Satellite angular momentum unloading method using a rotating mechanism

Abstract

The present application relates to a kind of satellite angular momentum unloading method using rotating mechanism, belong to spacecraft attitude control technical field.The present application solves the technical problem that if satellite requires attitude on ground in on-orbit operation, existing method is not applicable.The method of the present application includes the following steps: calculating the change of rotational inertia caused by satellite rotating mechanism angle;Calculate the influence of satellite attitude and inertia matrix on gravity gradient torque;Use inertia product to unload angular momentum;And rotating mechanism angle planning.The satellite angular momentum unloading method using rotating mechanism of the present application, for satellite angular momentum unloading problem, using the characteristics of gravity gradient torque that can be generated by inertia product in satellite rotational inertia matrix.According to the current angular momentum of satellite, calculate the desired inertia product in satellite rotational inertia matrix.Further, the desired angle of rotating machine is calculated, so as to complete the unloading of angular momentum.

Description

Technical Field

[0001] This invention relates to the field of spacecraft attitude control technology, and in particular to a method for unloading the angular momentum of a satellite using a rotation mechanism. Background Technology

[0002] During its operation in orbit, a satellite is subject to space disturbance torques such as gravitational gradient torque, solar pressure torque, aerodynamic torque, and remanent magnetization torque. The continuous action of these disturbance torques causes the satellite's angular momentum to gradually accumulate. This accumulated angular momentum is first absorbed by the satellite's momentum exchange actuators, and after accumulating to a certain threshold, it needs to be unloaded by the angular momentum unloading actuators.

[0003] Satellite angular momentum unloading typically involves offsetting angular momentum using the magnetic torque generated by a magnetic torque generator and the jet torque generated by the propulsion system. However, these methods have significant limitations. Magnetic torque generators rely on the Earth's magnetic environment, making unloading extremely inefficient when the satellite is in a high-altitude Earth orbit, or impossible when the satellite is in orbit around a non-magnetic celestial body. Using the propulsion system for unloading consumes additional propulsion fuel and increases the satellite's weight.

[0004] Tu Shancheng's paper (Tu Shancheng et al., Satellite Attitude Dynamics and Control, Aerospace Press, 2001) discloses a method for unloading angular momentum in both the orbital plane and perpendicular to the orbital plane by establishing the relationship between the satellite's gravity gradient torque, moment of inertia, and attitude, and utilizing the gravity gradient torque caused by the satellite's pitch and roll angles. This paper only considers angular momentum unloading when the satellite's moment of inertia remains constant, and does not analyze the unloading capacity of the inertia product in the moment of inertia matrix. This method is not applicable if the satellite's attitude must be aligned with the Earth during on-orbit operation.

[0005] Geng Yunhai's published paper (Geng Yunhai et al., A Method for Rapidly Unloading Angular Momentum of Rolling and Yaw Axes Using Rolling Axe Maneuvers, CN201310156932.0) discloses a method for analyzing the accumulation of angular momentum caused by satellite attitude yaw and the satellite's ability to unload angular momentum using attitude yaw angle offsets. The method balances the accumulation of angular momentum with the amount of angular momentum unloaded, analyzes the yaw angle required for angular momentum unloading, and describes the satellite's attitude yaw maneuver process. However, this paper only analyzes the unloading of angular momentum within the orbital plane and does not analyze the unloading of angular momentum perpendicular to the orbital plane. Summary of the Invention

[0006] The present invention aims to solve the technical problems in the prior art by providing a method for unloading the angular momentum of a satellite using a rotation mechanism.

[0007] To solve the above-mentioned technical problems, the technical solution of the present invention is as follows:

[0008] A method for unloading the angular momentum of a satellite using a rotating mechanism includes the following steps:

[0009] Step 1: Calculate the change in moment of inertia caused by the angle of the satellite's rotation mechanism;

[0010] Step 2: Calculate the influence of satellite attitude and inertia matrix on gravity gradient torque;

[0011] Step 3: Unload the angular momentum using the product of inertia;

[0012] Step 4: Planning the angle of the rotating mechanism.

