A method for attitude magnetic tracking control in satellite orbit transfer

Abstract

The present invention is applicable to the field of aerospace control technology, and provides a method for attitude magnetic tracking control in satellite orbit transfer, the method comprising: controlling the satellite attitude by three orthogonal magnetic torquers installed along the +X, +Y and +Z axis directions of the satellite; obtaining the expected angle during the satellite orbit transfer, and when the actual angle is close to the expected angle, compensating the torque generated by thrust with the torque generated by gravity; tracking control of the satellite attitude is performed by using a preset sliding mode control law based on an auxiliary compensator and taking the difference between the actual magnetic control torque and the ideal magnetic control torque as the input of the auxiliary compensator; the present invention uses the magnetic torquer as an attitude control actuator in the satellite orbit transfer, plans the expected angle during the satellite orbit transfer, and can compensate the torque generated by thrust with the torque generated by gravity when the actual angle is close to the target angle, thereby ensuring the stability of the satellite system and reducing the energy consumption of the magnetic torquer.

Description

Technical Field

[0001] The invention belongs to the field of aerospace control technology, and in particular relates to an attitude magnetic tracking control method in satellite orbit transfer. Background Art

[0002] Gravity gradient stabilization is the property that artificial or natural satellites have a stable equilibrium posture under the gravitational field of a central celestial body, so that they can maintain their orientation to the central celestial body. Gravity gradient stabilization has a simple structure, extremely low energy consumption, good economy and reliability, and is suitable for long-term operation. Therefore, using gravity gradient torque, an environmental torque, to achieve passive stabilization has become one of the options for long-term in-orbit satellites. In recent years, microsatellites have played an increasingly important role in the field of space applications due to their advantages such as light weight, small size, flexible launch methods, short development cycle and low cost.

[0003] The gravity gradient stabilized microsatellite consists of a main satellite and a terminal payload, which are connected by a deployable robotic arm. When the robotic arm is deployed, the required mass distribution of the star body can be achieved, the gravity gradient capture is completed, and the gravity gradient stabilization is achieved. When the satellite is in orbit, due to various factors, it is necessary to transfer the orbit, but this process also puts forward requirements for the attitude stability of the satellite. However, due to the configuration characteristics of the satellite, if the traditional pulse orbit transfer strategy is adopted during the orbit transfer, it will cause the satellite's equilibrium position to change, resulting in unstable satellite attitude. The magnetic torquer has the advantages of continuous and constant thrust, high reliability and low weight. Therefore, the magnetic torquer is considered as an attitude control mechanism during orbit transfer to maintain the stability of the satellite attitude. However, the thrust generated by the magnetic torquer can only be generated in the plane perpendicular to the magnetic flux lines of the instantaneous geomagnetic field. The magnetic constraint has a greater impact on the control of the gravity gradient satellite. The direction of the force generated by it and gravity not only affects the attitude of the spacecraft during the orbit transfer, but also affects the tracking control of the spacecraft's attitude stability, so it needs to be improved. Summary of the invention

[0004] The purpose of the embodiment of the present invention is to provide a magnetic tracking control method for attitude in satellite orbit transfer, which uses a magnetic torquer as an attitude control actuator in satellite orbit transfer, plans the expected angle during satellite orbit transfer, and can compensate the torque generated by thrust with the torque generated by gravity when the actual angle is close to the target angle, thereby ensuring the stability of the system and reducing the energy consumption of the magnetic torquer; at the same time, a sliding mode control law based on an auxiliary compensator is designed in the attitude control system, and the difference between the actual magnetic control torque and the ideal magnetic control torque is used as the input of the auxiliary compensator, so as to achieve rapid attitude tracking control within a limited time, and effectively improve the robustness and stability of the satellite system; the embodiment of the present invention takes a gravity gradient stabilized microsatellite as a specific object, and the proposed control method has strong applicability, high reliability and low energy consumption, has practical engineering application value, and can solve the problems of satellite attitude instability caused by continuous thrust in a fixed direction and control torque limitation output by a magnetic torquer during the orbit transfer of a gravity gradient stabilized microsatellite.

