Cold air and magnetic control combined low-angular acceleration power spectral density optimization control method

Abstract

A cold air and magnetic control combined low-angular-acceleration power spectral density optimization control method comprises the following steps: firstly, according to orbit magnetic field characteristics and satellite inertia distribution characteristics, carrying out air injection control shaft / magnetic control shaft distribution design, and adopting an air injection control / magnetic control shaft fixed arrangement mode to ensure magnetic control continuity and reduce switching disturbance to the greatest extent; secondly, disturbance torque filtering estimation is carried out, disturbance torque feed-forward compensation is carried out during expected control torque calculation, and the disturbance suppression capacity of control is enhanced through feedback and feed-forward combined control. And jet phase plane protection calculation is carried out on the cold air control direction, cold air pulse width output is carried out when necessary, small disturbance magnetic moment distribution calculation is carried out on the magnetic control direction according to geomagnetic field information and expected control moment, and three-axis magnetic moment output is carried out.

Description

Technical Field

[0001] The present invention relates to the field of spacecraft attitude control, in particular to a low angular acceleration power spectrum density optimization control method combining cooling and magnetic control, and is applicable to all spacecraft that use magnetic control and thrust control to achieve high-precision three-axis attitude stabilization, such as gravity field measurement satellites and highly quiet scientific exploration satellites. The method can also be applied to all other spacecraft that require magnetic control or specific working modes of spacecraft. Background Art

[0002] Satellites used for precision gravity field measurement missions have payload configurations including extremely high-precision electrostatically suspended accelerometers. In order to reduce the impact of satellite disturbances on accelerometer measurements, attitude control must meet the requirements of low angular acceleration power spectrum density indicators. The attitude control system excludes rotating and shaking components such as momentum wheels and liquid fuels from the design, uses cold air thrusters and continuous voltage magnetic torquers as attitude control actuators, and adopts a control method that optimizes working fluid consumption to ensure that the satellite can work normally and meet the design life requirements. However, the existing control methods cannot meet the requirements of low angular acceleration power spectrum density indicators. Summary of the invention

[0003] The technical problem solved by the present invention is: to overcome the deficiencies of the prior art, to design a low angular acceleration power spectrum density optimization control method combining cooling air and magnetic control, and to achieve a good low angular acceleration power spectrum density attitude control effect.

[0004] The technical solution of the present invention is: a low angular acceleration power spectrum density optimization control method combining cooling and magnetic control, comprising the following steps:

[0005] According to the characteristics of the orbital magnetic field and the satellite inertia distribution, the jet control axis / magnetic control axis allocation design is carried out. After the allocation, the jet control / magnetic control axis is fixed throughout the control process;

[0006] According to the control torque output value of the previous cycle and the angular velocity information provided by the star-sensing attitude determination in this cycle, the environmental interference torque is filtered and estimated;

[0007] The control quantity is calculated according to the angular velocity of the fixed attitude angle and the angular velocity of the target attitude angle to obtain the desired torque of feedback control; the interference torque feedforward compensation is performed to calculate the desired control torque;

[0008] The magnetic moment distribution calculation is performed according to the expected control torque and the specified magnetic control axis, and the three-axis magnetic moment output is performed; the phase plane control protection calculation is performed on the specified jet control axis, and the cold air pulse width is output when the phase plane jet threshold is triggered.

[0009] Preferably, the jet control axis / magnetic control axis allocation design includes setting two of the three axes of the satellite as magnetic control and the other axis as the jet control axis, and setting the axis with an overall weaker magnetic control effect as the jet control axis, wherein the overall weaker magnetic control effect is because the inertia of the satellite along this axis is larger than that of the other two axes, or the direction of the geomagnetic field is closer to this axis than to the other two axes most of the time during the entire orbital period.

