Double-star electromagnetic formation dynamics modeling and control method of port Hamiltonian system

Abstract

The invention relates to a double-star electromagnetic formation dynamics modeling and control method for a port Hamiltonian system. The method comprises the following steps: defining two slave spacecraft mass center position coordinates in an ECI coordinate system and an LVLH coordinate system; kinetic energy and potential energy of the slave spacecraft under the ECI coordinate system are obtained according to the position coordinates of the mass center of the slave spacecraft; obtaining a Lagrange function L under an LVLH coordinate system according to the slave spacecraft mass center position coordinate and the coordinate system conversion matrix; establishing an Euler-Lagrange equation, selecting a generalized momentum coordinate pj according to Legendre transformation to obtain a Hamiltonian function H, and establishing a port Hamiltonian kinetic model; designing an electromagnetic formation controller according to a trajectory tracking passive control method based on interconnection-damping distribution; and obtaining an electromagnetic satellite formation trajectory tracking magnetic dipole intensity control law according to the electromagnetic formation controller. According to the method, the nonlinear term of the system is reserved, the inherent dissipation characteristic of the system is reflected, the problem that the precision of the system is reduced due to linearization can be avoided, and the passivity of the system is ensured.

Description

Technical Field

[0001] The present invention relates to the technical field of near-Earth dual-satellite electromagnetic formation dynamics modeling and control, and in particular to a dual-satellite electromagnetic formation dynamics modeling and control method of a port Hamiltonian system. Background Art

[0002] Satellite formation flying involves multiple satellites working closely together in a specific configuration. This approach demonstrates several significant advantages over traditional single large satellite systems, including improved cost-effectiveness, enhanced system redundancy, upgrade flexibility, and overall performance optimization. Due to these advantages, satellite formation flying has shown great potential and broad application prospects in the fields of earth monitoring, celestial observation, and deep space exploration, becoming an important trend in the future development of space exploration.

[0003] However, frequent maneuvering control is often required to achieve precise formation flying configuration and maintain its stability. Traditionally, such control mainly relies on control actuation systems that use propellants. This method not only consumes a lot of precious propellant resources, thereby limiting the duration of the mission, but also may cause plume contamination to sensitive payloads such as optical equipment on board the satellite, affecting observation effects and satellite performance.

[0004] Electromagnetic Formation Flying (EMFF) technology does not rely on traditional propellants, but uses the interaction of electromagnetic forces between satellites for control. Its core idea is to install high-temperature superconducting coils on each satellite in the formation, and generate the required electromagnetic force and electromagnetic torque through the interaction of the electromagnetic fields generated by the coils, which serves as the power source for formation control. However, the current research on electromagnetic formation satellites mainly focuses on the study of control strategies based on linear error dynamics, and there is basically no research on nonlinear controllers directly based on nonlinear dynamics. The traditional vector mechanics method based on the Newton-Euler equation mainly focuses on the relative dynamic behavior between spacecraft, and may not be able to fully reveal the working mechanism of the formation system under the action of inter-satellite internal forces. Especially in highly nonlinear systems such as electromagnetic formation flying, the strong nonlinear characteristics of inter-satellite electromagnetic forces make it impossible to achieve the expected control accuracy by simply applying linearized dynamics or control methods. Summary of the invention

[0005] In order to solve the technical problems existing in the above-mentioned prior art, the purpose of the present invention is to provide a dual-star electromagnetic formation dynamics modeling and control method for a port Hamiltonian system, to carry out a port Hamiltonian dynamics model for the low-Earth orbit electromagnetic formation system, and to design a passive control method based on interconnection-damping distribution for trajectory tracking control.

