Satellite magnetic control sun orientation method

Abstract

The application discloses a satellite magnetic control sun-oriented method, which comprises the following steps: firstly, calculating a conversion matrix from a satellite body coordinate system to an inertial principal axis coordinate system; then, calculating a satellite angular velocity and a magnetic torque controller expected output control torque; and finally, calculating a magnetic torque output magnetic moment. The application can complete the sun-oriented control of a satellite with a large inertia product by using only a magnetic torque controller as an actuator, and improves the adaptability of a control system to different inertia matrices.

Description

Technical Field

[0001] The invention belongs to the field of satellite technology, and in particular relates to a satellite magnetic control solar orientation method. Background Art

[0002] Low-Earth orbit microsatellites often use magnetotorque actuators as actuators for attitude control. Using only magnetotorque actuators for solar orientation control eliminates the need for flywheels or other actuators, meeting the satellite's solar energy needs. This is a common control method for microsatellites. It is particularly commonly used during initial solar acquisition and in safety modes after attitude anomalies. It is key to the low-power operation of microsatellite attitude control systems.

[0003] Common magnetically controlled Sun-pointing methods typically assume that the satellite's coordinate system is aligned with its principal inertial axis. The paper "Joseph Shoer, Leena Singh, Timothy Henderson, Conical Scanning Approach for Sun Pointing on the CYGNSS Microsatellite[C], 2015IEEE Aerospace Conference, AERO2015, v2015, pp. 1-6" designed a satellite Sun-pointing control system using only magnetic torquers as actuators. The satellite rotates around its principal inertial axis and is oriented toward the Sun. The paper "Huaizu You, Ying-Wen Jan, Jih-Run Tsai, Sun Pointing Attitude control with magnetic torquers only[C], AIAA 57th International Astronautical Congress, IAC 2006, v6, pp. 4101-4106" designed a purely magnetically controlled Sun-pointing method, using the satellite's principal inertial axis as the Sun-pointing axis.

[0004] Existing methods for purely magnetically controlled solar orientation of satellites typically assume that the satellite's coordinate system is aligned with the principal axes of inertia, meaning that the product of inertia is zero. This allows for solar orientation of a single axis of the satellite. However, if the satellite's coordinate system is inconsistent with the principal axes of inertia, and the product of inertia is large, the solar pointing deviation increases, or even makes it impossible to achieve solar orientation of the satellite's axis. Summary of the Invention

[0005] To overcome the shortcomings of the existing technology, the present invention provides a method for magnetically controlled solar orientation of a satellite. First, the transformation matrix from the satellite's body coordinate system to the inertial principal axis coordinate system is calculated; then, the desired angular velocity of the satellite and the desired output control torque of the magnetic torquer are calculated; and finally, the output magnetic torque of the magnetic torquer is calculated. The present invention can complete solar orientation control of a satellite with a large mass inertia product using only the magnetic torquer as an actuator, thereby improving the control system's adaptability to different inertia matrices.

[0006] The technical solutions adopted by the present invention to solve the technical problems are as follows:

[0007] Step 1: Calculate the transformation matrix from the satellite body coordinate system to the inertial principal axis coordinate system;

[0008] According to the inertia matrix in the satellite body coordinate system, calculate the transformation matrix between the satellite body coordinate system and the inertial principal axis coordinate system

[0009] Step 2: Calculate the desired angular velocity of the satellite and the desired output control torque of the magnetic torquer;

[0010] According to the satellite orientation requirements, the principal axis of inertia with the smallest angle with the axis that the satellite needs to face the sun is selected as the sun orientation axis, and the expected angular velocity of the satellite and the expected control torque of the magnetic torquer are calculated;

[0011] Step 3: Calculate the output magnetic torque of the magnetic torquer;

[0012] Calculate the output magnetic moment of the three-axis magnetic torquer in the body coordinate system.

[0013] Furthermore, the step 1 is specifically as follows:

[0014] Step 1-1: Assume the inertia matrix I in the satellite body coordinate system b for:

[0015]

[0016] Among them, I x , I y , I z Respectively represent the satellite's moment of inertia about the coordinate axes x, y, and z; I xy , I xz , I yz They represent the satellite's inertia product about the coordinate axes x and y, the coordinate axes x and z, and the coordinate axes y and z respectively;

[0017] Step 1-2: Find the eigenvalues ​​and eigenvectors of the inertia matrix:

[0018] (λ i EI b )e i =0 i=1,2,3 (2)

[0019] where λ i is the eigenvalue, E is the 3×3 unit matrix, e i is the feature vector.

