Satellite magnetic control sun orientation method

Abstract

The invention discloses a satellite magnetic control sun orientation method. The method comprises the following steps: firstly, calculating a conversion matrix from a satellite body coordinate system to an inertial principal axis coordinate system; calculating the expected angular velocity of the satellite and the expected output control torque of the magnetic torquer; and finally calculating the output magnetic moment of the magnetic torquer. Under the condition that only the magnetic torquer is used as an executing mechanism, sun-oriented control over the satellite with the large inertial product can be completed, and the adaptive capacity of the control system to different inertial matrixes is improved.

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 magnetic torquers as actuators for attitude control. Using only magnetic torquer actuators to achieve satellite solar orientation control does not require other actuators such as flywheels to meet the satellite's solar energy acquisition needs. This is a common control method for microsatellites. It is especially often used in the initial solar capture of the satellite and in the safety mode after an attitude anomaly occurs. It is the key to the low-power operation of the microsatellite attitude control system.

[0003] The commonly used magnetic control sun orientation method usually assumes that the satellite body coordinate system is consistent with the inertial principal axis. The document "Joseph Shoer, Leena Singh, Timothy Henderson, Conical Scanning Approach for Sun Pointing on the CYGNSS Microsatellite [C], 2015IEEE Aerospace Conference, AERO2015, v2015, p1-6" designed a satellite sun orientation control using only magnetic torquers as actuators. The satellite rotates around the inertial principal axis and orients it to the sun. The document "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, p4101-4106" designed a pure magnetic control sun orientation method, and the sun orientation axis is the satellite inertial principal axis.

[0004] The existing satellite pure magnetic control solar orientation method usually assumes that the satellite body coordinate system is consistent with the inertial principal axis, that is, the inertial product is zero. In this case, the solar orientation of a certain axis of the satellite body can be achieved. However, when the satellite body coordinate system is inconsistent with the inertial principal axis and the inertial product is large, the solar pointing deviation will increase, or the solar orientation of the satellite body axis cannot be completed. Summary of the invention

[0005] In order to overcome the shortcomings of the prior art, the present invention provides a method for magnetically controlled solar orientation of a satellite. First, the transformation matrix from the satellite 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; finally, the output magnetic torque of the magnetic torquer is calculated; the present invention can complete the solar orientation control of a satellite with a large inertial product when only the magnetic torquer is used as an actuator, thereby improving the adaptability of the control system to different inertia matrices.

[0006] The technical solution adopted by the present invention to solve the technical problem is 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 inertial principal axis 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 moment 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 I represents the moment of inertia of the satellite about the coordinate axes x, y, and z respectively; xy , I xz , I yz They represent the inertia product of the satellite 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 ) 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 e 1 , and the satellite body y b The smallest angle is recorded as e 2 , and the satellite body z b The smallest angle is recorded as e 3 ; 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 with the smallest angle e 1 Conduct day-to-day 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] Where 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 Angular velocity threshold for control law switching.

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

[0037] Step 3-1: Based on the above expected torque, calculate the expected 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 the 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 directs the satellite's inertial principal axis, which has the smallest angle with the axis of the satellite body that needs to be directed 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, the satellite attitude can be prevented from swinging over a large range and a stable attitude towards the sun can be achieved.

[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 its main inertial axis and the need for the satellite's main axis to obtain energy from the sun. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1Schematic 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 is further described below in conjunction with the accompanying drawings and embodiments.

[0053] The existing pure magnetic control solar orientation method for satellites usually assumes that the satellite body coordinate system is consistent with the main axis of inertia, that is, the product of inertia is zero. In this case, a certain axis of the satellite body can be oriented to the sun. However, when the satellite body coordinate system is inconsistent with the main axis of inertia and the product of inertia is large, the deviation of pointing to the sun will increase, or the orientation of the body axis to the sun cannot be completed. The present invention proposes a pure magnetic control solar orientation method that takes into account the large product of inertia in the body coordinate system, and points the satellite inertia main axis that has the smallest angle with the axis that needs to be pointed to the sun to the sun, so as to achieve 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 ) 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 minus sign is still an eigenvector, it is required that the component with the largest absolute value of each eigenvector is positive, which is convenient for 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 , and the satellite body y b The smallest angle is recorded as e 2 , and the satellite body z b The smallest angle is recorded as e 3 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 with the smallest angle e 1 Conduct day-oriented orientation.

[0068] Calculate the expected 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] Where 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, ωbi 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 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 moment vector m of the magnetic torquer:

[0079]

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

[0081] 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:

[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 maximum magnetic torque output by the magnetic torquer. 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 x facing the sun. b , choose x b The principal axis of inertia with the smallest angle e 1 Conduct day-oriented orientation.

[0097] The expected angular velocity scalar is 0.6° / s, and the expected 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). 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. Satellite inertial axis e 1 The angle with the sun vector is Figure 2 After about 6000s, the angle between the satellite's inertial axis and the sun 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 value 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. It is 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, calculate the transformation matrix between the satellite body coordinate system and the inertial principal axis coordinate system 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 inertial principal axis 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 3: Calculate the output magnetic moment of the magnetic torquer; Calculate the output magnetic moment of the three-axis magnetic torquer in the body coordinate system.

2. A method for magnetically controlling the sun orientation of a satellite according to claim 1, It is characterized in that The step 1 is specifically as follows: Step 1-1: Assume the inertia matrix I in the satellite body coordinate system b for: Among them, I x , I y , I z I represents the moment of inertia of the satellite about the coordinate axes x, y, and z respectively; xy , I xz , I yz They represent the inertia product of the satellite 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 ) i =0 i=1,2,3 (2)where λ i is the eigenvalue, E is the 3×3 unit matrix, e i is the feature vector; Step 1-3: The three eigenvectors are related to the satellite body x b The smallest angle is recorded as e 1 , and the satellite body y b The smallest angle is recorded as e 2 , and the satellite body z b The smallest angle is recorded as e 3 ; 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.

3. A method for magnetically controlling the sun orientation of a satellite according to claim 2, It is characterized in that The step 2 is specifically as follows: 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 with the smallest angle e 1 Conduct day-to-day 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: Where 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 Angular velocity threshold for control law switching.

4. A method for magnetically controlling the sun orientation of a satellite according to claim 3, It is characterized in that The step 3 is specifically as follows: Step 3-1: Based on the above expected torque, calculate the expected output magnetic moment 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 the maximum magnetic torque for the magnetic torquer; Similarly, the y-axis and z-axis components can be obtained.

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