[0013] In the above technical solution, step one specifically includes:

[0014] In the coordinate system of the rotating attachment, the translational and rotational coupling coefficients of the rotating attachment are B, respectively. tran and B rot The translational and rotational coupling coefficients of the rotating attachments in the satellite body coordinate system were calculated.

[0015] B trani =T SiB ·B tran

[0016] B roti =T SiB ·B rot +L pi B trani

[0017] Among them, T SiB To rotate the coordinate system O of the attachment i i x i y i z i The transformation matrix to the satellite body coordinate system Oxyz, l pi Let l be the vector from the satellite's center of mass O to the connection point of the solar panel. pi =[l pix ,l piy ,l piz ], L pi For vector l pi The cross product matrix is ​​as follows:

[0018]

[0019] Assuming the satellite has m rotating attachments, the satellite's overall rotational inertia matrix is:

[0020]

[0021] Among them, Ib The moment of inertia matrix of the satellite body;

[0022] Assume the initial matrix of the rotating attachment is T. SiB0 Furthermore, the rotating mechanism can drive the rotating attachment to rotate around the X and Y axes.

[0023] T SiB =R x (α)·R y (β)·T SiB0

[0024] Among them, R x (α),R y (β) are the elementary rotation matrices about the X and Y axes, respectively.

[0025] In the above technical solution, step two specifically involves:

[0026] The formula for the gravitational gradient torque of a satellite is:

[0027]

[0028] Where, r b It is the vector of the spacecraft's orbital position in the body coordinate system;

[0029] Due to the orbital angular velocity of the circular orbit At the same time The above expression can then be simplified to:

[0030]

[0031] Because in the satellite orbital coordinate system, the vector k pointing from the satellite to the Earth's center... o = [0 0 1], therefore k = C ob k o ;

[0032] Among them, C ob Let be the transformation matrix from the orbital system to the home system, and let:

[0033]

[0034] have to:

[0035]

[0036] Substituting into the gradient torque formula, we get:

[0037]

[0038] In the above technical solution, it is assumed that the satellite attitude roll angle Given a pitch angle θ and an attitude angle rotation sequence of 3-2-1, then:

[0039]

[0040] Discarding smaller quantities of second order and above, the gradient torque is obtained as follows:

[0041]

[0042] In the above technical solution, if we assume that the satellite maintains its three axes of attitude aligned with the Earth during its on-orbit operation, then the satellite's attitude roll angle... The pitch angle θ is 0; the gradient torque is:

[0043]

[0044] In the above technical solution, step three specifically involves:

[0045] Assume the satellite's cumulative angular momentum vector is H, where H can be decomposed into in-orbit angular momentum H0. p and the orbital plane exterior angular momentum H n ;

[0046] Unloading angular momentum H within time ΔT n :

[0047]

[0048] Product of inertia I yz This generates a gravitational gradient torque along the X-axis of the satellite's orbital system.

[0049]

[0050] If the satellite's orbit is near-circular, then assume that the satellite maintains an inertial product I from point A to point B. yz The torque is perpendicular to H p The angular momentum generated in the direction will cancel each other out, and only the angular momentum along H will be generated. p Angular momentum in direction;

[0051] The cumulative angular momentum unloading of the satellite from point A to point B is:

[0052]

[0053] In the above technical solution, regarding the unloading polarity, the gravitational gradient torque generated at the midpoint of the unloading arc AB should be equal to -H. p Consistent, the product of inertia I is determined based on the direction of the gravitational gradient torque. yz The sign of I, and yz The larger the absolute value of , the higher its angular momentum unloading efficiency. If the satellite still needs to unload angular momentum after passing point B, then the product of inertia should be -I. yzThis is to ensure the polarity of the gravitational gradient torque.