[0005] In the gravity gradient microsatellite attitude control system, the attitude control system is generally composed of the satellite body, deployable robotic arm, terminal payload, attitude control computer and magnetic torquer. Figure 1 ; The method provided in an embodiment of the present invention uses a magnetic torquer as an actuator in satellite orbit transfer to control the generated magnetic control torque to maintain the attitude stability of the satellite during orbital maneuvers.

[0006] The embodiment of the present invention is implemented as follows: a method for attitude magnetic tracking control in satellite orbit transfer, the method is applied to a gravity gradient stabilized microsatellite consisting of a main satellite and a terminal payload connected by a deployable mechanical arm, and a magnetic torquer is used as an attitude controller in satellite orbit transfer, the method comprising:

[0007] Establish the satellite coordinate system OXYZ, where the origin O is the satellite center of mass, the +X axis points to the satellite flight direction, the +Z axis points to the center of the earth, and the +Y axis satisfies the right-hand rule and is perpendicular to the plane formed by XOZ. The satellite attitude is controlled by three orthogonal magnetic torquers installed along the +X, +Y and +Z axes of the satellite.

[0008] Obtain the expected angle of the satellite orbit transfer, and when the actual angle is close to the expected angle, compensate the torque generated by the thrust with the torque generated by gravity;

[0009] Through the preset sliding mode control law based on the auxiliary compensator, the difference between the actual magnetic control torque and the ideal magnetic control torque is used as the input of the auxiliary compensator to track the satellite attitude.

[0010] Furthermore, the method further comprises:

[0011] Establish the attitude dynamics equation and kinematics equation of the gravity gradient stabilized microsatellite:

[0012]

[0013] f(ω, t) = -ω x Iω+M G +M F ,

[0014] Among them, M C =U×B is the actual magnetic control torque generated by the magnetic torquer, I is the overall moment of inertia of the satellite, ω=[ω x ,ω y ,ω z ] T represents the angular velocity of the satellite, ω x is the cross-product antisymmetric matrix of ω, M G and M F are the torques generated by gravity and thrust, respectively, Δf(ω, t) represents the uncertainty of the satellite system, and ||Δf(ω, t)|| ∞ =Δf(ω, t), Δd is the external disturbance torque, and ||Δd(t)||=Δd max (t);

[0015] At the same time, the attitude kinematic model of the gravity gradient stabilized microsatellite is established as follows:

[0016]

[0017] in, is the satellite attitude angle, ψ, θ, are the yaw angle, pitch angle and roll angle respectively, ω r =ω-ω0=[ω x ,ω y ,ω z ] T is the angular velocity of the satellite body relative to the orbital system, ω0 is the angular velocity of the orbital system, so:

[0018]

[0019] R(Φ) is the rotation matrix for satellite attitude control.

[0020] Furthermore, the step of obtaining the expected angle when the satellite orbit is transferred specifically includes:

[0021] Based on the lateral orbit transfer strategy, polar coordinates are used to derive and establish the functions of the satellite's polar angle, distance from the center of the earth and time, so as to calculate the orbit transfer time and lateral thrust acceleration as follows:

[0022]

[0023]

[0024] in, μ=3.986×10 5 km 3 / s 2 is the gravitational constant of the earth, r0 is the initial value of the distance between the satellite's center of mass and the center of the earth, and f u is the value of the lateral thrust acceleration, and f u =F(m+M) -1 , F is the value of thrust;

[0025] The functions of polar angle u and distance from the center of the earth r with respect to time t are obtained as follows:

[0026]

[0027]

[0028] Where u0 is the initial value of the polar angle; when u-u0 = 2nπ, the satellite orbit returns to a circular orbit, at which time the orbit change time T and the lateral thrust acceleration f u It can be expressed as:

[0029]

[0030]

[0031] Among them, r0 and r f are the distances between the satellite and the center of the Earth in the original orbit and the orbit after transfer, respectively;

[0032] Considering the torque generated by thrust and gravity during orbit transfer, the expected three-axis attitude angle position is obtained, and then the expected angle of the satellite orbit transfer is obtained.

