps S232-S233.

[0116] Step S232, when the track inclination angle satisfies sini = 0, q = 2 and 3, the instantaneous equilibrium points under the corresponding track inclination angle include: the second instantaneous equilibrium point. and the third instantaneous equilibrium point Where θ2 is the in-plane angle corresponding to the second instantaneous equilibrium point; θ1 is the exterior angle corresponding to the second instantaneous equilibrium point; i2 is the orbital inclination angle corresponding to the second instantaneous equilibrium point; ε2 is the characteristic parameter corresponding to the second instantaneous equilibrium point; v2 is the latitudinal argument corresponding to the second instantaneous equilibrium point; θ3 is the interior angle corresponding to the third instantaneous equilibrium point. i3 is the out-of-plane angle corresponding to the third instantaneous equilibrium point; i3 is the orbital inclination angle corresponding to the third instantaneous equilibrium point; ε3 is the characteristic parameter corresponding to the third instantaneous equilibrium point; v3 is the latitudinal argument corresponding to the third instantaneous equilibrium point.

[0117] Where v2 and v3 are arbitrary values, the calculation formulas for the in-plane angle, out-of-plane angle, orbital inclination angle, and characteristic parameters corresponding to the second instantaneous equilibrium point are as follows:

[0118]

[0119] Where, μ m The dipole moment of the dipole model is denoted by I; I is the current in the conducting tether; m t The mass of the conductive tether; m s The mass of the sub-star; μ g is the gravitational constant.

[0120] The formulas for calculating the interior angle, exterior angle, orbital inclination, and characteristic parameters corresponding to the third instantaneous equilibrium point are as follows:

[0121]

[0122] Specifically, when sinini = 0, i = 0 or π, then equations (3) and (4) will become:

[0123]

[0124] It can be seen that if and only if When equations (17) and (18) have solutions, the solutions are shown in equation (15) or (16). Here, θ2 and θ3 represent the different θ values ​​corresponding to the two sets of solutions, and the solutions correspond to... The value has only zero solution, and when sini = 0, there is no restriction on v for the instantaneous equilibrium point. This result indicates that the electro-dynamic rope system on the equatorial orbit has only 2 static instantaneous equilibrium points.

[0125] Step S233: When intermediate parameters A, B, and C are all 0, q = 4, and the instantaneous equilibrium point under the corresponding track inclination angle is: the fourth instantaneous equilibrium point. Wherein, θ4 is the in-plane angle corresponding to the fourth instantaneous equilibrium point; i4 is the out-of-plane angle corresponding to the fourth instantaneous equilibrium point; i4 is the orbital inclination angle corresponding to the fourth instantaneous equilibrium point; ε4 is the characteristic parameter corresponding to the fourth instantaneous equilibrium point; v4 is the latitudinal argument corresponding to the fourth instantaneous equilibrium point.

[0126] Where ε4 and v4 are arbitrary values, the formulas for calculating the in-plane angle, out-of-plane angle, and orbital inclination angle corresponding to the fourth instantaneous equilibrium point are as follows:

[0127]

[0128] Specifically, when A = B = C = 0, it is easy to obtain from C = 0:

[0129]

[0130] Furthermore considering (3cos 2 θ+1) 2 >0, (3sin 2 θ+1) 2 >0, from which it can be deduced Substituting A = B = 0 further, the solution corresponding to A = B = C = 0 is shown in equation (19). This result indicates that there is a static instantaneous equilibrium point for the electrodynamic rope on the polar track.

[0131] Step S24: Based on the instantaneous equilibrium points under the corresponding track inclination angle, draw them in scattered form on the plane corresponding to the characteristic parameters and the exterior angle to obtain the distribution area of ​​the instantaneous equilibrium points of the electro-dynamic rope system.

[0132] Specifically, the data from the instantaneous equilibrium point distribution table at a specified track inclination angle are plotted as scatter plots on... On the plane, the instantaneous equilibrium point distribution area of ​​the required electrodynamic rope is obtained.

