Non-contact orbit change control method for space-dead satellites in pyramid-type electromagnetic formation

Abstract

The present invention provides a non-contact orbit change control method for a space-dead satellite in a pyramid-shaped electromagnetic formation, which belongs to the field of electromagnetic control of space targets and active removal of space debris. The specific steps are: determining the maximum thrust acceleration applied to the space-dead satellite; determining the expected thrust acceleration during the orbit transfer process and the duration of the entire transfer process; establishing an orbital motion model to obtain the expected position and expected speed; designing a nonlinear model predictive controller to obtain the 2-norm and rotational angular velocity of the electromagnetic spacecraft magnetic moment, and realizing non-contact orbit change control of the space-dead satellite in the pyramid-shaped electromagnetic formation. The present invention generates an electromagnetic force / torque of the deactivated satellite through the rotation of the electromagnetic spacecraft magnetic moment. The method can realize orbit change control of the deactivated satellite without magnetic moment without making contact with the deactivated satellite.

Description

Technical Field

[0001] The present invention belongs to the field of electromagnetic control of space targets and active removal of space debris, and in particular relates to a non-contact orbit change control method for a space-deactivated satellite in a pyramid-shaped electromagnetic formation. Background Art

[0002] In recent years, with the rapid development of space technology, the number of satellites in orbit has exploded, and space orbits have become increasingly crowded. However, due to satellite aging, collisions, and other factors, the number of inoperative satellites is increasing, severely wasting precious orbital resources and impacting the safety of in-orbit satellites. The in-orbit removal of inoperative satellites has become both a hot topic and a challenge in space services.

[0003] A space electromagnetic manipulation method, which utilizes controllable electromagnetic forces / torques to achieve contactless control of disabled satellites in space, has attracted the attention of aerospace experts. This method uses controllable electromagnetic forces / torques between satellites to perform contactless control of disabled satellites. Compared to traditional contact control and inertial thrust control methods, electromagnetic control offers numerous advantages, such as avoiding the risks of collision, propellant consumption, and plume contamination, while also offering contactless, continuous, and reversible control. Electromagnetic control technology has a wide range of applications, including spacecraft docking and separation, in-orbit assembly, formation flying, failed satellite rescue, and despinning tumbling satellites.

[0004] However, existing electromagnetic manipulation technology often requires satellites to be equipped with devices capable of generating magnetic torque, such as electromagnetic coils or permanent magnets. However, a disabled satellite does not necessarily possess this capability and cannot generate electromagnetic manipulation forces or torques, making electromagnetic orbit maneuvering impossible. To address this issue, this paper proposes a non-contact orbit maneuvering method for disabled space satellites in a pyramid-shaped electromagnetic formation, providing a new approach for in-orbit servicing of space targets and active debris removal. Summary of the Invention

[0005] Technical issues to be solved:

[0006] In order to avoid the shortcomings of the existing technology, the present invention provides a non-contact orbit change control method for a space-dead satellite in a pyramid-shaped electromagnetic formation, which generates electromagnetic force / torque of the disabled satellite through the rotation of the magnetic moment of the electromagnetic spacecraft. This method can realize orbit change control of a magnetic-torque-free disabled satellite without contacting the disabled satellite.

[0007] The technical solution of the present invention is: a non-contact orbit change control method for space-deactivated satellites in a pyramid-shaped electromagnetic formation, the specific steps of which are as follows:

[0008] Determine the maximum thrust acceleration applied to a satellite that fails in space;

[0009] Determine the expected thrust acceleration during the orbit transfer process and the duration of the entire transfer process;

[0010] Establish an orbital motion model to obtain the desired position and desired velocity;

[0011] A nonlinear model predictive controller is designed to obtain the 2-norm and rotational angular velocity of the electromagnetic spacecraft, and to realize non-contact orbit change control of a space-failed satellite in a pyramid-type electromagnetic formation.

[0012] A further technical solution of the present invention is: the maximum thrust acceleration applied to the space failure satellite is

[0013]

[0014] Among them, F max is the maximum electromagnetic force, m t is the mass of the satellite that fails in space.