[0006] To achieve the above-mentioned object of the invention, the present invention provides a dual-satellite electromagnetic formation dynamics modeling and control method of a port Hamiltonian system, comprising the following steps:

[0007] Step S1, defining two coordinates of the center of mass position of the slave spacecraft in the ECI coordinate system and the LVLH coordinate system;

[0008] Step S2, according to the coordinates of the center of mass position of the slave spacecraft, obtain the kinetic energy and potential energy of the slave spacecraft in the ECI coordinate system;

[0009] Step S3, obtaining the Lagrangian function L in the LVLH coordinate system according to the coordinates of the center of mass position of the spacecraft and the coordinate system conversion matrix;

[0010] Step S4: Establish the Euler-Lagrange equation, select the generalized momentum coordinate p according to the Legendre transformation j , get the Hamiltonian function H, and establish the port Hamiltonian dynamics model;

[0011] Step S5, designing an electromagnetic formation controller according to a trajectory tracking passive control method based on interconnection-damping allocation;

[0012] Step S6: obtaining the electromagnetic satellite formation trajectory tracking magnetic dipole intensity control law according to the electromagnetic formation controller.

[0013] According to a technical solution of the present invention, in step S1, the two slave spacecraft are slave spacecraft A and slave spacecraft B, then:

[0014] In the ECI coordinate system, the coordinate of the spacecraft A is defined as Q a =[X a , Y a , Z a ] T , from the spacecraft B coordinates Q b =[X b , Y b , Z b ] T , the center of mass coordinates of the spacecraft formation is Q0 = [X0, Y0, Z0] T ;

[0015] In the LVLH coordinate system, the center of mass coordinates of the spacecraft formation is defined as q0 = [q0, 0, 0] T , define the vector between the center of mass of the spacecraft formation and the slave spacecraft A as q a =[x a ,y a , z a ] T , the vector between the center of mass of the spacecraft formation and the slave spacecraft B is q b =[x b,y b , z b ] T ;

[0016] In the LVLH coordinate system, the vector from the center of the Earth to the spacecraft A is defined as .

[0017] According to a technical solution of the present invention, in step S2, the kinetic energy and potential energy of slave spacecraft A in the ECI coordinate system are calculated according to the center of mass position and velocity of slave spacecraft A, wherein the potential energy includes gravitational potential energy and magnetic potential energy;

[0018] The kinetic energy of the slave spacecraft A in the ECI coordinate system is expressed as:

[0019]

[0020] The gravitational potential energy of the slave spacecraft A under the influence of J2 perturbation in the ECI coordinate system is expressed as:

[0021]

[0022] Among them, R a represents the distance from spacecraft A to the center of the earth, μ, R e , J2 represents the Earth's gravitational constant, the Earth's equatorial mean radius, and the second-order zone harmonic coefficient respectively;

[0023] The magnetic field generated from spacecraft B is expressed as:

[0024]

[0025] Among them, μ b represents the magnetic dipole strength from spacecraft B, ρ represents the vector pointing from spacecraft A to B, and μ0 is the magnetic permeability of vacuum;

[0026] Then the magnetic potential energy from spacecraft A is expressed as:

[0027]

[0028] Where μ a represents the magnetic dipole strength from spacecraft A, and T represents the transposed matrix.

[0029] According to a technical solution of the present invention, step S3 specifically includes:

[0030] The coordinate transformation between the ECI coordinate system and the LVLH coordinate system is performed using the following formula:

[0031]

[0032] Among them, s o= sin(o), c o = cos(o), Ω represents the right ascension of the ascending node, θ represents the argument of perigee, o represents the orbital inclination of the center of mass of the spacecraft formation, T r is an orthogonal matrix, that is

[0033] because For an antisymmetric matrix, define the antisymmetric matrix function Then we have:

[0034]

[0035] In an undisturbed orbit, the orbital parameters are constant, the last two terms of formula (6) are equal to zero, and the antisymmetric matrix function is expressed as S;

[0036] The transformation relationship between the ECI coordinate system and the LVLH coordinate system is expressed as:

[0037]

[0038] In the LVLH coordinate system, the kinetic energy from spacecraft A is expressed as:

[0039]

[0040] In the LVLH coordinate system, the gravitational potential energy from spacecraft A is expressed as:

[0041]

[0042] Then in the LVLH coordinate system, the Lagrange equation is expressed as:

[0043]

[0044] According to a technical solution of the present invention, the step S4 specifically includes:

[0045] Select q a As a basis variable, according to the Legendre transformation And the Euler-Lagrange equation, we get the relative motion dynamics equation

[0046]

[0047] After finishing, we get:

[0048]

[0049] Where g = [O3, I3] T ,

[0050] The Hamiltonian function H is obtained from the Lagrange equation:

[0051]

[0052] Formula (13) is the port Hamiltonian dynamic model of the binary star electromagnetic formation.