[0033] Furthermore, the step of taking into account the torque generated by the thrust and gravity during the orbit transfer to obtain the expected three-axis attitude angle position specifically includes:

[0034] The satellite's three-axis attitude angles ψ, θ, φ are defined by the projection of the unit vector l in the orbital coordinate system as follows:

[0035]

[0036] According to the momentum theorem, the attitude dynamics equation of the satellite in the uncontrolled state can be expressed as:

[0037]

[0038] Among them, M G and M Fare the moments generated by gravity gradient and thrust respectively; angular momentum H = I × ω, I is the tensor of the moment of inertia around the principal axis of inertia, angular velocity

[0039] At the same time, the moment M generated by the gravity gradient G It can be expressed as:

[0040] M G ≈3μr -3 k×(I·k)=3μr -3 I(l×k)(l·k),

[0041] Where r is the distance between the satellite and the center of the earth, μ = 3.986 × 10 5 km 3 / s 2 is the gravitational constant of the earth, I=Mm(M+m) -1 l 2 ;

[0042] At the same time, the torque M generated by the thrust F It can be expressed as:

[0043] M F =-lm(M+m) -1 F×l,

[0044] The dynamic model expression of angular acceleration is as follows:

[0045]

[0046]

[0047] In the formula, It can be seen that in the obtained kinetic model, there exists The equilibrium position of

[0048] At time t = τ, the distance from the center of the earth r(t) is expressed as r| t＝τ , so the expected attitude trajectory of the pitch angle θc(t) and roll angle φc(t) during the coplanar orbit transfer can be expressed as:

[0049]

[0050]

[0051] in, is θ e The stable center point, f u is the value of the lateral thrust acceleration, l is the unit vector pointing from the satellite's center of mass to the center of the earth;

[0052] in, Assume parameter k u is a constant, and the equilibrium position obtained under this assumption is defined as the expected attitude angle at that moment.

[0053] Furthermore, the method further comprises: calculating an actual magnetic control torque acting on the satellite, specifically comprising:

[0054] The magnetic dipole moment U is defined as:

[0055]

[0056] in, is the ideal magnetic control torque, M C for The component perpendicular to the geomagnetic field vector B, and M C It can be expressed as a singular matrix Γ B and The product of

[0057] The actual magnetic control torque acting on the satellite can be expressed as:

[0058]

[0059] Furthermore, the method further comprises: designing an auxiliary compensator, specifically comprising:

[0060] The actual magnetic control torque M C With ideal magnetic control torque The difference ΔM C The auxiliary compensator for input drive has:

[0061]

[0062] Among them, λ = [λ1, λ2, λ3, λ4, λ5, λ6] T ,

[0063]

[0064] To ensure the characteristic root λ i →0(i=1,2,...6), the matrix A is set to the Hurwitz matrix, so there is a i >0 (i=1, 2, 3, ..., 6).

[0065] Furthermore, in the sliding mode control law based on the auxiliary compensator, the sliding mode surface of the initial controller satisfies:

[0066] s=(ω r -ω rc )+k q (q r -qrc ),

[0067] Among them, ω rc =[0,0,0] T is the expected angular velocity, let Q c =[q 1c ,q rc ] T is the expected attitude quaternion, when s≡[0, 0, 0] T When the actual attitude quaternion converges to the expected quaternion in an exponential form, k q is any positive real number;

[0068] The sliding surface is improved as follows:

[0069]

[0070] In the formula,

[0071] The sliding mode control law based on the auxiliary compensator is obtained, which satisfies:

[0072]

[0073]

[0074] Where η>Δf max (ω, t)+Δd max (t), k s represents the exponential term, and has:

[0075]

[0076] The embodiment of the present invention provides a method for attitude magnetic tracking control in satellite orbit transfer. After planning the expected angle during satellite orbit transfer, when the actual angle is close to the target angle, the torque generated by gravity can be used to compensate the torque generated by thrust, thereby ensuring the stability of the system while reducing the energy consumption of the magnetic torquer. At the same time, a sliding mode control law based on an auxiliary compensator is designed in the attitude control system, and the difference between the actual magnetic control torque and the ideal magnetic control torque is used as the input of the auxiliary compensator, which can realize rapid tracking control of the attitude within a limited time, and effectively improve the robustness and stability of the system. Taking the gravity gradient stabilized microsatellite as a specific object, it is verified that the proposed method has strong applicability, high reliability and low energy consumption. BRIEF DESCRIPTION OF THE DRAWINGS