[0054] In the above technical solution, step four specifically involves:

[0055] Based on the current angular momentum state of the satellite, the desired inertial product I is calculated through step three. xz and I yz The desired angles α and β of the rotating mechanism are calculated.

[0056] In the above technical solution, step four specifically involves:

[0057] Determine the satellite's current angular momentum;

[0058] Angular momentum is decomposed into in-plane angular momentum and perpendicular angular momentum.

[0059] Calculate the product of inertia in the desired inertia matrix to calculate the desired angle of the rotating mechanism;

[0060] The rotating mechanism drives the rotating attachment to the desired angle.

[0061] The present invention has the following beneficial effects:

[0062] This invention relates to a satellite angular momentum unloading method utilizing a rotational mechanism. Addressing the satellite angular momentum unloading problem, it leverages the gravitational gradient torque generated by the inertia product in the satellite's moment of inertia matrix. Based on the satellite's current angular momentum, the desired inertia product in the satellite's moment of inertia matrix is ​​calculated. This is then used to calculate the desired angle of the rotational maneuver, thereby completing the unloading of angular momentum. Attached Figure Description

[0063] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0064] Figure 1 H is the in-plane angular momentum component. p A schematic diagram.

[0065] Figure 2 This is a schematic diagram of the satellite angular momentum unloading process.

[0066] Figure 3 This is a schematic diagram showing the relationship between the satellite's inertial product and the angle along the A-axis. Detailed Implementation

[0067] The inventive concept of this invention is as follows: This invention provides a satellite angular momentum unloading method utilizing a rotating mechanism. This method drives a rotating accessory on the satellite through a rotating mechanism to change the satellite's moment of inertia matrix. The gravitational gradient torque generated by the inertia product in the moment of inertia matrix unloads the satellite's angular momentum. This ensures that the satellite's angular momentum remains within the angular momentum envelope of the momentum exchange actuator, guaranteeing attitude safety.

[0068] The present invention will now be described in detail with reference to the accompanying drawings.

[0069] The satellite angular momentum unloading method utilizing a rotation mechanism of the present invention includes the following steps:

[0070] Step 1: Calculate the change in moment of inertia caused by the angle of the satellite's rotation mechanism;

[0071] A satellite is equipped with multiple rotating mechanisms that drive rotating accessories to rotate within a certain range. The influence of the angles of these rotating mechanisms on the satellite's moment of inertia is analyzed as follows:

[0072] Using the finite element method, the translational and rotational coupling coefficients of the rotating attachment in the coordinate system can be obtained as B. tran and B rot .

[0073] The translational and rotational coupling coefficients of the rotating attachments in the satellite body coordinate system can be calculated:

[0074] B trani =T SiB ·B tran

[0075] B roti =T SiB ·B rot +L pi B trani

[0076] Among them, T SiB To rotate the coordinate system O of the attachment i i x i y i z i The transformation matrix to the satellite's body coordinate system Oxyz. pi Let l be the vector from the satellite's center of mass O to the connection point of the solar panel. pi =[l pix ,l piy ,l piz ], L pi For vector l pi The cross product matrix is ​​as follows:

[0077]

[0078] Assuming the satellite has m rotating attachments, the satellite's overall rotational inertia matrix is:

[0079]

[0080] Among them I bLet T be the rotational inertia matrix of the satellite body. According to the formula above, only matrix T... SiB The trajectory can be changed; assuming the initial matrix of the rotating attachment is T. SiB0 Furthermore, the rotating mechanism can drive the rotating attachment to rotate around the X and Y axes.

[0081] T SiB =R x (α)·R y (β)·T SiB0

[0082] Among them, R x (α),R y (β) are the elementary rotation matrices about the X and Y axes, respectively. Therefore, the overall satellite rotation inertia matrix can be changed by altering the values ​​of α and β.