[0015] A further technical solution of the present invention is: the method for determining the maximum thrust acceleration applied to the inoperative satellite in space is as follows:

[0016] In the magnetic moment spherical coordinate system, the electromagnetic force F exerted by electromagnetic spacecraft j on the non-cooperative failed satellite in space is established. tj and electromagnetic torque T tj for:

[0017]

[0018]

[0019] Where, Represents the three coordinate basis vectors of the magnetic moment spherical coordinate system, r tj Represents the relative distance between space failure satellites, m Bj,n =||m Bj ||2 means m Bj 2-norm, n represents the norm, m Bj (j=1,2,...,6) represents the magnetic moment of electromagnetic spacecraft j, ω mj (j=1,2,...,6) represents the rotational angular velocity of the magnetic moment; let l tj =||r tj ||2 represents r tj 2-norm, μ0 is the vacuum permeability, ω mn =||ω mj ||2 represents ω mj The 2-norm of Represents ω mj and r tjThe angle between them, where atan(·) is the inverse tangent function, then F r (m Bj,n ,ω mj ) is calculated as:

[0020]

[0021] in,

[0022]

[0023] F φ (m Bj,n ,ω mj ) is calculated as:

[0024]

[0025] in,

[0026] T r (m Bj,n ,ω mj ) is calculated as:

[0027]

[0028] in,

[0029] T θ (m Bj,n ,ω mj ) is calculated as:

[0030]

[0031] in,

[0032] Calculate the maximum electromagnetic force F max for:

[0033]

[0034] Calculate the maximum electromagnetic torque T max :

[0035]

[0036] Thus, the maximum thrust acceleration a applied to the space failure satellite is obtained max for

[0037]

[0038] A further technical solution of the present invention is that the duration of the entire transfer process t f for

[0039]

[0040] Where, ΔV tot Represents the velocity increment of the entire orbit transfer process; a max Indicates the maximum thrust acceleration.

[0041] A further technical solution of the present invention is: the desired thrust acceleration a d (t) is

[0042]

[0043] Where,

[0044] A further technical solution of the present invention is: the method for determining the expected thrust acceleration during the orbit transfer process and the duration of the entire transfer process is as follows:

[0045] The initial orbital height r of the space failure satellite h0 and the final orbital height r h1 The initial orbital velocity v0 and the final orbital velocity v1 are calculated as

[0046]

[0047] Where G M represents the gravitational constant;

[0048] The absolute value of the inclination change during the entire orbit transfer process is calculated as Δi tot =|i f -i0|, then the thruster yaw angle β0 at the initial moment is

[0049]

[0050] The velocity increment ΔV during the entire orbit transfer process tot for

[0051]

[0052] The duration of the entire transfer process is t f for

[0053]

[0054] The thruster yaw angle β(t) at time t during the orbit transfer process is:

[0055]

[0056] The expected thrust acceleration a at time t during the orbit transfer process is d (t) is

[0057]

[0058] Where,

[0059] A further technical solution of the present invention is: the method for obtaining the desired position and the desired speed is:

[0060] Establish the initial value problem of the ordinary differential equation for the orbital motion of the space failure satellite:

[0061]

[0062] Solve the initial value problem of the ordinary differential equation and obtain the desired position r td (t) and the desired velocity v td (t).

[0063] A nonlinear model predictive controller is designed to obtain the 2-norm and rotational angular velocity of the electromagnetic spacecraft, and to realize non-contact orbit change control of a space-failed satellite in a pyramid-type electromagnetic formation.

[0064] A further technical solution of the present invention is that the objective function of the nonlinear model predictive controller is:

[0065]

[0066] in, The superscript T on the right represents the transpose operation of the vector, and N represents the prediction step size of the model predictive controller; m t Indicates the mass of a satellite that has failed in space.