[0020] Step 1-3: The three eigenvectors are related to the satellite body x b The smallest angle is recorded as e1, which is the same as the satellite body y b The smallest angle is recorded as e2, which is the same as the satellite body z b The smallest angle is recorded as e3; then the transformation matrix E from the satellite body coordinate system to the inertial principal axis coordinate system is gb for:

[0021]

[0022] Inertia matrix I in the satellite inertial principal axis coordinate system g for:

[0023]

[0024] The eigenvalues ​​of the inertia matrix are the principal moments of inertia, and the eigenvectors are the directions of the principal axes of inertia.

[0025] Furthermore, the step 2 is specifically as follows:

[0026] Step 2-1: Assume that the axis of the satellite body that needs to face the sun is x b , then choose b The principal axis of inertia e1 with the smallest angle is used for solar orientation;

[0027] Step 2-2: Calculate the desired angular velocity vector ω in the body coordinate system c for:

[0028]

[0029] where v c Represents the desired angular velocity scalar:

[0030] Calculate the sun direction vector in the inertial principal axis coordinate system:

[0031]

[0032] Among them S g is the sun direction vector in the inertial principal axis coordinate system, S b is the sun direction vector in the body coordinate system, S gx 、S gy 、S gz are the three components of the sun direction vector in the satellite’s inertial principal axis coordinate system;

[0033] Step 2-3: The expected output control torque is as follows:

[0034]

[0035] Where T c is the desired control torque vector, ω bi is the vector of the satellite’s relative inertial angular velocity in the body coordinate system, k v 、k s is the control coefficient, ω max is the angular velocity threshold for control law switching.

[0036] Furthermore, the step 3 is specifically as follows:

[0037] Step 3-1: Based on the above desired torque, calculate the desired output magnetic moment vector m of the magnetic torquer:

[0038]

[0039] Among them B b is the magnetic field vector in the body coordinate system;

[0040] Step 3-2: Considering that the output of the magnetic torquer is limited, the relationship between the three-axis components of the actual output magnetic moment vector m′ and the expected output magnetic moment vector m is as follows:

[0041]

[0042] where m x is the x-axis component of the desired output magnetic moment vector m, m x ′ is the x-axis component of the actual output magnetic moment vector m′, m max Output maximum magnetic torque for the magnetic torquer;

[0043] Similarly, the y-axis and z-axis components can be obtained.

[0044] The beneficial effects of the present invention are as follows:

[0045] The present invention aligns the satellite's inertial principal axis, which has the smallest angle with the axis of the satellite body that needs to be oriented toward the sun, toward the sun, thereby achieving stable pointing control of the satellite.

[0046] (1) When the inertial product in the body coordinate system is large, it can avoid large-scale swing of the satellite attitude and achieve stable attitude towards the sun.

[0047] (2) The satellite's main inertial axis with the smallest angle to the main body's axis facing the sun is pointed toward the sun, taking into account both the satellite's stable orientation toward the sun around the main inertial axis and the need for the satellite's main body axis to obtain energy from the sun. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 Schematic diagram of the relative inertial angular velocity of the satellite in an embodiment of the present invention.

[0049] Figure 2 Schematic diagram of the angle between the satellite's principal axis of inertia and the sun vector in an embodiment of the present invention.

[0050] Figure 3 Schematic diagram of the angle between the satellite body and the sun vector in an embodiment of the present invention.

[0051] Figure 4 Schematic diagram of the actual output magnetic torque of the magnetic torquer in an embodiment of the present invention. DETAILED DESCRIPTION

[0052] The present invention will be further described below with reference to the accompanying drawings and examples.

[0053] Existing purely magnetic control solar orientation methods for satellites typically assume that the satellite's coordinate system is aligned with the principal axis of inertia, meaning that the product of inertia is zero. In this case, a single axis of the satellite can be oriented toward the sun. However, when the satellite's coordinate system is inconsistent with the principal axis of inertia, and the product of inertia is large, the solar pointing deviation increases, or the satellite's axis cannot be oriented toward the sun. The present invention proposes a purely magnetic control solar orientation method that takes into account the large product of inertia in the satellite's coordinate system. This method aligns the satellite's principal axis of inertia with the smallest angle with the axis to be oriented toward the sun, achieving stable pointing control of the satellite.