[0010] Preferably, the environmental interference torque filtering estimation is as follows:

[0011] First, the environmental disturbance torque is dynamically estimated, and the formula is as follows:

[0012]

[0013] in is the 6*1-dimensional upper periodic filter state value, is the estimated state value of this cycle in 6*1 dimension, is the 3*1 dimensional estimated control torque output value obtained by the previous cycle control calculation, A dist and B dist They are 6*6 dimensional state coefficient matrix and 6*3 dimensional output coefficient matrix respectively, in the following form, where I x , I y , I z are the satellite's three-axis principal inertia values, Δt is the control cycle length, and ω0′ is the satellite's orbital angular velocity:

[0014]

[0015]

[0016] Then the environmental interference torque is filtered and corrected, for The first three-dimensional vector values ​​are calculated according to the following formula:

[0017]

[0018] in, is the 3*1 dimensional three-axis inertial angular velocity value, K dist is a 6*3 dimensional filter coefficient matrix, is the 6*1-dimensional filter state value of this cycle, denoted by T d for The three-dimensional vector value of the back, T d This is the estimated result of the environmental disturbance torque in this period.

[0019] Preferably, the feedback desired control torque is calculated Where K p and K dare 3*3 dimensional control coefficients, Φ and are the three-axis fixed-attitude Euler attitude angle and the three-axis fixed-attitude Euler attitude angular velocity, I sat is the 3*3 dimensional satellite inertia matrix, It is the 3*1 dimensional three-axis inertial angular velocity value, and × represents vector cross product calculation.

[0020] Preferably, the desired control torque T excomp =T ex +T d ;

[0021] Preferably, the small perturbation magnetic moment distribution is calculated as follows:

[0022] First, determine which two of the three axes of pitch, yaw and roll are magnetically controlled axes and the third axis is the jet control axis; calculate two candidate magnetic moment values ​​according to the component values ​​of the desired control torque after torque compensation in the two magnetically controlled axes, and determine the magnetic moment of the jet control axis according to whether the signs of the two candidate magnetic moment values ​​are the same;

[0023] The magnetic moments of the two magnetron axes are calculated based on the magnetic moment of the jet control axis mentioned above.

[0024] Preferably, two alternative magnetic moment values ​​M are calculated i1 =-T cj / B k , M i2 =T ck / B j , j and k represent two magnetic control axes, and i represents the jet control axis; where T cj , T ck are the expected control torque after torque compensation on the magnetic control axis j and k, respectively, j , B k are the component values ​​of the geomagnetic induction intensity in the magnetic control axis j and k of the body coordinate system, respectively. If M i1 With M i2 The same sign, then the jet control axis i magnetic moment M i The calculation formula is: i =sgn(M i1 )min(M i1 ,M i2 ); otherwise, let M i =0;

[0025] Then calculate the magnetic moment M of the magnetostriction axis k k =(T cj +M i B k ) / B i , magnetic moment M of magnetostriction axis j j =(M i B j -Tck ) / B i , where B i It is the component value of the geomagnetic induction intensity of the jet control axis in the body coordinate system.

[0026] Preferably, the calculated three-axis magnetic moment is written as a vector form M out =[M x M y M z ] T , for the triaxial magnetic moment M out After limiting, output M outlim , that is, if the absolute value of the magnetic moment of a certain axis does not exceed the maximum magnetic moment value allowed by the axis, then the output is based on the magnetic moment value; otherwise, the output is based on the maximum magnetic moment value allowed by the axis while retaining the positive and negative signs of the magnetic moment; calculate the output value of the magnetic control torque T mag =M outlim ×B, where B = [B x B y B z ] T It is the three-axis component representation of the geomagnetic induction intensity vector in the satellite body coordinate system.

[0027] Preferably, the jet torque output value is T thrust , calculate the control torque output value of this cycle Used for next cycle calculation.

[0028] A low angular acceleration power spectrum density optimization control method combining cooling and magnetic control is applied in gravity field measurement satellites and high-quietness scientific exploration satellites, all spacecraft requiring magnetic control or spacecraft specific working modes.