[0083] Step 2: Calculate the influence of satellite attitude and inertia matrix on gravity gradient torque;

[0084] The formula for the gravitational gradient torque of a satellite is:

[0085]

[0086] In the formula, r b It is a vector representing the spacecraft's orbital position in the body coordinate system. Its sign does not affect the gradient torque. It can be understood as a vector pointing from the Earth's center to the satellite or from the satellite to the Earth's center.

[0087] Due to the orbital angular velocity of the circular orbit At the same time The above expression can then be simplified to:

[0088]

[0089] Because in the satellite orbital coordinate system, the vector k pointing from the satellite to the Earth's center... o = [0 0 1], therefore k = C ob k o .

[0090] In the formula C ob Let be the transformation matrix from the orbital frame to the home frame, which is also the satellite attitude matrix. Therefore, let:

[0091]

[0092] We can obtain:

[0093]

[0094] Abbreviated representation: k = [A x A y A z ]

[0095] Substituting into the gradient torque formula, we get:

[0096]

[0097] Assuming satellite attitude roll angle Given a pitch angle θ and an attitude angle rotation sequence of 3-2-1, then:

[0098]

[0099] Substituting this into the gradient torque formula, and discarding smaller quantities of second order or higher, we get:

[0100]

[0101] If we assume that the satellite maintains its attitude with all three axes aligned with the Earth during its orbital operation, i.e., we do not consider the influence of the satellite's attitude on the gravitational gradient torque, then the satellite's attitude roll angle is... The pitch angle θ is always 0. Therefore, the above equation can be further simplified to:

[0102]

[0103] As shown in the above equation, the gravitational gradient torque along the satellite's X-axis depends on the product of inertia I. yz The gravitational gradient torque along the satellite's Y-axis depends on the product of inertia I. xz .

[0104] Step 3: Unload the angular momentum using the product of inertia;

[0105] Satellite angular momentum management is typically studied in an inertial reference frame, where the satellite orbital nodal coordinate system can be used as an inertial frame when orbital plane precession is not considered.

[0106] Assume the satellite's cumulative angular momentum vector is H, where H can be decomposed into components H0 in the orbital plane. p And the component H perpendicular to the orbital plane n .

[0107] (1) Out-of-plane angular momentum H n

[0108] Satellite inertial product I xz The resulting gravitational gradient torque In inertial space, the direction is fixed and perpendicular to the orbital plane; therefore, at any position on the orbit, the angular momentum H perpendicular to the orbital plane can be expressed. n Uninstall.

[0109] Unloading angular momentum H within time ΔT n :

[0110]

[0111] I xz The polarity should be consistent with the current H of the satellite. n The polarity is consistent, that is, when H n In the +Y direction, let I xz A positive value indicates a positive integer, and a negative value indicates a negative integer. And I... xz The larger the absolute value, the higher its angular momentum unloading efficiency.

[0112] (2) Angular momentum H in the orbital plane p

[0113] Assume the satellite's angular momentum in the orbital plane is H. p ,like Figure 1 Product of inertia I yz It can generate a gravitational gradient torque along the X-axis of the satellite orbital system.

[0114]

[0115] like Figure 1 As shown, if the satellite's orbit is a near-circular orbit, then it is assumed that the satellite maintains an inertial product I from point A to point B. yz Based on the distribution of the gravitational gradient torque, it can be known that the torque is perpendicular to H. p The angular momentum generated in the direction will cancel each other out, and only the angular momentum along H will be generated. p Angular momentum in direction.

[0116] The cumulative angular momentum unloading of the satellite from point A to point B is:

[0117]

[0118] Regarding the unloading polarity, the gravitational gradient torque generated at the midpoint of the unloading arc AB should be equal to -H. p Consistent, the product of inertia I is determined based on the direction of the gravitational gradient torque. yz The positive or negative sign of I. yz The larger the absolute value of , the higher the efficiency of angular momentum unloading. If the satellite needs to continue unloading angular momentum after passing point B, then the product of inertia should be -I. yz This is to ensure the polarity of the gravitational gradient torque.