[0077] Figure 1 A schematic diagram of a gravity gradient micro-satellite provided by an embodiment of the present invention;

[0078] Figure 2 A schematic diagram of a coordinate system established based on a gravity gradient stabilized microsatellite in an embodiment of the present invention;

[0079] Figure 3 A schematic flow chart of a method for attitude magnetic tracking control in satellite orbit transfer provided by an embodiment of the present invention;

[0080] Figure 4 It is a three-axis attitude angle definition diagram of the gravity gradient micro-satellite in an embodiment of the present invention;

[0081] Figure 5 is the instantaneous geomagnetic field vector B, the magnetic dipole moment U generated by the magnetic torquer, and the actual control torque M generated by the magnetic torquer in the embodiment of the present invention. C , the desired control torque Direction diagram of

[0082] Figure 6 1 is a principle block diagram of a sliding mode controller (sliding mode control law) based on an auxiliary compensator in an embodiment of the present invention;

[0083] Figure 7 The curves showing the changes of attitude angle and orbit height in orbit transfer under control and uncontrolled conditions in the embodiment of the present invention;

[0084] Figure 8 The curve of the change of attitude angle in the orbit transfer when the compensator is used and when the compensator is not used in the embodiment of the present invention;

[0085] Fig. 9 This is a curve showing how the gravity gradient torque, the torque generated by the thrust, the control torque output by the magnetic torquer, and the difference between the actual control torque and the ideal control torque change over time after the sliding mode controller based on the auxiliary compensator is adopted in the embodiment of the present invention. DETAILED DESCRIPTION

[0086] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0087] like Figure 1-Figure 9 As shown, in one embodiment, a method for attitude magnetic tracking control in satellite orbit transfer is applied to a gravity gradient stabilized microsatellite consisting of a main satellite and a terminal payload connected by a deployable mechanical arm, and a magnetic torquer is used as an attitude controller in satellite orbit transfer. The method includes:

[0088] Establish the satellite coordinate system OXYZ, where the origin O is the satellite center of mass, the +X axis points to the satellite flight direction, the +Z axis points to the center of the earth, and the +Y axis satisfies the right-hand rule and is perpendicular to the plane formed by XOZ. The satellite attitude is controlled by three orthogonal magnetic torquers installed along the +X, +Y and +Z axes of the satellite.

[0089] Obtain the expected angle of the satellite orbit transfer, and when the actual angle is close to the expected angle, compensate the torque generated by the thrust with the torque generated by gravity;

[0090] The satellite attitude is tracked and controlled by using the preset sliding mode control law based on the auxiliary compensator and taking the difference between the actual magnetic control torque and the ideal magnetic control torque as the input of the auxiliary compensator.

[0091] In this embodiment, the gravity gradient microsatellite is composed of a satellite platform (main satellite), a deployable mechanical arm (or gravity gradient rod) and a terminal payload, which can be regarded as a dumbbell model;

[0092] It is understandable that the connection between the main satellite, the deployable robotic arm and the terminal payload is a conventional technical means in the art and will not be described in detail here;

[0093] Among them, the gravity gradient stabilized microsatellite is regarded as a dumbbell model, and the attitude dynamics equation and kinematics equation of the gravity gradient stabilized microsatellite are established by considering the actuator, i.e., the magnetic torquer, and external interference:

[0094]

[0095] Where f(ω, t) = -ω x Iω+M G +M F , M C =U×B is the actual magnetic control torque generated by the magnetic torquer, I is the overall moment of inertia of the satellite, ω=[ω x ,ω y ,ω z ] T represents the angular velocity of the satellite, ω x is the cross-product antisymmetric matrix of ω.

[0096] M G and M F are the torques generated by gravity and thrust, respectively, Δf(ω, t) represents the uncertainty of the satellite system, and ||Δf(ω, t)|| ∞ =Δf(ω, t), Δd is the external disturbance torque, including the atmospheric drag torque and the solar pressure torque, and ||Δd(t)||=Δd max (t).