[0053] According to a technical solution of the present invention, in step S5, the electromagnetic formation controller is designed according to the trajectory tracking passive control method based on interconnection-damping allocation, which specifically includes:

[0054] The electromagnetic formation satellite trajectory tracking control, the closed-loop system is designed as follows:

[0055]

[0056] The closed-loop Hamiltonian function is designed as:

[0057]

[0058] in,

[0059] According to a technical solution of the present invention, in step S5, the existence condition of the trajectory tracking passive controller based on interconnection-damping allocation is:

[0060] By designing the parameters of the closed-loop system K j , L j , so that the closed-loop system meets the existence condition of the interconnected-damping distribution trajectory tracking passive control method controller, and at the same time the closed-loop system shrinks to the desired reference trajectory, completing the trajectory tracking controller design;

[0061] Design matrix L j , design the ideal reference trajectory Then we have:

[0062]

[0063] Bring it into the closed-loop system and satisfy the conditions at the desired equilibrium point:

[0064]

[0065] For a closed-loop system, the second-order partial derivative of the Hamiltonian function is expressed as:

[0066]

[0067] If there are positive constants α1, α2, and α1<α2, then the condition is satisfied:

[0068]

[0069] For a given positive constant ∈, the following matrix N has no eigenvalues ​​on the imaginary axis, then:

[0070]

[0071] in, A d =J d -R d .

[0072] According to a technical solution of the present invention, in step S5, the electromagnetic formation controller is designed based on the interconnection-damping allocation trajectory tracking passive control method in the form of:

[0073]

[0074] The control system of the electromagnetic satellite formation tracks the desired trajectory x at an exponential rate. * (t).

[0075] According to a technical solution of the present invention, in step S6, the control force of the satellites in the dual-satellite electromagnetic formation is coupled with the formation position and the satellite magnetic field strength, and the practical form of the electromagnetic formation satellite trajectory tracking passive controller is expressed as:

[0076]

[0077] Compared with the prior art, the present invention has the following beneficial effects:

[0078] The present invention proposes a dual-satellite electromagnetic formation dynamics modeling and control method of a port Hamiltonian system. The near-Earth electromagnetic formation dynamics is modeled by the port Hamiltonian system, the nonlinear terms of the system are retained, the inherent dissipative characteristics of the system are reflected, the linearization is avoided to reduce the accuracy of the system, and the passivity of the system is ensured.

[0079] Aiming at the near-Earth binary-satellite electromagnetic formation dynamics system of port Hamiltonian system, a trajectory tracking passive controller with interconnection-damping distribution is designed, which is beneficial to solving the formation reconstruction problem in the near-Earth electromagnetic satellite formation flight. In the presence of nonlinearity and disturbance, the trajectory tracking passive controller with interconnection-damping distribution has higher accuracy.

[0080] The interconnected-damping distributed trajectory tracking passive controller designed in the present invention can provide a reference for formation design and control law design.

[0081] The present invention provides a practical form of a passive controller for tracking the trajectory of electromagnetic formation satellites, and has good engineering realization value. BRIEF DESCRIPTION OF THE DRAWINGS

[0082] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments are briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention, and for ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0083] Figure 1 A flowchart schematically showing a method for dynamics modeling and control of a dual-satellite electromagnetic formation of a port Hamiltonian system provided in accordance with an embodiment of the present invention;

[0084] Figure 2 A schematic diagram of a simulation experiment coordinate system according to an embodiment of the present invention is schematically shown;

[0085] FIG. 3( a to 3 ) schematically show simulation experiment result diagrams according to an embodiment of the present invention. DETAILED DESCRIPTION

[0086] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0087] like Figure 1 and Figure 2 As shown, a dual-satellite electromagnetic formation dynamics modeling and control method of a port Hamiltonian system of the present invention comprises the following steps:

[0088] Step S1, define two slave spacecraft center of mass position coordinates in the ECI coordinate system and the LVLH coordinate system.