[0067] A further technical solution of the present invention is: a non-contact orbit change control method for a space-inoperative satellite in the pyramid-type electromagnetic formation is as follows:

[0068] The objective function of designing a nonlinear model predictive controller is:

[0069]

[0070] in, The superscript T on the right represents the transpose operation of the vector, and N represents the prediction step size of the model predictive controller;

[0071] The kinetic equation is

[0072]

[0073] The function f in equation (18) d(·,·) is the fourth-order Runge-Kutta discretization of the following differential equation:

[0074]

[0075] in,

[0076] The physical constraints are

[0077]

[0078] Among them, 1 3×1 =[1 1 1] T represents a column vector with 3 rows and 1 column and all elements are 1, 0 3×1 represents a column vector with 3 rows and 1 column and all elements are 0;

[0079] The model predictive control optimization problem is then

[0080]

[0081] Satisfy the constraints:

[0082] Solve the model predictive control optimization problem at time t and obtain the optimal solution Then the m of electromagnetic spacecraft j at time t is Bj,n (t) and ω mj (t) is

[0083]

[0084] By solving the model predictive control optimization problem (21) in real time, we can obtain m Bj,n (t) and ω mj (t); By setting the magnetic moment of the electromagnetic spacecraft to m Bj,n (t), the angular velocity of magnetic moment rotation is ω mj (t), the non-contact orbit change control of the space-invalid satellite in the pyramid-shaped electromagnetic formation can be realized.

[0085] Beneficial effects

[0086] The beneficial effects of the present invention are as follows: a non-contact orbit change control method for a space-dead satellite in a pyramid-type electromagnetic formation provided by the present invention does not require the disabled satellite to have a magnetic moment, but only needs to be a conductor, thereby expanding the target object range of electromagnetic control; secondly, since the electromagnetic non-contact force / torque is only at the millinewton level, the present invention combines the continuous low-thrust orbit transfer theory and the model predictive controller to obtain the magnetic moment rotation angular velocity and magnetic moment size of each electromagnetic spacecraft in the non-contact orbit change control process of the space-dead satellite in the pyramid-type electromagnetic formation, and can realize non-contact orbit change control of a satellite with no magnetic moment without contact with the target, providing a new method for on-orbit service of space targets and active debris removal. BRIEF DESCRIPTION OF THE DRAWINGS

[0087] Figure 1 Schematic diagram of non-contact orbit change control for a space-deactivated satellite in a pyramid-shaped electromagnetic formation;

[0088] Among them, 1 to 6 electromagnetic spacecraft are electromagnetic spacecraft that constitute the pyramid electromagnetic formation flight, and each electromagnetic spacecraft is equipped with the same three-axis superconducting coil; t represents the center of mass of the failed satellite, represents the x-axis basis vector of the geocentric inertial system, represents the y-axis basis vector of the geocentric inertial system, Represents the z-axis basis vector of the geocentric inertial system; m Bj (j=1,2,...,6) represents the magnetic moment of electromagnetic spacecraft j, ω mj (j=1,2,...,6) represents the rotational angular velocity of the magnetic moment of electromagnetic spacecraft j, r tj (j=1,2,...,6) represents the relative position between electromagnetic spacecraft j and the failed satellite;

[0089] Figure 2 is a schematic diagram of the magnetic moment coordinate system of electromagnetic spacecraft j;

[0090] Among them, O mj represents the center of mass of electromagnetic spacecraft j, The x-axis basis vector of the rectangular coordinate system representing the magnetic moment of electromagnetic spacecraft j represents the y-axis basis vector of the rectangular coordinate system of the magnetic moment of electromagnetic spacecraft j, The z-axis basis vector of the rectangular coordinate system representing the magnetic moment of electromagnetic spacecraft j; represents the r-axis coordinate basis vector of the magnetic moment spherical coordinate system of the electromagnetic spacecraft j, represents the φ-axis coordinate basis vector of the magnetic moment spherical coordinate system of the electromagnetic spacecraft j, represents the θ-axis coordinate basis vector of the magnetic moment spherical coordinate system of the electromagnetic spacecraft j; r tj represents the relative distance between electromagnetic spacecraft j and the space failure satellite.

