A method for dynamic analysis and attitude control of an electric power multi-rope structure

Abstract

The application discloses a kind of dynamics analysis and attitude control methods of electric power multi-rope structure, belong to the dynamics and control field of spacecraft orbit and attitude.The application implementation method is: based on the operation law of vector array, six generalized coordinate dynamics equations of electric power multi-rope structure are derived by Lagrange equation;Through the dynamics analysis to electric power multi-rope structure, the dynamics model of electric power multi-rope structure is constructed, the coupling dynamics characteristics between tether and host star are characterized by the dynamics model of electric power multi-rope structure;Through the extended time-delay self-synchronization control strategy, the attitude of virtual pole is controlled based on the dynamics equation of virtual pole attitude angle and the dynamics equation of virtual pole attitude angle;The attitude of host star is controlled based on the dynamics equation of host star attitude angle, the dynamics equation of host star attitude angle, the dynamics equation of host star attitude angle γ, realize the purpose of simultaneously stabilizing virtual pole and host star attitude movement, reduce the complexity of control system.

Description

Technical Field

[0001] This invention relates to a dynamic analysis and attitude control method for an electrodynamic multi-rope structure, belonging to the field of dynamics and control of spacecraft orbit and attitude. Background Technology

[0002] In recent years, with the rapid development of mega-constellation programs worldwide, the number of space launches and the number of spacecraft in orbit have exploded, leading to a surge in space debris. This poses a threat to the safety of spacecraft in orbit and future space activities, making active debris removal essential. Among numerous active debris removal technologies, electro-powered ropes have attracted considerable attention due to their advantages of no fuel consumption, ease of implementation, and low cost.

[0003] Electro-dynamic tethers typically consist of three parts: the primary satellite, the secondary satellite, and a conductive tether, with the primary and secondary satellites connected by the conductive tether. Currently, electro-dynamic tethers are mainly single-tether structures. However, this single-tether structure not only has low redundancy and poor survivability, but also generates excessive current and voltage, damaging circuit structures and electronic components, thus leading to the failure of space debris removal missions. To address the problems and shortcomings of this type of electro-dynamic single-tether structure, the structural design of the electro-dynamic tether must be improved to increase system redundancy and survivability, thereby improving the success rate of space debris removal missions. Summary of the Invention

[0004] To address the issues of low redundancy, poor survival rate, and excessive current in a single tether of an electrodynamic single-tether structure, this invention aims to provide a dynamic analysis and attitude control method for an electrodynamic multi-tether structure. This method utilizes an electrodynamic multi-tether structure, connecting the primary and secondary satellites via multiple conductive tethers. While achieving the same deorbit efficiency as a single-tether structure, it also improves redundancy and survival rate, and reduces the maximum current in a single tether. By performing dynamic analysis and attitude control on the electrodynamic multi-tether structure, the method simultaneously stabilizes the attitude motion of the virtual rod and the primary satellite, avoiding the need for separate attitude control of the primary satellite and virtual rod, thus reducing the complexity of the control system.

[0005] The objective of this invention is achieved through the following technical solutions.

[0006] This invention discloses a dynamic analysis and attitude control method for an electrodynamic multi-rope structure, comprising the following steps:

[0007] Step 1: Accelerate the primary star's deorbiting using an electrodynamic multi-tether structure. Release the secondary star and conductive tethers when acceleration is required. The electrodynamic multi-tether structure consists of the primary star, the secondary star, and multiple conductive tethers. In this structure, the primary star is treated as a rigid body, the secondary star as a point mass, and the conductive tethers as massless elastic rods. The line connecting the primary star's center of mass and the secondary star is defined as a virtual rod. The three attitude angles of the primary star, the two attitude angles of the virtual rod, and the length of the virtual rod are selected as generalized coordinates.