[0089] Assume that there are two electromagnetic satellites in orbit, named slave spacecraft A and slave spacecraft B. Figure 2 As shown, in the ECI coordinate system, the coordinate of the spacecraft A is defined as Q a =[X a , Y a , z a ] T , from the spacecraft B coordinates Q b =[X b , Y b , Z b ] T , the center of mass coordinates of the spacecraft formation is Q0 = [X0, Y0, Z0] T ;

[0090] In the LVLH coordinate system, the center of mass coordinates of the spacecraft formation is defined as q0 = [q0, 0, 0] T ,, define the vector between the center of mass of the spacecraft formation and the slave spacecraft A as q a =[x a ,u a , z a ] T , the vector between the center of mass of the spacecraft formation and the slave spacecraft B is q b =[x b ,y b , z b ] T .

[0091] At the same time, for the convenience of description, the vector pointing from the center of the earth to the spacecraft A is defined in the LVLH coordinate system.

[0092] Step S2: According to the coordinates of the center of mass of the slave spacecraft, the kinetic energy and potential energy of the slave spacecraft in the ECI coordinate system are obtained.

[0093] Among them, potential energy includes gravitational potential energy and magnetic potential energy.

[0094] The kinetic energy of the slave spacecraft A in the ECI coordinate system is expressed as:

[0095]

[0096] The gravitational potential energy of the slave spacecraft A under the influence of J2 perturbation in the ECI coordinate system is expressed as:

[0097]

[0098] Among them, R a represents the distance from spacecraft A to the center of the earth, μ, R e , J2 represents the Earth's gravitational constant, the Earth's equatorial mean radius, and the second-order zone harmonic coefficient respectively;

[0099] By considering the electromagnetic coils on each satellite as controllable magnetic dipoles, the magnetic field generated from spacecraft B is expressed as:

[0100]

[0101] Among them, μ b represents the magnetic dipole strength from spacecraft B, ρ represents the vector pointing from spacecraft A to B, and μ0 is the magnetic permeability of vacuum;

[0102] Then the magnetic potential energy from spacecraft A is expressed as:

[0103]

[0104] Where μ a represents the magnetic dipole strength from spacecraft A, and T represents the transposed matrix.

[0105] R a is the distance from spacecraft A to the center of the Earth, and μ is the Earth's gravitational constant, which is 3.98603×10 14 m 3 / s 2 , R e is the average radius of the earth's equator, which is 6878.137 km, and the second-order harmonic coefficient of J2 is 1.08263×10 -3 , μ b Designed for strength, always 5×10 5 [1, 1, 1] T .

[0106] Step S3: Obtain the Lagrangian function L in the LVLH coordinate system according to the coordinates of the center of mass position of the spacecraft and the coordinate system conversion matrix.

[0107] In order to describe the dynamics of the following spacecraft in the LVLH coordinate system, the following coordinate transformation is required between the LVLH and ECI frames, as given by:

[0108]

[0109] Among them, s o = sin(o), c o =cos(o), Ω represents the right ascension of the ascending node, θ represents the argument of perigee, and i represents the orbital inclination of the center of mass of the spacecraft formation;

[0110] Where T r is an orthogonal matrix, that is By taking the derivative of both sides of the formula, we can get Right now is an antisymmetric matrix, so we can define an antisymmetric matrix function Then we have:

[0111]

[0112] In an undisturbed orbit, the orbital parameters are constant, the last two terms of formula (6) are equal to zero, and the antisymmetric matrix function is expressed as S;

[0113] The transformation relationship between the ECI coordinate system and the LVLH coordinate system is expressed as:

[0114]

[0115] In the LVLH coordinate system, the kinetic energy from spacecraft A is expressed as:

[0116]

[0117] In the LVLH coordinate system, the gravitational potential energy from spacecraft A is expressed as:

[0118]

[0119] Then in the LVLH coordinate system, the Lagrange equation is expressed as:

[0120]

[0121] For example, the orbital parameters may be set to r0=6878.137 km, e=0, i=60°, ω=90°, Ω=0°, υ=0°.

[0122] Step S4: Establish the Euler-Lagrange equation, select the generalized momentum coordinate p according to the Legendre transformation j , obtain the Hamiltonian function H, and establish the port Hamiltonian dynamics model.