[0091] Figure 3 This is a flow chart of the non-contact orbit change control method for a space-failed satellite in a pyramid-type electromagnetic formation according to the present invention;

[0092] Figure 4 The expected position of the failed satellite during the orbit transfer process;

[0093] Figure 5 The expected speed of the failed satellite orbit transfer process;

[0094] Figure 6 the magnetic dipole norm of each electromagnetic spacecraft;

[0095] Figure 7 The norm of the angular velocity of the magnetic dipole rotation of each electromagnetic spacecraft;

[0096] Figure 8 The electromagnetic thrust exerted on the failed satellite;

[0097] Figure 9 The three-dimensional position of the failed satellite;

[0098] Figure 10 Three-dimensional position deviation of the failed satellite;

[0099] Figure 11 Changes in the orbital radius of failed satellites.

[0100] Explanation of the accompanying drawings: 1. First electromagnetic spacecraft, 2. Second electromagnetic spacecraft, 3. Third electromagnetic spacecraft, 4. Fourth electromagnetic spacecraft, 5. Fifth electromagnetic spacecraft, 6. Sixth electromagnetic spacecraft, 7. Space failure satellite. DETAILED DESCRIPTION

[0101] The embodiments described below with reference to the accompanying drawings are exemplary and are intended to explain the present invention, but should not be construed as limiting the present invention.

[0102] This embodiment provides a method for non-contact orbit change control of a space-deactivated satellite in a pyramid-shaped electromagnetic formation, and the specific steps are as follows:

[0103] Step 1: According to the radius R of the space failure satellite t , conductivity σ t , mass m t , and the magnetic moment m of the electromagnetic spacecraft j Bj (j=1,2,...,6), the rotational angular velocity ω of the magnetic moment mj (j=1,2,...,6), and the relative distance r between the electromagnetic spacecraft j (j=1,2,...,6) and the space failure satellite tj (As attached Figure 1As shown), determine the maximum thrust acceleration a applied to the space failure satellite max ;

[0104] Reference Figure 2 As shown, in the magnetic moment spherical coordinate system, the electromagnetic force F of the electromagnetic spacecraft j on the non-cooperative failed satellite in space is established tj and electromagnetic torque T tj for

[0105]

[0106]

[0107] Where, Represents the three coordinate basis vectors of the magnetic moment spherical coordinate system,

[0108] m Bj,n =||m Bj ||2 means m Bj 2-norm of ; n represents the norm;

[0109] Let l tj =||r tj ||2 represents r tj 2-norm, μ0 is the vacuum permeability, ω mn =||ω mj ||2 represents ω mj The 2-norm of Represents ω mj and r tj The angle between them, where atan(·) is the inverse tangent function, then F r (m Bj,n ,ω mj ) is calculated as:

[0110]

[0111] in,

[0112]

[0113] F φ (m Bj,n ,ω mj ) is calculated as

[0114] F φ (m Bj,n ,ω mj )=F φ1 sin(θ tj ) (26)

[0115] in,

[0116] T r (m Bj,n ,ω mj ) is calculated as

[0117] T r (m Bj,n ,ω mj )=T r1 cos(θ tj ) (27)

[0118] in,

[0119] T θ (m Bj,n ,ω mj ) is calculated as

[0120] T θ (m Bj,n ,ω mj )=T θ1 sin(θ tj ) (28)

[0121] in,

[0122] Calculate the maximum electromagnetic force F max for:

[0123]

[0124] Calculate the maximum electromagnetic torque T max :

[0125]

[0126] Thus, the maximum thrust acceleration a applied to the space failure satellite can be obtained max for

[0127]

[0128] Step 2: According to the initial orbital height r of the space failure satellite h0 , final orbit height r h1 , initial orbital inclination i0, final orbital inclination i1, and maximum thrust acceleration a max , the position r of the satellite with space failure at time t t (t) and velocity v t (t), the expected thrust acceleration a at time t during the orbit transfer process can be determined d (t) and the duration of the entire transfer process t f .