[0008] Step 2: Define the inertial frame, Earth-following coordinate system, orbital frame, primary star coordinate system, and virtual rod coordinate system used to construct the dynamic model of the electrodynamic multi-rope structure; based on the vector matrix operation rules, derive the dynamic equations for the six generalized coordinates of the electrodynamic multi-rope structure through the Lagrange equations. The dynamic equations for each generalized coordinate are: the dynamic equation for the primary star attitude angle α, the dynamic equation for the primary star attitude angle β, the dynamic equation for the primary star attitude angle γ, the dynamic equation for the virtual rod attitude angle θ, and the dynamic equation for the virtual rod attitude angle γ. The dynamic equations regarding the virtual rod length l s,m The dynamic equations are derived. Based on the six generalized coordinate dynamic equations, a dynamic model of the electrodynamic multi-tether structure is constructed, and the coupling dynamic characteristics between the tether and the host star are characterized through the dynamic model of the electrodynamic multi-tether structure.

[0009] In the dynamic modeling of electrodynamic multi-rope structures, a coordinate system is defined. The following are represented, in order: inertial frame, Earth-following coordinate system, orbital frame, primary celestial frame, and virtual rod frame. The inertial frame... The origin O is located at the Earth's center of mass, the OX axis points to the vernal equinox, the OZ axis is aligned with the Earth's rotation axis, and the OY axis, along with the other two axes, forms a right-handed coordinate system; Earth-following coordinate system. The origin is O, the OZ′ axis is aligned with the OZ axis, and the OX′ axis and OY′ axis rotate around the OZ′ axis simultaneously with the Earth's rotational angular velocity; orbital coordinate system. The origin is located at the center of mass of the primary star. m o m x o The axis points from the Earth's center O to o m o m z o The axis is perpendicular to the orbital plane and aligns with the direction of the primary star's orbital angular momentum. m y o The axis, together with the other two axes, forms a right-handed coordinate system; the primary star's body coordinate system. The origin is located at the mass center of the primary star. m Its coordinate system's principal axes are aligned with the principal inertial axes of the primary star; the virtual rod's body coordinate system Origin and the center of mass of the primary star m Overlap, its o mx v The axis points from the sub-star to o. m o m y v The axis is always located within the orbital plane and perpendicular to o. m x v Axis, o m z o The axis forms a right-handed frame with the other two axes. We select three attitude angles α, β, and γ of the primary star, and two attitude angles θ and γ of the virtual rod. and the length l of the virtual rod s,m As a generalized coordinate:

[0010]

[0011] The attitude angle rotation sequence of the primary star is defined as "3-1-2", corresponding to attitude angles α, β, and γ respectively.

[0012] Based on the operational rules of vector arrays, the generalized coordinate dynamic equations of the system can be derived and simplified through the Lagrange equations. Among them, the dynamic equation concerning the attitude angle α of the primary star is:

[0013]

[0014] J x J y and J z These are the moments of inertia of the primary star about its three principal axes, Ω. o The orbital angular velocity, and Let be the components of the position vector from the mass center of the primary star to the connection point of the i-th tether with the primary star on the three coordinate axes of the primary star's body. and Let n represent the first and second derivatives of α with respect to time, respectively. t Let k = E, where E is the number of ropes. t A t / L i0 E is the elastic modulus of the rope. t Let A be the elastic modulus of the tether. t L is the cross-sectional area of ​​the tether. i0 U(ε) is the original length of the tethering rope. i ) is a step function, ε i Let be the elastic deformation of the i-th tether. and Let be the components of the total Lorentz force on the i-th tether along the three coordinate axes of the primary star's body. f i Take the partial derivative of f with respect to α. i for:

[0015]

[0016] The dynamic equation for the primary star's attitude angle β is:

[0017]

[0018] The dynamic equation for the primary star's attitude angle γ is:

[0019]

[0020] The dynamic equation for the virtual rod attitude angle θ is:

[0021]

[0022] Where I m For the current of a single tether, μ m Let i be the magnetic moment constant of the geomagnetic dipole. o Indicates the orbital inclination angle, m s Let v = Ω, where Ω is the mass of the sub-star. o t is the true perihelion angle of the principal star's orbit, t is time, and r is... m The distance between the center of mass of the principal star and the center of the Earth. This is the generalized control torque acting on the generalized coordinate θ.