[0097] At the same time, the attitude kinematic model of the gravity gradient stabilized microsatellite is established as follows:

[0098]

[0099] in, is the satellite attitude angle, ψ, θ, are the yaw angle, pitch angle and roll angle, which rotate in a 3-2-1 order, ω r =ω-ω0=[ω x ,ω y ,ω z ] T is the angular velocity of the satellite body relative to the orbital system, ω0 is the angular velocity of the orbital system, so:

[0100]

[0101] R(Φ) is the rotation matrix for satellite attitude control.

[0102] The method in this embodiment also includes: applying continuous small thrust to the satellite based on the lateral orbit transfer strategy, and using polar coordinates to derive and establish functions of the polar angle of the satellite's position and the distance from the center of the earth and time respectively;

[0103] In one example, by describing in a polar coordinate system, the function of the satellite orbit transfer time and the distance from the center of the earth can be obtained, thereby calculating the orbit transfer time and the lateral thrust acceleration;

[0104] In one example, the step of obtaining the expected angle of the satellite orbit transfer specifically includes:

[0105] Based on the lateral orbit transfer strategy, polar coordinates are used to derive and establish the functions of the satellite's polar angle, distance from the center of the earth and time, so as to calculate the orbit transfer time and lateral thrust acceleration as follows:

[0106]

[0107]

[0108] in, μ=3.986×10 5 km 3 / s 2 is the gravitational constant of the earth, r0 is the initial value of the distance between the satellite's center of mass and the center of the earth, and f u is the value of the lateral thrust acceleration, and f u =F(m+M) -1 , F is the value of thrust;

[0109] The functions of polar angle u and distance from the center of the earth r with respect to time t are obtained as follows:

[0110]

[0111]

[0112] Where u0 is the initial value of the polar angle; when u-u0 = 2nπ, the satellite orbit returns to a circular orbit, at which time the orbit change time T and the lateral thrust acceleration f u It can be expressed as:

[0113]

[0114]

[0115] Among them, r0 and r f are the distances between the satellite and the center of the Earth in the original orbit and the orbit after transfer, respectively;

[0116] Since the thrust generated by gravity and thrust has a great influence on the satellite attitude motion, the satellite is regarded as a dumbbell model with a rigid rod connecting the two ends of the mass, and an ideal attitude motion trajectory is designed to avoid the attitude disorder of the gravity gradient microsatellite. In addition, as the actual pitch angle θ of the satellite approaches the expected attitude trajectory, the torque M generated by the thrust F The gravity gradient moment M G Compensation can be performed to effectively reduce the energy consumption of the attitude controller.

[0117] Considering the torque generated by thrust and gravity during orbit transfer, the expected three-axis attitude angle position is obtained, and then the expected angle of the satellite orbit transfer is obtained.

[0118] like Figure 4 As shown, in an example of an embodiment, the step of considering the torque generated by the thrust and gravity in the orbit transfer to obtain the expected three-axis attitude angle position specifically includes:

[0119] The satellite's three-axis attitude angles ψ, θ, φ are defined by the projection of the unit vector l in the orbital coordinate system as follows:

[0120]

[0121] According to the momentum theorem, the attitude dynamics equation of the satellite in the uncontrolled state can be expressed as:

[0122]

[0123] Among them, M G and M F are the moments generated by gravity gradient and thrust respectively; angular momentum H = I × ω, I is the tensor of the moment of inertia around the principal axis of inertia, angular velocity

[0124] At the same time, the moment M generated by the gravity gradient G It can be expressed as:

[0125] M G ≈3μr -3 k×(I·k)=3μr -3 I(l×k)(l·k),

[0126] Where r is the distance between the satellite and the center of the earth, μ = 3.986 × 10 5 km 3 / s 2 is the gravitational constant of the earth, I=Mm(M+m) -1 l 2 ;

[0127] At the same time, the torque M generated by the thrust F It can be expressed as:

[0128] M F =-lm(M+m) -1 F×l,

[0129] The dynamic model expression of angular acceleration is as follows:

[0130]

[0131]

[0132] In the formula,

[0133] It can be seen that in the obtained kinetic model, there exists At the same time, since the initial value of the roll angle is small, the coupling between the pitch angle and the roll angle can be ignored in the orbit transfer. Therefore, the equilibrium position and characteristics of the pitch angle θ≡0 can be seen in Table 1 below.