[0129] From the initial orbit height r h0 and the final orbital height r h1 The initial orbital velocity v0 and the final orbital velocity v1 can be calculated as

[0130]

[0131] Where G M represents the gravitational constant;

[0132] The absolute value of the inclination change during the entire orbit transfer process is calculated as Δi tot =|i f -i0|, then the thruster yaw angle β0 at the initial moment is

[0133]

[0134] The velocity increment ΔV during the entire orbit transfer process tot for

[0135]

[0136] The duration of the entire transfer process is t f for

[0137]

[0138] The thruster yaw angle β(t) at time t during the orbit transfer process is:

[0139]

[0140] The expected thrust acceleration a at time t during the orbit transfer process is d (t) is

[0141]

[0142] Where,

[0143] Step 3: Based on the initial position r of the space failure satellite t (0) and initial velocity v t (0), the duration of the entire transfer process t f , and the expected thrust acceleration a at time t during the orbit transfer process d (t), get the expected position r td (t) and the desired velocity v td (t);

[0144] Establish the initial value problem of the ordinary differential equation for the orbital motion of the space failure satellite:

[0145]

[0146] Solve the initial value problem of the ordinary differential equation and obtain the desired position r td (t) and the desired velocity v td (t).

[0147] Step 4: According to the position r of the space failure satellite at time t during the orbit transfer process t (t), speed v t (t), expected position r td (t), expected speed v td (t), expected thrust acceleration a d (t), the relative distance r between electromagnetic spacecraft j (j = 1, 2, ..., 6) and the space failure satellite tj , with the 2-norm m of the magnetic moment of electromagnetic spacecraft j Bj,n (j=1,2,...,6), the rotational angular velocity ω of the magnetic moment mj (j=1,2,...,6) is the controlled variable, and a nonlinear model predictive controller is designed to obtain the m of the electromagnetic spacecraft j at time t. Bj,n (t) and ω mj (t) to realize the contactless orbit change control of the space-inoperative satellite under the pyramid-type electromagnetic formation.

[0148] The objective function of designing a nonlinear model predictive controller is:

[0149]

[0150] in, The superscript T on the right represents the transpose operation of the vector, and N represents the prediction step size of the model predictive controller;

[0151] The kinetic equation is

[0152]

[0153] The function f in equation (40) d (·,·) is the fourth-order Runge-Kutta discretization of the following differential equation:

[0154]

[0155] in,

[0156] The physical constraints are

[0157]

[0158] Among them, 1 3×1 =[1 1 1] T represents a column vector with 3 rows and 1 column and all elements are 1, 03×1 Represents a column vector with 3 rows and 1 column whose elements are all 0.

[0159] The model predictive control optimization problem is then

[0160]

[0161] Satisfy the constraints:

[0162] Solve the model predictive control optimization problem at time t and obtain the optimal solution Then the m of electromagnetic spacecraft j at time t is Bj,n (t) and ω mj (t) is

[0163]

[0164] By solving the model predictive control optimization problem (43) in real time, we can obtain m Bj,n (t) and ω mj (t). By setting the magnetic moment of the electromagnetic spacecraft to m Bj,n (t), the angular velocity of magnetic moment rotation is ω mj (t), the non-contact orbit change control of the space-invalid satellite in the pyramid-shaped electromagnetic formation can be realized.

[0165] Numerical simulation verification

[0166] The physical parameters of the failed satellite in the numerical simulation are: mass m t =1413.7(kg), conductivity σ t =3.767×10 7 (S / m), radius R t =0.5(m); orbital parameters are: initial orbital height r of the space failure satellite h0 =3.5786×10 7 (m), final track height r h1 =3.8786×10 7 (m), initial orbital inclination i0 = 0 (deg), final orbital inclination i1 = 0 (deg); initial position r of the space failure satellite t (0) = [4.2164 × 10 7 ;0;0](m) and initial velocity v t (0) = [0; 3.0747 × 10 3 ;0](m).