[0023] Regarding the virtual rod attitude angle The dynamic equation is:

[0024]

[0025] in For acting on generalized coordinates The generalized control torque.

[0026] Regarding the length l of the virtual rod s,m The dynamic equation is:

[0027]

[0028] Step 3: By using the Extended Time-Delay Autosynchronization (ETDA) control strategy, the generalized coordinates θ of the virtual link are... Control is performed based on the generalized coordinates θ of the virtual rod. Based on the dynamic equations of the virtual rod attitude angle θ constructed in step two, and the virtual rod attitude angle... The attitude of the virtual rod is controlled by the dynamic equations. Based on the generalized coordinates α, β, and γ of the primary star, the attitude of the primary star is controlled by the dynamic equations of the primary star attitude angle α, β, and γ constructed in step two. This simultaneously stabilizes the attitude motion of the virtual rod and the primary star, avoiding the need to control the attitude of the primary star and the virtual rod separately, and reducing the control complexity of the electrodynamic multi-rope structure.

[0029] The control input for the ETDA-based control strategy for multi-rope electrodynamic structures is:

[0030]

[0031] in and They are respectively and The state before time jτ, where j varies from 1 to the current orbital number, and k θ and θ and The adjustable feedback gain coefficient, R θ and These are the corresponding control parameters, and these parameters satisfy...

[0032]

[0033] Substitute the two control inputs obtained from equation (9) into the dynamic equation of the virtual rod attitude angle θ and the virtual rod attitude angle obtained in step two, respectively. In the dynamic equations, the attitude angle of the virtual rod can be controlled. Then, by combining equations (2), (4), and (5), the attitude motion of the virtual rod and the main star of the electrodynamic multi-rope structure can be stabilized simultaneously.

[0034] Beneficial effects:

[0035] 1. This invention discloses a dynamic analysis and attitude control method for an electrodynamic multi-rope structure. Based on the operational rules of vector arrays, six generalized coordinate dynamic equations for the electrodynamic multi-rope structure are derived through the Lagrange equations. The dynamic equations for each generalized coordinate are: the dynamic equation for the primary star attitude angle α, the dynamic equation for the primary star attitude angle β, the dynamic equation for the primary star attitude angle γ, the dynamic equation for the virtual rod attitude angle θ, and the dynamic equation for the virtual rod attitude angle γ. The dynamic equations regarding the virtual rod length l s,m The dynamic equations are derived. A dynamic model of the electrodynamic multi-tether structure is constructed through dynamic analysis, and this model characterizes the coupling dynamics between the tether and the host star, thereby improving the accuracy of the dynamic model.

[0036] 2. This invention discloses a dynamic analysis and attitude control method for an electrodynamic multi-rope structure. Through an extended time-delay self-synchronization control strategy, it is based on the constructed dynamic equations of the virtual rod attitude angle θ and the virtual rod attitude angle... The attitude of the virtual rod is controlled by the dynamic equations of the virtual rod. The attitude of the primary star is controlled by the dynamic equations of the primary star attitude angle α, β, and γ, thereby achieving the goal of simultaneously stabilizing the attitude motion of the virtual rod and the primary star, avoiding the need to control the attitude of the primary star and the virtual rod separately, and reducing the complexity of the control system.

[0037] 3. The present invention discloses a dynamic analysis and attitude control method for an electro-dynamic multi-tether structure. When it is necessary to accelerate the deorbiting of the primary star, the secondary star and the conductive tether are released. The dynamic analysis and attitude control method described in Benefit 1 is used to control the attitude angle of the electro-dynamic multi-tether structure to accelerate the deorbiting of the primary star. Since multiple conductive tethers are used to connect the primary star and the secondary star, the redundancy and survival rate of the structure are improved while ensuring that the total current of the electro-dynamic tether structure remains unchanged. The current value of a single tether is reduced, and the success rate of the deorbiting of the electro-dynamic tether structure is improved. Attached Figure Description

[0038] Figure 1 A schematic diagram of an electro-powered multi-rope structure operating in orbit;