[0133] Pick The different orbital inclination angles within the orbit are analyzed, and θ is used in the analysis. Values The final representative results are as follows Figure 3 As shown. Figure 3 In the diagram, the horizontal axis represents the track inclination angle ε, and the vertical axis represents the exterior angle. Figure 3 Orange and blue correspond to the two equilibrium points in the case of double solutions in equation (5). When there is only one solution in equation (5), blue is used.

[0134] Depend on Figure 3 As can be seen from Figures (a) to (i), the evolution patterns corresponding to the instantaneous equilibrium point distribution areas fall into two categories. 1) The first category: when Or, when the tilt angle is smaller, the instantaneous equilibrium point distribution area is divided into upper and lower strip-shaped areas and a heart-shaped area in the middle; 2) Second case: when Or, at a larger tilt angle, the instantaneous equilibrium point distribution areas connect to each other, forming a unified whole, with a dense distribution of equilibrium points in the middle, and in... The distribution range is all within the image. On both sides of the image, two instantaneous equilibrium point distribution areas gradually form in a band-shaped region. As the orbital inclination angle increases, the band-shaped regions gradually narrow and converge.

[0135] when When the interval is within which the image gradually transitions from the first case to the second case; when At that time, the central heart-shaped region will connect with the two end strip-shaped regions; when At this point, the central heart-shaped region and the two end strip-shaped regions have connected and are beginning to transition to the next stage; when By then, the transition was basically complete, and subsequent images and... The corresponding images exhibit very similar properties.

[0136] It is noteworthy that, starting from where the central heart-shaped region and the two end strip-shaped regions meet, a spindle-shaped blank region appears on both sides of ε=0. This region gradually becomes more prominent as the orbital inclination angle increases. This range forms a range constraint, which is also the asymptote of the boundary line of the central equilibrium zone.

[0137] Since the smaller |ε| is, the better the stability of the system, the range constraint actually shows the distribution and changing trend of the instantaneous equilibrium point in the most stable region of the system, which is of great significance for the parameter design and control of the system.

[0138] Step S3: Locate the optimal equilibrium zone of the electric power rope system within the instantaneous equilibrium point distribution area of ​​the electric power rope system.

[0139] As an optional implementation, step S3 specifically includes:

[0140] Step S31, when the track inclination angle is less than At that time, the optimal balance zone of the electric power rope system is located in the first preset zone of the instantaneous balance point distribution area.

[0141] Specifically, when locating the optimal equilibrium zone based on the distribution areas of different instantaneous equilibrium points:

[0142] If the track inclination is small, before the transition zone (i.e., the track inclination is less than...), (At that time), the optimal equilibrium region is the two heart-shaped regions near the origin (i.e., the first preset region), such as Figure 4 As shown, Figure 4 The area enclosed in the green box is the optimal equilibrium zone at this point.

[0143] Step S32, when the track inclination angle is greater than At that time, the optimal balance zone of the electric power rope system is located in the second preset zone within the instantaneous balance point distribution area.

[0144] Specifically, when the inclination angle is large, a transition zone appears (i.e., the track inclination angle is greater than...). (At that time), the optimal equilibrium region corresponds to two conical regions near the origin (i.e., the second preset region), such as Figure 5 As shown, Figure 5 The area enclosed in the medium green square is the optimal equilibrium zone at this time.

[0145] Step S4: Obtain the attitude angle of the electro-dynamic rope system at the current moment, and determine the degree of instability of the electro-dynamic rope system at the current moment based on the attitude angle, instantaneous equilibrium point distribution area, and optimal equilibrium area of ​​the electro-dynamic rope system at the current moment; the attitude angle includes: in-plane angle and out-of-plane angle; the degree of instability is low, medium or high level.

[0146] As an optional implementation, step S4 specifically includes:

[0147] Step S41: Determine whether the attitude angle of the electric power rope system at the current moment is located within the instantaneous equilibrium point distribution area, and obtain the first determination result.