[0167] By using the above parameters, the first step of the implementation can calculate the maximum thrust acceleration a applied to the space failure satellite. max =7.0154×10 -6 (m / s2 );

[0168] The second step of implementation is to calculate the duration t of the entire transfer process. f =1.5404×10 6 (s), the expected thrust acceleration a at time t during the orbit transfer process d (t) = [0; 7.0154 × 10 -6 ;0];

[0169] Implementation steps Step 3 Expected position r td (t) and the desired velocity v td (t), as follows Figure 4 and 5 As shown;

[0170] The fourth step of implementation is to calculate the magnetic moment of each electromagnetic spacecraft in real time as m Bj,n (t), the angular velocity of magnetic moment rotation is ω mj (t), as follows Figure 6 and 7 As shown: The electromagnetic thrust acting on the failed satellite is as follows Figure 8 As shown; under the action of this electromagnetic thrust, the position, position deviation and orbital radius changes of the space failure satellite are as follows Figure 9-11 shown.

[0171] from Figure 10 It can be seen from the figure that during the entire non-contact orbit change control process, the deviation between the three-dimensional position of the failed satellite and the expected trajectory does not exceed 2mm, that is, the electromagnetic thrust achieves precise position control of the failed satellite. Figure 11 It can be seen that the orbital radius of the failed satellite gradually increased and finally reached the required orbital radius, realizing the non-contact orbit change control of the failed satellite in space by the pyramid-shaped electromagnetic formation.

[0172] Although the embodiments of the present invention have been shown and described above, it will be understood that the above embodiments are illustrative and are not to be construed as limitations on the present invention. A person skilled in the art may change, modify, replace and modify the above embodiments within the scope of the present invention without departing from the principles and purpose of the present invention.

Claims

1. A non-contact orbit change control method for space-failed satellites in a pyramid-shaped electromagnetic formation, characterized in that The specific steps are as follows: Determine the maximum thrust acceleration applied to a satellite that fails in space; Determine the expected thrust acceleration during the orbit transfer process and the duration of the entire transfer process; Establish an orbital motion model to obtain the desired position and desired velocity; A nonlinear model predictive controller is designed to obtain the 2-norm and rotational angular velocity of the electromagnetic spacecraft, and to realize non-contact orbit change control of a space-failed satellite in a pyramid-type electromagnetic formation.

2. The non-contact orbit change control method for space-failed satellites in a pyramid-shaped electromagnetic formation according to claim 1, characterized in that: The maximum thrust acceleration applied to the space failure satellite is: Among them, F max is the maximum electromagnetic force, m t is the mass of the satellite that fails in space.

3. The non-contact orbit change control method for a space-failed satellite in a pyramid-shaped electromagnetic formation according to claim 1, characterized in that: The method for determining the maximum thrust acceleration applied to the inoperative satellite in space is as follows: In the magnetic moment spherical coordinate system, the electromagnetic force F exerted by electromagnetic spacecraft j on the non-cooperative failed satellite in space is established. tj and electromagnetic torque T tj for: Where, Represents the three coordinate basis vectors of the magnetic moment spherical coordinate system, r tj Represents the relative distance between space failure satellites, m Bj,n =||m Bj ||2 means m Bj 2-norm, n represents the norm, m Bj (j=1,2,...,6) represents the magnetic moment of electromagnetic spacecraft j, ω mj (j=1,2,...,6) represents the rotational angular velocity of the magnetic moment; let l tj =||r tj ||2 represents r tj 2-norm, μ0 is the vacuum permeability, ω mn =||ω mj ||2 represents ω mj The 2-norm of Represents ω mj and r tj The angle between them, where atan(·) is the inverse tangent function, then F r (m Bj,n ,ω mj ) is calculated as: in, F φ (m Bj,n ,ω mj ) is calculated as: F φ (m Bj,n ,oh mj )=F φ1 sin(θ tj ) (4) in, T r (m Bj,n ,ω mj ) is calculated as: T r (m Bj,n ,oh mj )=T r1 cos(θ tj ) (5) in, T θ (m Bj,n ,ω mj ) is calculated as: T θ (m Bj,n ,oh mj )=T θ1 sin(θ tj ) (6) in, Calculate the maximum electromagnetic force F max for: Calculate the maximum electromagnetic torque T max : Thus, the maximum thrust acceleration a applied to the space failure satellite is obtained max for 。 4. The non-contact orbit change control method for a space-failed satellite in a pyramid-shaped electromagnetic formation according to claim 2 or 3, characterized in that: The duration of the entire transfer process t f for Where, ΔV tot Represents the velocity increment of the entire orbit transfer process; a max Indicates the maximum thrust acceleration.