[0054] Step 1: Calculate the transformation matrix from the satellite body coordinate system to the inertial principal axis coordinate system.

[0055] Assume the inertia matrix I in the satellite body coordinate system b for:

[0056]

[0057] Find the eigenvalues ​​and eigenvectors of the inertia matrix:

[0058] (λ i EI b )e i =0 (i=1,2,3) (2)

[0059] where λ i is the eigenvalue, E is the 3×3 unit matrix, e i is the feature vector.

[0060] Considering that an eigenvector with a negative sign is still an eigenvector, we require that the component with the largest absolute value of each eigenvector be positive to facilitate subsequent calculations. If the component with the largest absolute value of the eigenvector is negative, the eigenvector can be negative.

[0061] The three eigenvectors are related to the satellite body x b The smallest angle is recorded as e1, which is the same as the satellite body y b The smallest angle is recorded as e2, which is the same as the satellite body z bThe smallest angle is recorded as e3. Then the transformation matrix E from the satellite body coordinate system to the inertial principal axis coordinate system is gb for:

[0062]

[0063] Inertia matrix I in the satellite inertial principal axis coordinate system g for:

[0064]

[0065] It can be seen that the eigenvalue of the inertia matrix is ​​the principal moment of inertia, and the eigenvector is the direction of the principal axis of inertia.

[0066] Step 2: Calculate the desired angular velocity and desired output control torque of the satellite.

[0067] Assume that the axis of the satellite body facing the sun is x b (The situation of other axes is similar), then select b The principal axis of inertia e1 with the smallest angle is used for solar orientation.

[0068] Calculate the desired angular velocity vector ω in the body coordinate system c for:

[0069]

[0070] where v c represents the desired angular velocity scalar.

[0071] Calculate the sun direction vector in the inertial principal axis coordinate system:

[0072]

[0073] Among them S g is the sun direction vector in the inertial principal axis coordinate system, S b is the sun direction vector in the body coordinate system, S gx 、S gy 、S gz are the three components of the sun direction vector in the satellite's inertial principal axis coordinate system.

[0074] The expected output control torque is as follows:

[0075]

[0076] Where T c is the desired control torque vector, ω bi is the vector of the satellite’s relative inertial angular velocity in the body coordinate system, k v 、k s is the control coefficient, ω max is the angular velocity threshold for control law switching.

[0077] Step 3: Calculate the output magnetic torque of the magnetic torquer.

[0078] According to the above expected torque, calculate the expected output magnetic torque vector m of the magnetic torquer:

[0079]

[0080] Among them B b is the magnetic field vector in the body coordinate system.

[0081] Considering the limited output of the magnetic torquer, the relationship between the three-axis components of the actual output magnetic moment vector m′ and the expected output magnetic moment vector m is as follows:

[0082]

[0083] where m x is the x-axis component of the desired output magnetic moment vector m, m x ′ is the x-axis component of the actual output magnetic moment vector m′, m max The other two axis components are in the same form as the x-axis component.

[0084] Example:

[0085] This embodiment is a mathematical simulation of the process of a satellite moving from a certain initial attitude to the sun orientation.

[0086] Step 1: Calculate the transformation matrix from the satellite body coordinate system to the inertial principal axis coordinate system.

[0087] In this embodiment, the inertia matrix I in the satellite body coordinate system b for:

[0088]

[0089] The three eigenvectors of the inertia matrix are:

[0090]

[0091] The transformation matrix from the satellite body coordinate system to the inertial principal axis coordinate system is:

[0092]

[0093] Inertia matrix I in the satellite inertial principal axis coordinate system g for:

[0094]

[0095] Step 2: Calculate the desired angular velocity and desired output control torque of the satellite.

[0096] In this embodiment, the satellite body needs to have an axis facing the sun as x b , choose the same as x b The principal axis of inertia e1 with the smallest angle is used for solar orientation.

[0097] The desired angular velocity scalar is 0.6° / s, and the desired angular velocity vector in the body coordinate system is:

[0098]

[0099] The sun direction vector in the body coordinate system is obtained by measuring and solving the sun sensor, and the sun direction vector in the inertial principal axis coordinate system is calculated according to formula (6).

[0100] The expected output control torque is calculated according to formula (7). max Take 0.2° / s, control coefficient k v Take it as 0.05, k s Take 3×10 -4 .

[0101] Step 3: Calculate the output magnetic torque of the magnetic torquer.