[0039] Figure 2 Schematic diagram of the attitude angle of a multi-rope virtual rod in an electric motor;

[0040] Figure 3 The diagram shows the change in the virtual lever attitude angle under uncontrolled conditions, where: Figure 3 (a) is a diagram showing the change of the interior angle of the virtual rod surface under uncontrolled conditions. Figure 3 (b) is a diagram showing the change of the exterior angle of the virtual rod surface under uncontrolled conditions;

[0041] Figure 4 The diagram shows the attitude angle changes of the primary star under uncontrolled conditions, where: Figure 4 (a) is a diagram showing the change in the first attitude angle of the primary star under uncontrolled conditions. Figure 4 (b) shows the change in the second attitude angle of the primary star under uncontrolled conditions. Figure 4 (c) shows the change of the third attitude angle of the primary star in the uncontrolled state;

[0042] Figure 5 The diagram shows the change in the virtual lever attitude angle under controlled conditions, where: Figure 5 (a) is a diagram showing the change of the interior angle of the virtual rod plane under controlled conditions. Figure 5 (b) is a diagram showing the change of the exterior angle of the virtual rod surface under controlled conditions;

[0043] Figure 6 The diagram shows the attitude angle changes of the primary star under controlled conditions, where: Figure 6 (a) is a diagram showing the change in the first attitude angle of the primary star under controlled conditions. Figure 6 (b) shows the change in the second attitude angle of the primary star under controlled conditions. Figure 6 (c) shows the change of the third attitude angle of the primary star under controlled conditions;

[0044] Figure 7 Flowchart for extended time-delay self-synchronization control strategy.

[0045] Figure 8 This is a flowchart of a dynamic analysis and attitude control method for an electrodynamic multi-rope structure according to the present invention. Detailed Implementation

[0046] To better illustrate the purpose and advantages of the present invention, the specific embodiments and effects of the present invention will be further described in detail below with reference to examples and accompanying drawings.

[0047] like Figure 8 As shown in the figure, the specific implementation steps of the electrodynamic multi-rope structure dynamic analysis and attitude control method disclosed in this embodiment are as follows:

[0048] Step 1: Accelerate the primary satellite's deorbiting using an electrodynamic multi-tether structure. Release the secondary satellite and conductive tethers when acceleration is required. The electrodynamic multi-tether structure consists of the primary satellite, the secondary satellite, and multiple conductive tethers. In this structure, the primary satellite is treated as a rigid body, the secondary satellite as a point mass, and the conductive tethers as massless elastic rods. The line connecting the primary satellite's center of mass and the secondary satellite is defined as a virtual rod. The three attitude angles of the primary satellite, the two attitude angles of the virtual rod, and the length of the virtual rod are chosen as generalized coordinates. The on-orbit motion diagram and structural composition diagram of the electrodynamic multi-tether structure are shown below. Figure 1 and Figure 2 As shown.

[0049] Step 2: Define the inertial frame, Earth-following coordinate system, orbital frame, primary star coordinate system, and virtual rod coordinate system used to construct the dynamic model of the electrodynamic multi-rope structure; based on the vector matrix operation rules, derive the dynamic equations for the six generalized coordinates of the electrodynamic multi-rope structure through the Lagrange equations. The dynamic equations for each generalized coordinate are: the dynamic equation for the primary star attitude angle α, the dynamic equation for the primary star attitude angle β, the dynamic equation for the primary star attitude angle γ, the dynamic equation for the virtual rod attitude angle θ, and the dynamic equation for the virtual rod attitude angle γ. The dynamic equations regarding the virtual rod length l s,m The dynamic equations are derived. Based on the six generalized coordinate dynamic equations, a dynamic model of the electrodynamic multi-tether structure is constructed, and the coupling dynamic characteristics between the tether and the host star are characterized through the dynamic model of the electrodynamic multi-tether structure.

[0050] The total kinetic energy of the electrodynamic multi-rope structure is:

[0051]

[0052] Where m m The mass of the main star.

[0053] The total potential energy is:

[0054]

[0055] Where μ g is the Earth's gravitational constant.