[0123] Select q a As a basis variable, according to the Legendre transformation And the Euler-Lagrange equation, we get the relative motion dynamics equation

[0124]

[0125] After finishing, we get:

[0126]

[0127]

[0128] Where g = [O3, I3] T ,

[0129] The Hamiltonian function H is obtained from the Lagrange equation:

[0130]

[0131] Formula (13) is the port Hamiltonian dynamic model of the binary star electromagnetic formation.

[0132] For the near-Earth electromagnetic satellite formation dynamics, x represents the function variable, that is, (q a , p a ).

[0133] Step S5: designing an electromagnetic formation controller according to a trajectory tracking passive control method based on interconnection-damping allocation.

[0134] The electromagnetic formation controller is designed according to the trajectory tracking passive control method based on interconnection-damping allocation, which includes:

[0135] The electromagnetic formation satellite trajectory tracking control, the closed-loop system is designed as follows:

[0136]

[0137] The closed-loop Hamiltonian function is designed as:

[0138]

[0139] in,

[0140] According to a technical solution of the present invention, in step S5, the existence condition of the trajectory tracking passive controller based on interconnection-damping allocation is:

[0141] In order to complete the trajectory tracking controller design, it is necessary to design the closed-loop system parameters K j , L j , so that the closed-loop system satisfies the existence condition of the controller of the interconnected-damping distribution trajectory tracking passive control method, and the closed-loop system shrinks to the desired reference trajectory;

[0142] Design matrix L j , design the ideal reference trajectory Then we have:

[0143]

[0144] Bring it into the closed-loop system and satisfy the conditions at the desired equilibrium point:

[0145]

[0146] For a closed-loop system, the second-order partial derivative of the Hamiltonian function is expressed as:

[0147]

[0148] If there are positive constants α1, α2, and α1<α2, then the condition is satisfied:

[0149]

[0150] For a given positive constant ∈, the following matrix N has no eigenvalues ​​on the imaginary axis, then:

[0151]

[0152] in, A d =J d -Rd .

[0153] The existence condition of the controller u in the interconnected-damping distribution trajectory tracking passive control method can be met, that is, there is a controller.

[0154] The design of electromagnetic formation controller based on the trajectory tracking passive control method of interconnection-damping allocation is as follows:

[0155]

[0156] The control system of the electromagnetic satellite formation tracks the desired trajectory x at an exponential rate. * (t).

[0157] In step 5, the system reference trajectory is set to:

[0158]

[0159] Among them, α 0j and β 0j are the usually equal in-plane and out-of-plane phase angles, parameter c 1j , c 2j and c 3j is the integral constant that determines the trajectory configuration. In the PCO formation configuration, c 2j =0, α 0j =0,β 0j =0.

[0160] K j =10 -4 diag(2.4, 4, 6) can verify that conditions (19) and (20) are met, and the controller existence conditions are met.

[0161] Step S6: obtaining the electromagnetic satellite formation trajectory tracking magnetic dipole intensity control law according to the electromagnetic formation controller.

[0162] For electromagnetic formation satellites, the change of control force is accomplished by adjusting the strength of its magnetic dipole, which is coupled with the formation position and the satellite magnetic field strength. Therefore, the control force is not simply applied directly to the satellite. Instead, it is based on the current magnetic field strength to change the satellite's own magnetic dipole strength to keep consistent with the required control force. Then the practical form of the electromagnetic formation satellite trajectory tracking passive controller should be as follows:

[0163]

[0164] Simulation experiment

[0165] The simulation experiment is carried out with the above parameters to obtain the satellite formation trajectory and control input.

[0166] Figure 3(a) shows the motion of slave spacecraft A and slave spacecraft B relative to the reference trajectory. It can be seen that when the two electromagnetic satellites have initial errors relative to the reference trajectory, the system completes convergence within 5200 seconds. Each slave satellite gradually approaches the target point under the action of thrust and finally tracks the ideal reference trajectory. At the terminal moment, the three-axis accuracy is less than 0.001m.

[0167] Figure 3(b) shows the error variation from spacecraft A on the x, y, and z axes.

[0168] Figure 3(c) shows the variation of magnetic dipole strength from spacecraft A in the x, y, and z axes, which is consistent with the range of magnetic dipole strength.