[0102] The magnetic field vector in the body coordinate system is measured by the magnetometer, and the output magnetic moment of the magnetic torquer is calculated by equations (8) and (9). In this embodiment, the maximum output magnetic moment of the magnetic torquer is m max Take 8Am 2 .

[0103] The relative inertial angular velocity of the satellite in this embodiment is as follows: Figure 1 , the satellite angular velocity changes from the initial three-axis angular velocity [0.1, -0.5, 0.2] T ° / s, and the desired angular velocity can be achieved after about 2000s. The angle between the satellite's inertial axis e1 and the sun vector is as follows: Figure 2 After about 6000s, the angle between the satellite's inertial axis and the solar vector is controlled within 40°, with an average value of 18°. b The angle with the sun vector is Figure 3 , after about 6000s satellite body x b The angle with the sun vector is controlled within 50°, with an average of 25°, which can meet the solar orientation requirements under the control of the magnetic torquer. The actual output magnetic torque of the magnetic torquer is as follows Figure 4 , during the control process, the magnetic torque output is within the maximum output range of the magnetic torquer.

Claims

1. A method for magnetically controlling the sun orientation of a satellite, characterized in that: The steps include: Step 1: Calculate the transformation matrix from the satellite body coordinate system to the inertial principal axis coordinate system; According to the inertia matrix in the satellite body coordinate system, the transformation matrix between the satellite body coordinate system and the inertial principal axis coordinate system is calculated; Step 1-1: Assume the inertia matrix I in the satellite body coordinate system b for: Among them, I x , I y , I z Respectively represent the satellite's moment of inertia about the coordinate axes x, y, and z; I xy , I xz , I yz They represent the satellite's inertia product about the coordinate axes x and y, the coordinate axes x and z, and the coordinate axes y and z respectively; Step 1-2: Find the eigenvalues ​​and eigenvectors of the inertia matrix: (λ i EI b )And i =0 i=1,2,3 (2) where λ i is the eigenvalue, E is the 3×3 unit matrix, e i is the eigenvector; Step 1-3: The three eigenvectors are related to the satellite body x b The smallest angle is recorded as e1, which is the same as the satellite body y b The smallest angle is recorded as e2, which is the same as the satellite body z b The smallest angle is recorded as e3; then the transformation matrix E from the satellite body coordinate system to the inertial principal axis coordinate system is gb for: Inertia matrix I in the satellite inertial principal axis coordinate system g for: The eigenvalues ​​of the inertia matrix are the principal moments of inertia, and the eigenvectors are the directions of the principal axes of inertia; Step 2: Calculate the desired angular velocity of the satellite and the desired output control torque of the magnetic torquer; According to the satellite orientation requirements, the principal axis of inertia with the smallest angle with the axis that the satellite needs to face the sun is selected as the sun orientation axis, and the expected angular velocity of the satellite and the expected control torque of the magnetic torquer are calculated; Step 2-1: Assume that the axis of the satellite body that needs to face the sun is x b , then choose b The principal axis of inertia e1 with the smallest angle is used for solar orientation; Step 2-2: Calculate the desired angular velocity vector ω in the body coordinate system c for: where v c represents the desired angular velocity scalar; Calculate the sun direction vector in the inertial principal axis coordinate system: Among them S g is the sun direction vector in the inertial principal axis coordinate system, S b is the sun direction vector in the body coordinate system, S gx 、S gy 、S gz are the three components of the sun direction vector in the satellite’s inertial principal axis coordinate system; Step 2-3: The expected output control torque is as follows: Where T c is the desired control torque vector, ω bi is the vector of the satellite’s relative inertial angular velocity in the body coordinate system, k v 、k s is the control coefficient, ω max is the angular velocity threshold for control law switching; Step 3: Calculate the output magnetic torque of the magnetic torquer; Calculate the output magnetic moment of the three-axis magnetic torquer in the body coordinate system; Step 3-1: Based on the above desired control torque vector, calculate the desired output magnetic torque vector m of the magnetic torquer: Among them B b is the magnetic field vector in the body coordinate system; Step 3-2: Considering that the output of the magnetic torquer is limited, the relationship between the three-axis components of the actual output magnetic moment vector m′ and the expected output magnetic moment vector m is as follows: where m x is the x-axis component of the desired output magnetic moment vector m, m x ′ is the x-axis component of the actual output magnetic moment vector m′, m max Output maximum magnetic torque for the magnetic torquer; Similarly, the y-axis and z-axis components can be obtained.

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