[0056] The system's Lagrangian function L can be expressed as:

[0057]

[0058] Substituting the above equation into the Lagrange equation, we can obtain the dynamic equations of the six generalized coordinates of the electrodynamic multi-rope structure. The final results are equations (2), (4)-(8).

[0059] For the electrodynamic multi-tether structure involved in this invention, the external environmental forces mainly considered are Earth's gravity and the Lorentz force, where Earth's gravity is a conservative force and has already been considered in the Lagrange function. The three components of the Lorentz force acting on the i-th tether in the primary star system are... and It can be represented as:

[0060]

[0061]

[0062]

[0063] The forces represented by equations (14)-(16) are the Lorentz forces in equations (2) and (4)-(5).

[0064] Step 3: Using the ETDA control strategy, adjust the generalized coordinates θ of the virtual rod and Control is performed based on the generalized coordinates θ of the virtual rod. Based on the dynamic equations of the virtual rod attitude angle θ constructed in step two, and the virtual rod attitude angle... The attitude of the virtual rod is controlled by the dynamic equations. Based on the generalized coordinates α, β, and γ of the primary star, the attitude of the primary star is controlled by the dynamic equations of the primary star attitude angle α, β, and γ constructed in step two. This achieves the goal of simultaneously stabilizing the attitude motion of the virtual rod and the primary star, avoiding the need to control the attitude of the primary star and the virtual rod separately, and reducing the control complexity of the electrodynamic multi-rope structure.

[0065] The control input of the ETDA control strategy is shown in equation (9). The control input of equation (9) is... and The attitude of the virtual lever can be controlled by substituting the values ​​into equations (6) and (7) respectively. The control flow of the ETDA control strategy is shown in the figure.

[0066] Step 4: Using the dynamic equations of the electrodynamic multi-rope structure derived in Step 2, analyze the attitude dynamic characteristics of the electrodynamic multi-rope structure under uncontrolled conditions. Then, use the ETDA control strategy from Step 3 to control the electrodynamic multi-rope structure and verify the effectiveness of the control strategy in the multi-rope structure.

[0067] Given the electrodynamic multi-tether structure and initial orbital conditions as shown in Tables 1 and 2, it is assumed that at the initial moment, the virtual rod is located at the local vertical, the host star's body system coincides with the orbital system, neither the virtual rod nor the host star has an initial attitude angular velocity, and all tether elastic deformations are zero. The multi-tether structure is as follows: Figure 2 As shown in the figure, there are four conductive tethers, and their connection points to the main star are located at the midpoints of the four sides of the same face of the main star.

[0068] Table 5.1 Parameters of Multi-Rope Structure

[0069]

[0070] Table 5.2 Initial conditions of the orbit

[0071]

[0072] When no control is applied to the electrodynamic multi-wire structure, the attitude motion of the virtual rod is as follows: Figure 3 As shown. In the simulation, the current of each tether is 0.19A. Under uncontrolled conditions, the outer angle of the virtual rod surface shows a gradually increasing amplitude, exceeding 80° at the 100th orbital cycle, as... Figure 3 As shown in (a). It is generally believed that when the amplitude of the attitude angle swing exceeds 90°, it is in an unstable state. Obviously, it is already very close to the unstable state at this time. Although the in-plane angle of the virtual rod is in a relatively stable motion state in the first 80 orbital cycles, it can be seen from equation (6) that there is a coupling relationship between the in-plane angle and the out-of-plane angle. When the out-of-plane angle increases rapidly and approaches the unstable state in the 80th to 100th orbital cycles, the amplitude of the in-plane angle also increases rapidly during this period and eventually exceeds 90°, entering the unstable state before the out-of-plane angle.