[0134] Table 1 shows the pitch angle equilibrium position and its properties

[0135]

[0136] in, Assume parameter k u is a constant, and the equilibrium position obtained under this assumption is defined as the expected attitude angle at that moment;

[0137] At time t = τ, the distance from the center of the earth r(t) is expressed as r| t＝τ , so the pitch angle θ during the coplanar orbit transfer process C (t) and roll angle φ C The expected posture trajectory of (t) can be expressed as:

[0138]

[0139]

[0140] in, is θ e The stable center point, f u is the value of the lateral thrust acceleration, l is the unit vector pointing from the satellite's center of mass to the center of the earth; it can be defined as the expected attitude angle at that moment based on the obtained equilibrium position.

[0141] In one embodiment, the actual magnetic control torque acting on the satellite is calculated to solve the problem of limited direction of the control torque generated by the magnetic torquer. Figure 5 , define B, U, M C , Direction; M C for The component perpendicular to the geomagnetic field vector B, and M C It can be expressed as a singular matrix Γ B and The product of in, is the ideal magnetic control torque.

[0142] In an example of this embodiment, the method further includes: calculating an actual magnetic control torque acting on the satellite, specifically including:

[0143] The magnetic dipole moment U is defined as:

[0144]

[0145] The actual magnetic control torque acting on the satellite can be expressed as:

[0146]

[0147] In an example of this embodiment, since the control torque output by the magnetic torquer is constrained by the magnetic field direction vector, the global controllability of the designed controller cannot be guaranteed; further improvements can be made.

[0148] In an example of this embodiment, it can be obtained that the global stability of the system is related to ω and Γ B The value of is closely related to and is largely limited by the direction of the output torque of the magnetic torquer. Figure 6 , design an adaptive auxiliary compensator;

[0149] For example: Design auxiliary compensators, including:

[0150] The actual magnetic control torque M C With ideal magnetic control torque The difference ΔM C The auxiliary compensator for input drive has:

[0151]

[0152] Among them, λ = [λ1, λ2, λ3, λ4, λ5, λ6] T ,

[0153]

[0154] To ensure the characteristic root λ i →0(i=1,2,...6), the matrix A is set to the Hurwitz matrix, so there is a i >0 (i=1, 2, 3, ..., 6), and to avoid ΔM C Too large will cause system instability, so you need to ensure a i Big enough.

[0155] In one embodiment, for the designed auxiliary compensator, an improved sliding mode controller is designed according to the planned attitude path to perform attitude tracking control;

[0156] For example, in the sliding mode control law based on the auxiliary compensator, the sliding mode surface of the initial controller satisfies:

[0157] s=(ω r -ω rc )+k q (q r -q rc ),

[0158] Among them, ω rc =[0,0,0] T is the expected angular velocity, let Q c =[q 1c ,q rc ] T is the expected attitude quaternion, when s≡[0,0,0] T When the actual attitude quaternion converges to the expected quaternion in an exponential form, k q is any positive real number;

[0159] The sliding surface is improved as follows:

[0160]

[0161] In the formula,

[0162] The sliding mode control law based on the auxiliary compensator is obtained, which satisfies:

[0163]

[0164]

[0165] Where η>Δf max (ω, t)+Δd max (t), k s represents the exponential term, and has:

[0166]

[0167] like Figure 7-Figure 9 As shown, in one embodiment, a magnetic torquer product of Beijing Zhongke Jiuzhang Space Technology Development Co., Ltd. is used to conduct a simulation experiment on a micro-satellite with stable gravity gradient. The micro-satellite consists of a satellite platform, a deployable mechanical arm and a terminal payload. The satellite parameters and initial conditions are given as follows:

[0168] 1) Orbital altitude r0 = 7000 km, given thrust F = 0.1 mN (in the lateral direction);

[0169] 2) Satellite moment of inertia I = diag(18.141, 18.141, 0.458) kg·m 2 , satellite platform mass m main =30kg, effective load (rigid satellite) m sub =5kg, deployable robotic arm length L = 2m;

[0170] 3) Satellite initial attitude angle ψ0 = 1°, θ0 = 1°, The total simulation duration is 10 orbital periods.