[0029] The advantages of the present invention compared with the prior art are:

[0030] (1) The present invention ensures the continuity of magnetic control by fixing the magnetic control axis / jet control axis, avoids the disturbance of satellite attitude caused by magnetic control / jet switching, further reduces the consumption of thrust fluid and also further improves the satellite attitude control accuracy;

[0031] (2) The present invention performs filtering estimation and feedforward compensation on the satellite environment disturbance torque, and enhances the disturbance suppression capability through feedback and feedforward joint control, thereby effectively improving the satellite attitude control accuracy, optimizing the satellite angular acceleration power spectrum density, and reducing the thrust working fluid consumption;

[0032] (3) The present invention performs low-fluid consumption and high-precision satellite attitude control based on magnetic control and thrusters. When other actuators such as momentum wheels or CMGs fail to be used, or when other actuators are not used or configured for low power consumption or low cost requirements, low angular acceleration spectral density satellite attitude control can still be achieved, thereby greatly improving the reliability of satellite operation and extending the service life of the satellite. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 This is a flow chart of the low angular acceleration power spectrum density optimization control method combining cooling and magnetic control of the present invention; DETAILED DESCRIPTION

[0034] A low angular acceleration power spectrum density optimization control method combining cooling and magnetic control comprises the following steps:

[0035] (1) Based on the characteristics of the orbital magnetic field and the satellite inertia distribution, the jet control axis / magnetic control axis allocation design is carried out. After the allocation, the jet control / magnetic control axis is fixed throughout the control process;

[0036] Two of the three axes of the satellite are set as magnetic control axes, and the other axis is set as the jet control axis. When setting the magnetic control axis / jet control axis, the axis with the weaker overall magnetic control effect should generally be set as the jet control axis. For example, the inertia of the satellite along this axis is relatively large, or the direction of the geomagnetic field is closer to this axis most of the time during the entire orbital cycle. The set magnetic control axis / jet control axis is fixed during the entire control process to ensure the continuity of magnetic control.

[0037] (2) Filter and estimate the environmental interference torque based on the control torque output value of the previous cycle and the angular velocity information provided by the star-sensing attitude determination in this cycle;

[0038] First, the environmental disturbance torque is dynamically estimated, and the formula is as follows:

[0039]

[0040] in It is the state value of the periodic filter on the 6*1 dimension. The initial value can be [000000] T , is the estimated state value of this cycle in 6*1 dimension, is the 3*1-dimensional control torque output value of the previous cycle, obtained by the previous cycle control calculation, A dist and B dist They are 6*6 dimensional state coefficient matrix and 6*3 dimensional output coefficient matrix respectively, in the following form, where I x , I y , I z are the satellite's three-axis principal inertia values, Δt is the control cycle length, and ω0′ is the satellite's orbital angular velocity:

[0041]

[0042] Then the environmental interference torque is filtered and corrected, for The first three-dimensional vector values ​​are calculated according to the following formula:

[0043]

[0044] in is the 3*1 dimensional three-axis inertial angular velocity value, given by the satellite attitude determination, K dist It is a 6*3 dimensional filter coefficient matrix, which can be designed by referring to the Kalman filter design method. is the 6*1-dimensional filter state value of this cycle, denoted by T d for The three-dimensional vector value of the back, T d This is the estimated result of the environmental disturbance torque in this period.

[0045] (3) Calculate the control quantity according to the angular velocity of the fixed attitude angle and the angular velocity of the target attitude angle to obtain the desired torque of feedback control;

[0046] Calculate the feedback desired control torque Where K p and K d are 3*3 dimensional control coefficients, Φ and are the three-axis Euler attitude angle and the three-axis Euler attitude angular velocity, respectively, which are given by the satellite attitude determination. sat is the 3*3 dimensional satellite inertia matrix, and × represents vector cross product calculation.

[0047] (4) Calculate the expected control torque based on the feedback control expected torque and the estimated value of the environmental disturbance torque: T excomp =T ex +T d ;

[0048] (5) Calculate the small disturbance magnetic moment distribution according to the desired control torque and the specified magnetic control axis;

[0049] First, two of the three axes of the satellite are set as magnetic control axes, and the other axis is set as the jet control axis. When setting the magnetic control axis / jet control axis, the axis with the weaker magnetic control effect should generally be set as the jet control axis. For example, the inertia of the satellite along this axis is relatively large, or the direction of the geomagnetic field is closer to this axis most of the time during the entire orbital cycle. The set magnetic control axis / jet control axis is fixed during the entire control process to ensure the continuity of magnetic control.