[0073] When no control is applied to the electrodynamic multi-tether structure, the primary star's attitude motion is as follows: Figure 4As shown in the figure, the first and third attitude angles of the primary star enter an unstable state after approximately 100 orbital periods. Since the rotation sequence of the primary star's attitude angles is "3-1-2," and the attitude motion of the virtual rod relative to the orbital system can also be considered as a "3-1-2" rotation, where the second rotation angle is 0°, therefore, the comparison... Figure 3 (a) and Figure 4 (a), and Figure 3 (b) and Figure 4 (c) It can be found that the changing trends of the first and third attitude angles of the primary star are consistent with the outer and inner angles of the virtual rod, respectively. This means that if the attitude motion of the virtual rod can be kept stable, the attitude motion of the primary star can be kept stable indirectly.

[0074] When the electrodynamic multi-rope structure is controlled based on the ETDA strategy, and the parameters of the electrodynamic multi-rope structure and the initial conditions of the track remain unchanged, the attitude motion of the virtual rod is as follows: Figure 5 As shown. The control parameters in the strategy at this time... Depend on Figure 5 It can be seen that the in-plane angle swing of the virtual rod converges to around -15° after approximately 10 orbital periods. Similarly, the out-of-plane angle also stabilizes around 0° under the control of the controller. When the virtual rod's attitude motion is controlled, the primary star's attitude motion is as follows: Figure 6 As shown. The primary star's first attitude angle is basically stable around -15°, as... Figure 6 As shown in (a); the second and third attitude angles move within the ranges of [-15°, 15°] and [-6°, 6°] respectively, as shown in (a); while the second and third attitude angles move within the ranges of [-15°, 15°] and [-6°, 6°] respectively, as shown in (a). Figure 6 (b) and Figure 6 As shown in (c), the simulation results demonstrate the effectiveness of the ETDA control strategy in electrodynamic multi-tether structures. This strategy can simultaneously stabilize the attitude motion of the virtual rod and the primary star in the multi-tether structure.

[0075] The above detailed description further illustrates the purpose, technical solution, and beneficial effects of the invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for dynamic analysis and attitude control of an electrically powered multi-rope structure, characterized in that: Comprising the following steps, Step one: using the electric power multi-rope structure to accelerate the primary star to orbit; releasing the secondary star and the conductive tether when the primary star needs to be accelerated to orbit; the electric power multi-rope structure is composed of the primary star, the secondary star and the multiple conductive tethers; in the electric power multi-rope structure, the primary star is equivalent to a rigid body, the secondary star is equivalent to a mass point, and the conductive tether is equivalent to an elastic rod without mass; the line connecting the mass center of the primary star and the secondary star is defined as a virtual rod; three attitude angles of the primary star, two attitude angles of the virtual rod and the length of the virtual rod are selected as generalized coordinates; Step two: define the inertial system, the earth-fixed coordinate system, the orbit system, the principal star body system, the virtual rod body system for building the dynamics model of the electric power multi-rope structure; based on the vector array operation rule, derive the dynamics equations of the six generalized coordinates of the electric power multi-rope structure through the Lagrange equation, and the dynamics equations of the respective generalized coordinates are as follows: the dynamics equation about the principal star attitude angle α, the dynamics equation about the principal star attitude angle β, the dynamics equation about the principal star attitude angle γ, the dynamics equation about the virtual rod attitude angle θ, the dynamics equation about the virtual rod attitude angle φ, and the dynamics equation about the virtual rod length l s,m ;​ A dynamics model of the electric power multi-rope structure is constructed based on the six generalized coordinate dynamics equations, and the coupling dynamics characteristics between the tether and the primary star are represented by the dynamics model of the electric power multi-rope structure; Step three: control the generalized coordinates θ and of the virtual bar by the extended time-delay self-synchronization ETDA control strategy; control the attitude of the virtual bar according to the generalized coordinates θ and the dynamics equation of the attitude angle θ of the virtual bar constructed in step two and the dynamics equation of the attitude angle of the virtual bar; control the attitude of the primary star according to the generalized coordinates α, β, γ, the dynamics equation of the attitude angle α of the primary star, the dynamics equation of the attitude angle β of the primary star, and the dynamics equation of the attitude angle γ of the primary star constructed in step two, thereby stabilizing the attitude motion of the virtual bar and the primary star simultaneously and reducing the control complexity of the electric power multi-rope structure.