[0148] Step S42: If the first judgment result is negative, then the instability level of the electric power rope system at the current moment is determined to be high.

[0149] Step S43: If the first judgment result is yes, then continue to judge whether the attitude angle of the electric power rope system at the current moment is within the optimal balance zone, and obtain the second judgment result.

[0150] Step S44: If the second judgment result is negative, then the instability level of the electric power rope system at the current moment is determined to be medium.

[0151] Step S45: If the second judgment result is yes, then the instability level of the electric power rope system at the current moment is determined to be low.

[0152] Furthermore, the method further includes step S5, which specifically includes:

[0153] Based on the optimal equilibrium zone, recommended system parameters and states for the arrangement and deployment of the electro-dynamic rope system are given, mainly including the initial electro-dynamic rope attitude angles, namely the in-plane angle θ and the out-of-plane angle θ. The primary star's latitudinal argument 'v', and the system's characteristic parameter 'ε', where 'ε' is a combination of parameters such as system mass and tether current. The selection is based on the instantaneous equilibrium point within the optimal equilibrium region; generally, a point at the center of the optimal equilibrium region is better.

[0154] Within the instantaneous equilibrium point distribution area, the smaller the ε, the lower the instability of the electrodynamic rope system. However, since a smaller ε also weakens the system's normal function, ε must be selected reasonably based on actual needs; exterior angle. If possible, choose an angle close to 0. The interior angle θ can be selected based on actual needs, or a value closer to 0 can be chosen; when the interior angle θ is selected, the exterior angle... After obtaining the characteristic parameter ε of the system, the corresponding latitudinal argument v can be found from the instantaneous equilibrium point solution set.

[0155] Furthermore, the method further includes step S6, which specifically includes:

[0156] The control law of the system is adjusted in real time based on the optimal equilibrium region and the distribution area of ​​the instantaneous equilibrium point.

[0157] When the optimal balance zone is exceeded, the opposite outer corner needs to be strengthened. Control; when it exceeds the range of the instantaneous equilibrium point distribution area, it is necessary to further strengthen the control of the opposite outer corner. While maintaining control, the control of the opposite interior angle θ can be appropriately relaxed to improve the motion state of the system.

[0158] Beneficial effects:

[0159] 1) The evaluation speed improvement is ≥3 orders of magnitude. Traditional methods require integrating the attitude dynamics equations for each set of attitude angles to obtain the instability time; this application can generate the instantaneous equilibrium point distribution area and the optimal equilibrium area offline by relying only on the track inclination angle, and output the instability level by looking up the table once in the online stage, saving numerical integration and reducing the time taken to traverse the entire parameter domain from hours to seconds.

[0160] 2) Balancing high reliability and high resolution. The offline phase uses an accurate analytical-numerical hybrid model to generate the region, while the online phase directly compares whether the current attitude angle falls within the optimal equilibrium region. This avoids the blind spot of traditional attitude dynamics simulation, which can only determine "neighborhood stability / instability," resulting in no false positives or false negatives.

[0161] 3) Achieve "three-level quantification" of instability. For the first time, the stable state of the EDT system is quantitatively divided into three levels: low, medium, and high, providing an operable threshold interface for task design, control law switching, and fault early warning.

[0162] 4) Provides a unique input source for subsequent parameter recommendations. Since the optimal equilibrium zone has been pre-calculated, subsequent steps (initial rope angle, current, and latitude argument recommendations) can be directly selected within this zone, ensuring "stability upon deployment" and significantly reducing mission risks and fuel / energy costs.

[0163] Based on the same inventive concept, this application also provides an instability determination system for an electro-powered rope system, which is used to implement the aforementioned method for determining the instability degree of the electro-powered rope system. The solution provided by this system is similar to the solution described in the above method. Therefore, the specific limitations of one or more embodiments of the instability determination system for an electro-powered rope system provided below can be found in the limitations of the instability determination method for an electro-powered rope system described above, and will not be repeated here.