[0119] Step 4: Planning the angle of the rotating mechanism;

[0120] As shown in step one, by setting the angles α and β of the rotation mechanism, the satellite's moment of inertia matrix can be changed, thereby altering the inertia product I within the inertia matrix. xz and I yz Therefore, based on the current angular momentum state of the satellite, the desired product of inertia I can be calculated through step three.xz and I yz Therefore, the desired angles α and β of the rotating mechanism can be calculated.

[0121] In actual implementation, depending on the installation method of the rotating mechanism, the satellite's inertial product I xz and I yz There is a certain degree of coupling, and the two cannot simultaneously obtain the optimal expected value. In the optimization process, the polarity of both should be ensured first, and then optimization should be carried out according to the principle of minimizing the overall unloading time of the angular momentum in the track plane and the angular momentum perpendicular to the track plane. The rotating mechanism drives the rotating attachment to rotate to the desired angle according to the desired angle information and holds it until the angular momentum is completely unloaded.

[0122] like Figure 2 As shown, the specific execution flow is as follows:

[0123] Determine the satellite's current angular momentum;

[0124] Angular momentum is decomposed into in-plane angular momentum and perpendicular angular momentum.

[0125] Calculate the product of inertia in the desired inertia matrix to calculate the desired angle of the rotating mechanism;

[0126] The rotating mechanism drives the rotating attachment to the desired angle.

[0127] The specific embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0128] A satellite has solar array drive mechanisms mounted on its ±Y sides, which drive two solar arrays respectively. The relevant parameters of the solar array drive mechanism and the satellite's relevant parameters are shown in the table below:

[0129] Table 1 Satellite Parameters

[0130]

[0131] Assuming the B-axis angle remains at 45°, then the A-axis angle with respect to the satellite's inertial product I xz and I yz The impact such as Figure 3 As shown. By Figure 3 It can be seen that I yz The maximum value is taken when the angle of axis A is 0° and 180°, respectively; while I xz The maximum value is taken when the A-axis angle is 45°, 135°, 225° and 315°.

[0132] The calculated maximum gravitational gradient moment of the satellite along the X-axis is 9.58 × 10⁻⁶. -4 The maximum gravitational gradient torque along the Y-axis is 3.01 × 10 Nm. -4Nm. Then, the unloading of 3.69 Nms of in-plane angular momentum or 1.82 Nms of angular momentum perpendicular to the orbital plane can be achieved through the gravitational gradient torque.

[0133] Assuming the satellite's current angular momentum vector to be unloaded is [2,2,2] Nms, then the angular momentum within the satellite's orbital plane and the angular momentum perpendicular to the orbital plane are 2.83 Nms and 2 Nms, respectively. Following the principle of minimizing the overall unloading time, let the B-axis be 45° and the A-axis be 45°, then at this point, I... yz It is 210.8, I xz The value is 94.4. The average gravitational gradient moment within the orbital plane is 4.34 × 10⁻⁴. -4 The average gravitational gradient torque along the Y-axis is 3.05 × 10 Nm. -4 Nm. Calculations show that the two unloading processes take 6521s and 6557s respectively, therefore the total angular momentum unloading time is 6557s.

[0134] This invention relates to a satellite angular momentum unloading method utilizing a rotational mechanism. Addressing the satellite angular momentum unloading problem, it leverages the gravitational gradient torque generated by the inertia product in the satellite's moment of inertia matrix. Based on the satellite's current angular momentum, the desired inertia product in the satellite's moment of inertia matrix is ​​calculated. This is then used to calculate the desired angle of the rotational maneuver, thereby completing the unloading of angular momentum.

[0135] Obviously, the above embodiments are merely illustrative examples for clear explanation and are not intended to limit the implementation. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is neither necessary nor possible to exhaustively list all possible implementations here. However, obvious variations or modifications derived therefrom are still within the scope of protection of this invention.