[0171] The simulation results are analyzed as follows:

[0172] Figure 7 The simulation results of the three-axis attitude angle and orbital altitude changes of a microsatellite using a controller and gravity gradient stabilization in an uncontrolled state during orbit transfer are shown in the following figure.

[0173] Attitude tracking control during orbit transfer can effectively avoid attitude angle disturbance and facilitate satellite mission execution.

[0174] Figure 8 The simulation results of the three-axis attitude angle change of a microsatellite with stable gravity gradient and controlled by a sliding mode controller when performing orbit transfer with and without a compensator are shown in the figure. The simulation results show that after adding the compensator, the three-axis attitude angle change is smaller and the attitude tracking speed is faster, which effectively improves the robustness and stability of the system.

[0175] Fig. 9The simulation results of the gravity gradient torque, the torque generated by the thrust, the control torque output by the magnetic torquer, and the difference between the actual control torque and the ideal control torque over time after the sliding mode controller based on the auxiliary compensator is adopted. The simulation results show that when the pitch angle is close to the expected attitude trajectory, the torque generated by the thrust can be compensated by the gravity gradient torque, which can maintain attitude stability while reducing energy consumption.

[0176] It can be seen from the above simulation results that the attitude magnetic tracking control method in satellite orbit transfer proposed in this embodiment is effective, which is not only conducive to avoiding attitude disorder, but also can reduce the energy consumption of the magnetic torquer, and provides a reference for the research of gravity gradient microsatellite in orbit transfer.

[0177] The above-mentioned embodiments only express several implementation methods of the present invention, and the description thereof is relatively specific and detailed, but it cannot be understood as limiting the scope of the patent of the present invention. It should be pointed out that, for ordinary technicians in this field, several variations and improvements can be made without departing from the concept of the present invention, which all belong to the protection scope of the present invention. Therefore, the protection scope of the patent of the present invention shall be subject to the attached claims.

[0178] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for attitude magnetic tracking control in orbit transfer of a gravity gradient stabilized microsatellite, the method being applied to a gravity gradient stabilized microsatellite consisting of a main satellite and a terminal payload connected by a deployable mechanical arm, using a magnetic torquer as an attitude controller in satellite orbit transfer, characterized in that: The method comprises: The satellite coordinate system OXYZ is established, where the origin O is the satellite center of mass, the +X axis points to the satellite flight direction, the +Z axis points to the center of the earth, the +Y axis satisfies the right-hand rule and is perpendicular to the plane formed by XOZ. Three orthogonal magnetic torquers are installed along the +X, +Y and +Z axis directions of the satellite to control the satellite attitude. Establish the attitude dynamics equation and kinematics equation of the gravity gradient stabilized microsatellite: f(ω,t)=-ω × Iω+M G +M F , M C =U×B is the actual magnetic control torque generated by the magnetic torquer, where U is the magnetic dipole moment, B is the geomagnetic field vector, I is the overall moment of inertia of the satellite, ω=[ω x ,ω y ,ω z ] T represents the angular velocity of the satellite, ω × is the cross-product antisymmetric matrix of ω, M G and M F are the torques generated by gravity and thrust, respectively, Δf(ω,t) represents the uncertainty of the satellite system, and ||Δf(ω,t)|| ∞ =Δf(ω,t), Δd is the external disturbance torque, and ||Δd(t)||=Δd max (t); At the same time, the posture kinematic model is established as follows: in, is the satellite attitude angle, ψ, θ, are the yaw angle, pitch angle and roll angle respectively, ω r =ω-ω0=[ω x ,ω y ,ω z ] T is the angular velocity of the satellite body relative to the orbital system, ω0 is the angular velocity of the orbital system, so: R(Φ) is the rotation matrix of satellite attitude control; Based on the lateral orbit transfer strategy, polar coordinates are used to derive and establish the functions of the satellite's polar angle, distance from the center of the earth and time, so as to calculate the orbit transfer time and lateral thrust acceleration as follows: in, μ=3.986×10 5 km 3 / s 2 is the gravitational constant of the earth, r0 is the initial value of the distance between the satellite's center of mass and the center of the earth, and f u is the value of the lateral thrust acceleration, and f u =F(m+M) -1 , F is the value of thrust F, m is the mass of the terminal payload, and M is the mass of the main satellite; rearranging the equation, the functions of polar angle u and geocentric distance r with respect to time t are as follows: Among them, u0 is the initial value of the polar angle; When u-u0=2nπ, that is, when the satellite orbit returns to a circular orbit, the orbit change time T and the lateral thrust acceleration f u It is expressed as: Among them, r0 and r f are the distances between the satellite and the center of the Earth in the original orbit and the orbit after transfer, respectively; Considering the torque generated by thrust and gravity during orbit transfer, the expected three-axis attitude angle position is obtained, and then the expected angle of the satellite orbit transfer is obtained; Calculate the actual magnetic control torque acting on the satellite, including: The magnetic dipole moment U is defined as: in, is the ideal magnetic control torque, M C for The component perpendicular to the geomagnetic field vector B, M C Represented as a singular matrix Γ B and The product of The actual magnetic control torque acting on the satellite is expressed as: Obtain the expected angle of the satellite orbit transfer, and when the actual angle is close to the expected angle, compensate the torque generated by the thrust with the torque generated by gravity; Through the preset sliding mode control law based on the auxiliary compensator, the difference between the actual magnetic control torque and the ideal magnetic control torque is used as the input of the auxiliary compensator to track the satellite attitude.