[0164] In one exemplary embodiment, a system for determining the degree of instability of an electro-powered rope system is provided, comprising:

[0165] The data acquisition unit is used to acquire the orbital inclination of the primary satellite's deployment orbit in the electro-hydrodynamic tether system.

[0166] The instantaneous equilibrium point distribution area determination unit is used to determine the instantaneous equilibrium point distribution area of ​​the electro-powered rope system based on the track inclination angle.

[0167] The optimal equilibrium zone determination unit is used to locate the optimal equilibrium zone of the electric power rope system within the distribution area of ​​the instantaneous equilibrium points of the electric power rope system.

[0168] The instability degree determination unit is used to obtain the attitude angle of the electro-dynamic rope system at the current moment, and determine the instability degree of the electro-dynamic rope system at the current moment based on the attitude angle, instantaneous equilibrium point distribution area and optimal equilibrium area of ​​the electro-dynamic rope system at the current moment; the attitude angle includes: in-plane angle and out-of-plane angle; the instability degree is low level, medium level or high level.

[0169] In one exemplary embodiment, a computer device is provided, 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 a method for determining the degree of instability of an electro-powered rope system.

[0170] In one exemplary embodiment, a computer-readable storage medium is provided having a computer program stored thereon that, when executed by a processor, implements a method for determining the degree of instability of an electro-powered rope system.

[0171] In one exemplary embodiment, a computer program product is provided, including a computer program that, when executed by a processor, implements a method for determining the degree of instability of an electro-powered rope system.

[0172] In one exemplary embodiment, a computer device is provided, which may be a server or a terminal, and its internal structure diagram may be as follows. Figure 6 As shown, the computer device includes a processor, memory, input / output (I / O) interfaces, and a communication interface. The processor, memory, and I / O interfaces are connected via a system bus, and the communication interface is also connected to the system bus via the I / O interfaces. The processor provides computational and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system, computer programs, and a database. The internal memory provides the environment for the operation of the operating system and computer programs stored in the non-volatile storage media. The I / O interfaces are used for exchanging information between the processor and external devices. The communication interface is used for communication with external terminals via a network connection. When executed by the processor, the computer program implements a method for determining the instability level of an electro-hydroelectric rope system.

[0173] Those skilled in the art will understand that Figure 6 The structure shown is merely a block diagram of a portion of the structure related to the present application and does not constitute a limitation on the computer device to which the present application is applied. Specific computer devices may include more or fewer components than those shown in the figure, or combine certain components, or have different component arrangements.

[0174] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, data stored, data displayed, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties, and the collection, use and processing of the relevant data must comply with relevant regulations.

[0175] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. Any references to memory, databases, or other media used in the embodiments provided in this application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM can take many forms, such as Static Random Access Memory (SRAM) or Dynamic Random Access Memory (DRAM).

[0176] The databases involved in the embodiments provided in this application may include at least one type of relational database and non-relational database. Non-relational databases may include, but are not limited to, blockchain-based distributed databases. The processors involved in the embodiments provided in this application may be general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic devices, quantum computing-based data processing logic devices, etc., and are not limited to these.

[0177] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are 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.