Claims

1. A method for unloading the angular momentum of a satellite using a rotating mechanism, characterized in that, Includes the following steps: Step 1: Calculate the change in moment of inertia caused by the angle of the satellite's rotation mechanism; Step 2: Calculate the influence of satellite attitude and inertia matrix on gravity gradient torque; Step 3: Unload the angular momentum using the product of inertia; Step 4: Planning the angle of the rotating mechanism; Step four is as follows: Determine the satellite's current angular momentum; Angular momentum is decomposed into in-plane angular momentum and perpendicular angular momentum. Based on the current angular momentum state of the satellite, the inertia product in the desired inertia matrix is ​​calculated in step three, and the desired angle of the rotating mechanism is then calculated. ; The rotating mechanism drives the rotating attachment to the desired angle.

2. The satellite angular momentum unloading method using a rotating mechanism according to claim 1, characterized in that, Step one is as follows: In the coordinate system of the rotating attachment, the translational and rotational coupling coefficients of the rotating attachment are respectively and The translational and rotational coupling coefficients of the rotating attachments in the satellite body coordinate system were calculated. in, To rotate the accessory coordinate system To the satellite body coordinate system The transformation matrix, For the satellite's center of mass The vector to the connection point of the windsurf board. , For vectors The cross product matrix is ​​as follows: Assuming the satellite is equipped with If there are rotating attachments, then the satellite's overall rotational inertia matrix is: in, The moment of inertia matrix of the satellite body; Assume the initial matrix of the rotating attachment is Furthermore, the rotating mechanism can drive the rotating attachment to rotate around the X and Y axes. in, These are the elementary rotation matrices about the X and Y axes, respectively.

3. The satellite angular momentum unloading method using a rotating mechanism according to claim 1, characterized in that, Step two is as follows: The formula for the gravitational gradient torque of a satellite is: in, It is the vector representing the spacecraft's orbital position in the body coordinate system; Due to the orbital angular velocity of the circular orbit At the same time, Then the above formula can be simplified to: Because in the satellite orbital coordinate system, the vector pointing from the satellite to the Earth's center... ,therefore ; in, Let be the transformation matrix from the orbital system to the home system, and let: have to: Substituting into the gradient torque formula, we get: 。 4. The satellite angular momentum unloading method using a rotating mechanism according to claim 3, characterized in that, Assuming satellite attitude roll angle Pitch angle And if the attitude angle rotation order is 3-2-1, then: Discarding smaller quantities of second order and above, the gradient torque is obtained as follows: 。 5. The satellite angular momentum unloading method using a rotating mechanism according to claim 4, characterized in that, If we assume that the satellite maintains its three axes of attitude relative to the Earth while in orbit, then the satellite's attitude roll angle... Pitch angle All are 0; the gradient torque is: 。 6. The satellite angular momentum unloading method using a rotating mechanism according to claim 1, characterized in that, Step three specifically involves: Assume the satellite's cumulative angular momentum vector is ,in Decomposed into in-plane angular momentum and orbital plane exterior angular momentum ; In time Internal unloading angular momentum : ； Inertial product This generates a gravitational gradient torque along the X-axis of the satellite's orbital system. If the satellite's orbit is near-circular, then it is assumed that the satellite maintains its inertial product from point A to point B. Torque is perpendicular to The angular momentum generated in the direction will cancel each other out, and only the angular momentum along the direction will be generated. Angular momentum in direction; The cumulative angular momentum unloading of the satellite from point A to point B is: 。 7. The satellite angular momentum unloading method using a rotating mechanism according to claim 6, characterized in that, Regarding the unloading polarity, the gravitational gradient torque generated at the midpoint of the unloading arc AB should be equal to... Consistent, the product of inertia is determined based on the direction of the gravitational gradient torque. The positive and negative, and The larger the absolute value of , the higher its angular momentum unloading efficiency. If the satellite still needs to unload angular momentum after passing point B, then the product of inertia should be made as . This is to ensure the polarity of the gravitational gradient torque.

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