5. The method for non-contact orbit change control of a space-failed satellite in a pyramid-shaped electromagnetic formation according to claim 4, characterized in that: The expected thrust acceleration a d (t) is Where, 6. The non-contact orbit change control method for space-failed satellites in a pyramid-shaped electromagnetic formation according to claim 5, characterized in that: The method for determining the expected thrust acceleration during the orbit transfer process and the duration of the entire transfer process is as follows: The initial orbital height r of the space failure satellite h0 and the final orbital height r h1 The initial orbital velocity v0 and the final orbital velocity v1 are calculated as Where G M represents the gravitational constant; The absolute value of the inclination change during the entire orbit transfer process is calculated as Δi tot =|i f -i0|, then the thruster yaw angle β0 at the initial moment is The velocity increment ΔV during the entire orbit transfer process tot for The duration of the entire transfer process is t f for The thruster yaw angle β(t) at time t during the orbit transfer process is: The expected thrust acceleration a at time t during the orbit transfer process is d (t) is Where, 7. The method for non-contact orbit change control of a space-failed satellite in a pyramid-shaped electromagnetic formation according to claim 6, characterized in that: The method for obtaining the desired position and desired speed is: Establish the initial value problem of the ordinary differential equation for the orbital motion of the space failure satellite: Solve the initial value problem of the ordinary differential equation and obtain the desired position r td (t) and the desired velocity v td (t); A nonlinear model predictive controller is designed to obtain the 2-norm and rotational angular velocity of the electromagnetic spacecraft, and to realize non-contact orbit change control of a space-failed satellite in a pyramid-type electromagnetic formation.

8. The non-contact orbit change control method for space-failed satellites in a pyramid-shaped electromagnetic formation according to claim 7, characterized in that: The objective function of the nonlinear model predictive controller is: in, The superscript T on the right represents the transpose operation of the vector, and N represents the prediction step size of the model predictive controller; m t Indicates the mass of a satellite that has failed in space.

9. The non-contact orbit change control method for space-failed satellites in a pyramid-shaped electromagnetic formation according to claim 8, characterized in that: The non-contact orbit change control method for a space-inoperative satellite in the pyramid-type electromagnetic formation is as follows: The objective function of designing a nonlinear model predictive controller is: in, The superscript T on the right represents the transpose operation of the vector, and N represents the prediction step size of the model predictive controller; The kinetic equation is The function f in the equation d (·,·) is the fourth-order Runge-Kutta discretization of the following differential equation: in, The physical constraints are Among them, 1 3×1 =[1 1 1] T represents a column vector with 3 rows and 1 column and all elements are 1, 0 3×1 represents a column vector with 3 rows and 1 column and all elements are 0; The model predictive control optimization problem is then Satisfy the constraints: Solve the model predictive control optimization problem at time t and obtain the optimal solution Then the m of electromagnetic spacecraft j at time t is Bj,n (t) and ω mj (t) is By solving the model predictive control optimization problem in real time, we can obtain m Bj,n (t) and ω mj (t); By setting the magnetic moment of the electromagnetic spacecraft to m Bj,n (t), the angular velocity of magnetic moment rotation is ω mj (t), the non-contact orbit change control of the space-invalid satellite in the pyramid-shaped electromagnetic formation can be realized.

Images