[0178] This document uses specific examples to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the methods, systems, and core ideas of this application. Furthermore, those skilled in the art will recognize that, based on the ideas of this application, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A method for determining the degree of instability of an electro-powered rope system, characterized in that, The methods for determining the degree of instability of the electro-powered rope system include: Obtain the orbital inclination of the primary satellite's deployment orbit in the electro-tether system; Based on the track inclination angle, determine the distribution area of ​​the instantaneous equilibrium point of the electro-powered rope system; Locate the optimal equilibrium zone of the electric power rope system within the instantaneous equilibrium point distribution area of ​​the electric power rope system; The attitude angles of the electro-dynamic rope system at the current moment are obtained, and based on the attitude angles, instantaneous equilibrium point distribution area, and optimal equilibrium area of ​​the electro-dynamic rope system at the current moment, the degree of instability of the electro-dynamic rope system at the current moment is determined; the attitude angles include: in-plane angles and out-of-plane angles; the degree of instability is low, medium, or high. Based on the track inclination angle, the instantaneous equilibrium point distribution area of ​​the electro-dynamic rope system is determined, specifically including: The interior angles and exterior angles of the face are traversed within the range of 0°-180° with a preset step size to obtain the list of interior angles and the list of exterior angles. Based on the track inclination angle, in-plane angle list, and out-of-plane angle list, calculate multiple characteristic parameters of the electro-powered rope system; Based on the aforementioned characteristic parameters, the instantaneous equilibrium point at the corresponding orbital inclination angle is determined; Based on the instantaneous equilibrium points under the corresponding track inclination angle, the distribution area of ​​the instantaneous equilibrium points of the electro-dynamic rope system is obtained by plotting them in the form of scattered points on the plane corresponding to the characteristic parameters and the exterior angle. The formula for calculating the feature parameters is as follows: ； ； ； ； in, These are characteristic parameters of the electro-powered rope system; It is an interior angle; It is an exterior angle; The inclination angle of the track; , , These are all intermediate parameters; Based on the aforementioned characteristic parameters, the instantaneous equilibrium point at the corresponding orbital inclination angle is determined. , Specifically, it includes: When the track inclination angle satisfies And intermediate parameters , , When not all are 0, The instantaneous equilibrium point corresponding to the orbital inclination angle is ;in, The in-plane angle corresponding to the first instantaneous equilibrium point; The exterior angle corresponding to the first instantaneous equilibrium point; The orbital inclination angle corresponding to the first instantaneous equilibrium point; These are the characteristic parameters corresponding to the first instantaneous equilibrium point; The latitude argument corresponding to the first instantaneous equilibrium point; in, Obtained through iteration Obtained through iteration As a preset value, It is calculated using the formula for characteristic parameters; The calculation process includes: Using formula Based on the in-plane angle corresponding to the first instantaneous equilibrium point, the values ​​of the corresponding intermediate parameters are calculated; where, For intermediate parameters, ; Using formula and Based on the in-plane angle corresponding to the first instantaneous equilibrium point, the out-of-plane angle corresponding to the first instantaneous equilibrium point, the first characteristic parameter of the electro-dynamic rope system, and the corresponding intermediate parameter, the latitudinal argument corresponding to the first instantaneous equilibrium point is calculated.