[0169] Modeling the dynamics of electromagnetic formation satellites in low Earth orbit within the framework of the port Hamiltonian system can effectively retain the nonlinear links of the system, reflect the passive characteristics of the system, and improve the modeling accuracy. More importantly, the electromagnetic formation is also a typical Euler-Lagrangian system, which can be modeled within the framework of the port Hamiltonian system, and passive control methods can be applied to perform energy-based control on this dynamic model, thereby improving the control accuracy.

[0170] Therefore, the present invention adopts the above-mentioned port Hamiltonian system dual-satellite electromagnetic formation dynamics modeling and control method, and models the near-Earth electromagnetic formation dynamics through the port Hamiltonian system, retaining the nonlinear terms of the system, reflecting the inherent dissipative characteristics of the system, avoiding linearization to reduce the accuracy of the system, and ensuring the passivity of the system. For the near-Earth dual-satellite electromagnetic formation dynamics system of the port Hamiltonian system, an interconnected-damping distribution trajectory tracking passive controller is designed, which is conducive to solving the formation reconstruction problem in the near-Earth electromagnetic satellite formation flight. In the presence of nonlinearity and disturbance, the interconnected-damping distribution trajectory tracking passive controller has higher accuracy.

[0171] Furthermore, the present invention provides a practical form of a passive controller for tracking the trajectory of electromagnetic formation satellites, which has good engineering implementation value.

[0172] It should be noted that although the embodiments of the present invention described above are illustrative, they are not intended to limit the present invention, and therefore the present invention is not limited to the above specific embodiments. Without departing from the principles of the present invention, any other embodiments obtained by those skilled in the art under the guidance of the present invention are deemed to be within the protection of the present invention.

Claims

1. A dual-satellite electromagnetic formation dynamics modeling and control method for a port Hamiltonian system, characterized in that: The following steps are involved: Step S1, defining two coordinates of the center of mass position of the slave spacecraft in the ECI coordinate system and the LVLH coordinate system; Step S2, according to the coordinates of the center of mass position of the slave spacecraft, obtain the kinetic energy and potential energy of the slave spacecraft in the ECI coordinate system; Step S3, obtaining the Lagrangian function L in the LVLH coordinate system according to the coordinates of the center of mass position of the spacecraft and the coordinate system conversion matrix; Step S4: Establish the Euler-Lagrange equation, select the generalized momentum coordinate p according to the Legendre transformation j , get the Hamiltonian function H, and establish the port Hamiltonian dynamics model; Step S5, designing an electromagnetic formation controller according to a trajectory tracking passive control method based on interconnection-damping allocation; Step S6: obtaining the electromagnetic satellite formation trajectory tracking magnetic dipole intensity control law according to the electromagnetic formation controller.

2. The dual-satellite electromagnetic formation dynamics modeling and control method of the port Hamiltonian system according to claim 1 is characterized in that: In step S1, the two slave spacecraft are slave spacecraft A and slave spacecraft B, respectively, then: In the ECI coordinate system, the coordinate of the spacecraft A is defined as Q a =[X a , Y a , Z a ] T , from the spacecraft B coordinates Q b =[X b , Y b , Z b ] T , the center of mass coordinates of the spacecraft formation is Q0 = [X0, Y0, Z0] T ; In the LVLH coordinate system, the center of mass coordinates of the spacecraft formation is defined as q0 = [q0, 0, 0] T , define the vector between the center of mass of the spacecraft formation and the slave spacecraft A as q a =[x a ,y a , z a ] T , the vector between the center of mass of the spacecraft formation and the slave spacecraft B is q b =[x b ,y b , z b ] T ; In the LVLH coordinate system, the vector from the center of the Earth to the spacecraft A is defined as 3. The dual-satellite electromagnetic formation dynamics modeling and control method of the port Hamiltonian system according to claim 1 is characterized in that: In the step S2, the kinetic energy and potential energy of the slave spacecraft A in the ECI coordinate system are calculated according to the center of mass position and velocity of the slave spacecraft A, wherein the potential energy includes gravitational potential energy and magnetic potential energy; The kinetic energy of the slave spacecraft A in the ECI coordinate system is expressed as: The gravitational potential energy of the slave spacecraft A under the influence of J2 perturbation in the ECI coordinate system is expressed as: Among them, R a represents the distance from spacecraft A to the center of the earth, μ, R e , J2 represents the Earth's gravitational constant, the Earth's equatorial mean radius, and the second-order zone harmonic coefficient respectively; The magnetic field generated from spacecraft B is expressed as: Among them, μ b represents the magnetic dipole strength from spacecraft B, ρ represents the vector pointing from spacecraft A to B, and μ0 is the magnetic permeability of vacuum; Then the magnetic potential energy from spacecraft A is expressed as: Where μ a represents the magnetic dipole strength from spacecraft A, and T represents the transposed matrix.