2. The method of claim 1, wherein: The implementation method of step two is that In the dynamic modeling of electrodynamic multi-rope structures, a coordinate system is defined. The following are represented, in order: inertial frame, Earth-following coordinate system, orbital frame, primary celestial frame, and virtual rod frame; where the inertial frame... The origin O is located at the Earth's center of mass, the OX axis points to the vernal equinox, the OZ axis is aligned with the Earth's rotation axis, and the OY axis, along with the other two axes, forms a right-handed coordinate system; Earth-following coordinate system. The origin is O, the OZ′ axis is aligned with the OZ axis, and the OX′ axis and OYv axis rotate around the OZ′ axis simultaneously with the Earth's rotational angular velocity; orbital coordinate system. The origin is located at the center of mass of the primary star. m o m x o The axis points from the Earth's center O to o m o m z o The axis is perpendicular to the orbital plane and aligns with the direction of the primary star's orbital angular momentum. m y o The axis, together with the other two axes, forms a right-handed coordinate system; the primary star's body coordinate system. The origin is located at the mass center of the primary star. m Its coordinate system's principal axes are aligned with the principal inertial axes of the primary star; the virtual rod's body coordinate system Origin and the center of mass of the primary star m Overlap, its o m x v The axis points from the sub-star to o. m o m y v The axis is always located within the orbital plane and perpendicular to o. m x v Axis, o m z o The axis forms a right-handed system with the other two axes; select three attitude angles α, β, and γ of the primary star, and two attitude angles θ and γ of the virtual rod. and the length l of the virtual rod s,m As a generalized coordinate: The rotation sequence of the attitude angle of the primary star is defined as "3-1-2", which corresponds to the attitude angles α, β and γ in sequence; Based on the operation law of vector array, the dynamics equations of each generalized coordinate of the system can be obtained by deducing the Lagrange equation, wherein the dynamics equation about the attitude angle α of the primary star is: where J x , J y and J z are the principal moments of inertia of the primary around its three principal axes of inertia, Ω o is the orbital angular velocity, and are the components of the position vector of the primary's center of mass to the point of attachment of the i-th tether to the primary in the primary's body-fixed coordinate system, and denote the first and second derivatives of a with respect to time, n t is the number of tethers, k = E t A t / L i0 is the elastic coefficient of the tether, E t is the elastic modulus of the tether, A t is the cross-sectional area of the tether, L i0 is the original length of the tether, U(ε i ) is the step function, ε i is the elastic deformation of the i-th tether, and are the components of the total Lorentz force on the i-th tether in the primary's body-fixed coordinate system, is the partial derivative of f i with respect to a, f i is: The dynamics equation about the attitude angle β of the primary star is: The dynamics equation about the attitude angle γ of the primary star is: The dynamics equation about the attitude angle θ of the virtual rod is: where I m is the single tether current, μ m is the geomagnetic field dipole moment constant, i o denotes the orbit inclination, m s is the sub-star mass, v = Ω o t is the main star orbit true anomaly, t is time, r m is the distance between the main star center of mass and the Earth center, is the generalized control moment acting on the generalized coordinate θ; Regarding the virtual bar attitude angle The dynamics equation is: wherein is a generalized control moment acting on the generalized coordinates of the system. Regarding the virtual rod length l s,m The equation of motion is:

3. The method for dynamic analysis and attitude control of an electrodynamic multi-rope structure as described in claim 2, characterized in that: The implementation method of step three is that The control input of the electric power multi-rope structure control strategy based on ETDA is: wherein and are respectively and the state at time jτ, j varying from 1 to the current track number, k θ and are respectively the adjustable feedback gain coefficients of θ and R θ and are respectively the corresponding control parameters, and the parameters satisfy The two control inputs obtained from formula (9) are respectively brought into the dynamic equation of the virtual bar attitude angle θ derived in step two and the dynamic equation of the virtual bar attitude angle θ , to achieve the control of the virtual bar attitude angle, and then formulae (2), (4) and (5) are combined, to achieve the simultaneous stabilization of the virtual bar and the main star attitude motion of the electromotive force multi-rope structure.

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