2. The method according to claim 1, characterized in that: The step of taking into account the torque generated by the thrust and gravity during the orbit transfer to obtain the expected three-axis attitude angle position specifically includes: The satellite's three-axis attitude angles ψ, θ, The projection of the unit vector l in the orbital coordinate system is defined as follows: According to the momentum theorem, the attitude dynamics equation of the satellite in the uncontrolled state is expressed as: Among them, M G and M F are the moments generated by gravity gradient and thrust respectively; angular momentum H = I × ω, I is the tensor of the moment of inertia around the principal axis of inertia, angular velocity At the same time, the moment M generated by the gravity gradient G It is expressed as: M G ≈3μr -3 k×(I·k)=3μr -3 I(l×k)(l·k), Where r is the distance between the satellite and the center of the earth, μ = 3.986 × 10 5 km 3 / s 2 is the gravitational constant of the earth, I=Mm(M+m) - 1 l 2 ; At the same time, the torque M generated by the thrust F It is expressed as: M F =-lm(M+m) -1 F×l, The dynamic model expression of angular acceleration is as follows: In the formula, In the obtained kinetic model, there exists The equilibrium position of At time t = τ, the distance from the center of the earth r(t) is expressed as r|t = τ , so the pitch angle θ during the coplanar orbit transfer process C (t) and roll angle The expected posture trajectory of is expressed as: in, is θ e The stable center point, f u is the value of the lateral thrust acceleration, l is the unit vector pointing from the satellite's center of mass to the center of the earth; in, Assume parameter k u is a constant, and the equilibrium position obtained under this assumption is defined as the expected attitude angle at that moment.

3. The method according to claim 1, characterized in that The method further includes: designing an auxiliary compensator, specifically including: The actual magnetic control torque M C With ideal magnetic control torque The difference ΔM C The auxiliary compensator for input drive has: Where, λ=[λ1,λ2,λ3,λ4,λ5,λ6] T , To ensure the characteristic root λ i →0(i=1,2,...6), the matrix A should be a Hurwitz matrix, so there is a i >0(i=1,2,3,…,6).

4. The method according to claim 3, characterized in that In the sliding mode control law based on the auxiliary compensator, the sliding mode surface of the initial controller satisfies: s=(ω r -ω rc )+k q (q r -q rc ), where ω rc =[0,0,0] T , is the expected angular velocity, let Q c =[q 1c ,q rc ] T is the expected attitude quaternion, when s≡[0,0,0] T When the actual attitude quaternion converges to the expected quaternion in an exponential form, k q For any positive real number, the sliding surface is improved to: In the formula, The sliding mode control law based on the auxiliary compensator is obtained, which satisfies: Where η>Δf max (ω,t)+Δd max (t), k s represents the exponential term, and has:

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