2. The method for determining the degree of instability of the electro-powered rope system according to claim 1, characterized in that, Based on the aforementioned characteristic parameters, the instantaneous equilibrium point at the corresponding orbital inclination angle is determined. , It also includes: When the track inclination angle satisfies hour, The instantaneous equilibrium points corresponding to the orbital inclination angle include: the second instantaneous equilibrium point. and the third instantaneous equilibrium point ;in, The in-plane angle corresponding to the second instantaneous equilibrium point; The exterior angle corresponding to the second instantaneous equilibrium point; This represents the orbital inclination angle corresponding to the second instantaneous equilibrium point; These are the characteristic parameters corresponding to the second instantaneous equilibrium point; The latitude argument corresponding to the second instantaneous equilibrium point; The in-plane angle corresponding to the third instantaneous equilibrium point; The exterior angle corresponding to the third instantaneous equilibrium point; This represents the orbital inclination angle corresponding to the third instantaneous equilibrium point; These are the characteristic parameters corresponding to the third instantaneous equilibrium point; The latitude argument corresponding to the third instantaneous equilibrium point; in, and For any value, the formulas for calculating the in-plane angle, out-of-plane angle, orbital inclination angle, and characteristic parameters corresponding to the second instantaneous equilibrium point are as follows: ； ； ； ； in, The dipole moment of the dipole model; The current in the conductive tether; The mass of the conductive tether; The mass of the sub-star; It is the gravitational constant; The formulas for calculating the interior angle, exterior angle, orbital inclination, and characteristic parameters corresponding to the third instantaneous equilibrium point are as follows: ； ； ； ； When intermediate parameters , , When all are 0, The instantaneous equilibrium point corresponding to the orbital inclination angle is: the fourth instantaneous equilibrium point. ;in, The in-plane angle corresponding to the fourth instantaneous equilibrium point; The exterior angle corresponding to the fourth instantaneous equilibrium point; This is the orbital inclination angle corresponding to the fourth instantaneous equilibrium point; These are the characteristic parameters corresponding to the fourth instantaneous equilibrium point; The latitude argument corresponding to the fourth instantaneous equilibrium point; in, and For any value, the formulas for calculating the in-plane angle, out-of-plane angle, and orbital inclination angle corresponding to the fourth instantaneous equilibrium point are as follows: ； ； 。 3. The method for determining the degree of instability of the electro-powered rope system according to claim 2, characterized in that, Locating the optimal equilibrium zone of the electro-electric rope system within the instantaneous equilibrium point distribution area specifically includes: When the track inclination angle is less than At that time, the optimal balance zone of the electric power rope system is located within the first preset zone of the instantaneous balance point distribution area; When the track inclination angle is greater than At that time, the optimal balance zone of the electric power rope system is located in the second preset zone within the instantaneous balance point distribution area.

4. The method for determining the degree of instability of the electro-powered rope system according to claim 3, characterized in that, Based on the current attitude angle, instantaneous equilibrium point distribution region, and optimal equilibrium region of the electro-dynamic rope system, the degree of instability of the electro-dynamic rope system at the current moment is determined, specifically including: Determine whether the attitude angle of the electro-powered rope system at the current moment is within the distribution area of ​​the instantaneous equilibrium point, and obtain the first determination result; If the first judgment result is negative, then the instability level of the electric rope system at the current moment is determined to be high. If the first judgment result is yes, then continue to judge whether the attitude angle of the electric power rope system at the current moment is within the optimal balance zone, and obtain the second judgment result; If the second judgment result is negative, then the instability level of the electric rope system at the current moment is determined to be medium. If the second judgment result is yes, then the instability level of the electric rope system at the current moment is determined to be low.

5. A system for determining the degree of instability of an electro-powered rope system, characterized in that, The instability determination system of the electro-powered rope system is used to implement the instability determination method of the electro-powered rope system according to any one of claims 1-4, and the instability determination system of the electro-powered rope system includes: The data acquisition unit is used to acquire the orbital inclination of the primary satellite's deployment orbit in the electro-hydrodynamic tether system; The instantaneous equilibrium point distribution area determination unit is used to determine the instantaneous equilibrium point distribution area of ​​the electro-powered rope system based on the track inclination angle. The optimal equilibrium zone determination unit is used to locate the optimal equilibrium zone of the electric power rope system in the instantaneous equilibrium point distribution area of ​​the electric power rope system; The instability degree determination unit is used to obtain the attitude angle of the electro-dynamic rope system at the current moment, and determine the instability degree of the electro-dynamic rope system at the current moment based on the attitude angle, instantaneous equilibrium point distribution area and optimal equilibrium area of ​​the electro-dynamic rope system at the current moment; the attitude angle includes: in-plane angle and out-of-plane angle; the instability degree is low level, medium level or high level.

6. A computer device, comprising: A memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that the processor executes the computer program to implement the method for determining the degree of instability of the electro-powered rope system according to any one of claims 1-4.

7. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the computer program implements a method for determining the degree of instability of the electro-powered rope system as described in any one of claims 1-4.

8. A computer program product, comprising a computer program, characterized in that, When executed by a processor, the computer program implements a method for determining the degree of instability of the electro-powered rope system as described in any one of claims 1-4.

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