4. The method for dynamic modeling and control of a dual-satellite electromagnetic formation of a port Hamiltonian system according to claim 3 is characterized in that: The step S3 specifically includes: The coordinate transformation between the ECI coordinate system and the LVLH coordinate system is performed using the following formula: Among them, s o = sin(o), c o = cos(o), Ω represents the right ascension of the ascending node, θ represents the argument of perigee, i represents the orbital inclination of the center of mass of the spacecraft formation, T r is an orthogonal matrix, that is because For an antisymmetric matrix, define the antisymmetric matrix function Then we have: In an undisturbed orbit, the orbital parameters are constant, the last two terms of formula (6) are equal to zero, and the antisymmetric matrix function is expressed as S; The transformation relationship between the ECI coordinate system and the LVLH coordinate system is expressed as: In the LVLH coordinate system, the kinetic energy from spacecraft A is expressed as: In the LVLH coordinate system, the gravitational potential energy from spacecraft A is expressed as: Then in the LVLH coordinate system, the Lagrange equation is expressed as:

5. The method for dynamics modeling and control of a dual-satellite electromagnetic formation of a port Hamiltonian system according to claim 4, characterized in that: The step S4 specifically includes: Select as the basis variable, according to the Legendre transformation and the Euler-Lagrange equation, we get the relative motion dynamics equation After finishing, we get: Where g = [03, I3] T , The Hamiltonian function is obtained from the Lagrange equation: Formula (13) is the port Hamiltonian dynamic model of the binary star electromagnetic formation.

6. The method for dynamics modeling and control of a dual-satellite electromagnetic formation of a port Hamiltonian system according to claim 5, characterized in that: In the step S5, the electromagnetic formation controller is designed according to the trajectory tracking passive control method based on interconnection-damping allocation, which specifically includes: The electromagnetic formation satellite trajectory tracking control, the closed-loop system is designed as follows: The closed-loop Hamiltonian function is designed as: in, 7. The method for dynamics modeling and control of a dual-satellite electromagnetic formation of a port Hamiltonian system according to claim 6, characterized in that: In step S5, the existence condition of the trajectory tracking passive controller based on interconnection-damping allocation is: By designing the parameters of the closed-loop system , so that the closed-loop system meets the existence condition of the interconnected-damping distribution trajectory tracking passive control method controller, and at the same time the closed-loop system shrinks to the desired reference trajectory, completing the trajectory tracking controller design; Design matrix, design ideal reference trajectory Then we have: Bring it into the closed-loop system and satisfy the conditions at the desired equilibrium point: For a closed-loop system, the second-order partial derivative of the Hamiltonian function is expressed as: If there are positive constants α1, α2, and α1<α2, then the condition is satisfied: For a given positive constant, the following matrix has no eigenvalues ​​on the imaginary axis, then: in, A d =J d -R d .

8. The method for dynamics modeling and control of a dual-satellite electromagnetic formation of a port Hamiltonian system according to claim 7, characterized in that: In step S5, the electromagnetic formation controller is designed based on the interconnection-damping allocation trajectory tracking passive control method in the form of: The control system enables the electromagnetic satellite formation to track the desired trajectory at an exponential rate.

9. The method for dynamics modeling and control of a dual-satellite electromagnetic formation of a port Hamiltonian system according to claim 8, characterized in that: In step S6, the control force of the satellites in the dual-satellite electromagnetic formation is coupled with the formation position and the satellite magnetic field strength, so the practical form of the electromagnetic formation satellite trajectory tracking passive controller is expressed as:

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