[0050] a. If the pitch axis and yaw axis are magnetically controlled axes, then:

[0051] First, calculate two alternative magnetic moment values ​​M x1 =-T cy / B z , M x2 =T cz / B y , where T cy , T cz are the desired control torque components on the pitch axis and yaw axis after torque compensation calculated in step (1), respectively, and B y , B z are the component values ​​of the geomagnetic induction intensity in the pitch axis and yaw axis of the body coordinate system, respectively. If M x1 With M x2 The same sign, then the rolling axis magnetic moment M x The calculation formula is: x =sgn(M x1 )min(M x1 ,M x2 ); otherwise, let M x =0;

[0052] Then calculate the yaw axis magnetic moment M z =(T cy +M x B z ) / B x , pitch axis magnetic moment M y =(M x B y -T cz ) / B x , where B x It is the component value of the geomagnetic induction intensity about the rolling axis of the body coordinate system.

[0053] b. If the roll axis and pitch axis are magnetically controlled axes, then:

[0054] First, calculate two alternative magnetic moment values ​​M z1 =-T cx / B y , M z2 =T cy / B x , where T cx , T cy are the expected control torque components on the roll axis and pitch axis after torque compensation calculated in step (1), respectively, x , B y are the component values ​​of the geomagnetic induction intensity in the rolling axis and the pitch axis of the body coordinate system respectively. If M z1 With M z2 The same sign, then the yaw axis magnetic moment M z The calculation formula is M z =sgn(M z1)min(M z1 ,M z2 ); otherwise, let M z =0;

[0055] Then calculate the pitch axis magnetic moment M y =(T cx +M z B y ) / B z , rolling axis magnetic moment M x =(M z B x -T cy ) / B z , where B z It is the component value of the geomagnetic induction intensity on the yaw axis of the body coordinate system.

[0056] c. If the roll axis and yaw axis are magnetically controlled axes, then:

[0057] First, two alternative magnetic moment values ​​M are calculated. y1 =T cx / B z , M y2 =-T cz / B x , where T cx , T cz are the expected control torque components on the roll axis and yaw axis after torque compensation calculated in step (1), respectively, x , B z are the component values ​​of the geomagnetic induction intensity in the roll axis and yaw axis of the body coordinate system, respectively. If M y1 With M y2 The same sign, then the pitch axis magnetic moment M y The calculation formula is M y =sgn(M y1 )min(M y1 ,M y2 ); otherwise, let M y =0;

[0058] Then calculate the rolling axis magnetic moment M x =(T cz +M y B x ) / B y , yaw axis magnetic moment M z =(M y B z -T cx ) / B y , where B y It is the component value of the geomagnetic induction intensity on the pitch axis of the body coordinate system.

[0059] Then the three-axis magnetic moment calculated above is written as a vector form Mout =[M x M y M z ] T , for the triaxial magnetic moment M out After limiting, output M outlim That is, if the absolute value of the magnetic moment of an axis does not exceed the maximum magnetic moment value allowed by the axis, it will be output according to the magnetic moment value; otherwise, it will be output according to the maximum magnetic moment value allowed by the axis while retaining the positive and negative signs of the magnetic moment.

[0060] Finally, calculate the output value of the magnetic control torque T mag =M outlim ×B, where B = [B x B y B z ] T It is the three-axis component representation of the geomagnetic induction intensity vector in the satellite body coordinate system.

[0061] (5) Perform phase plane control protection calculations on the specified jet control axis.

[0062] The jet phase plane protection calculation is as follows: The algorithm can be found in "Satellite Attitude Dynamics and Control" edited by Academician Tu Shancheng (Aerospace Press, 2001), page 442.

[0063] The jet torque output value is T thrust , calculate the control torque output value of this cycle Used for next cycle calculation.

[0064] Embodiment 1:

[0065] Take a low-orbit satellite with an orbital inclination of about 90 degrees as an example. Figure 1 As shown, the specific steps of the present invention are as follows:

[0066] (1) Based on the control output of the previous cycle and the angular velocity information provided by the star-sensing attitude determination in this cycle, the environmental disturbance torque is filtered and estimated; first, the environmental disturbance torque is dynamically estimated. in It is the state value of the periodic filter on the 6*1 dimension. The initial value can be [000000] T , is the estimated state value of this cycle in 6*1 dimension, is the 3*1 dimensional control torque output value, obtained by the previous cycle control calculation, A dist and B dist They are 6*6 dimensional state coefficient matrix and 6*3 dimensional output coefficient matrix respectively, in the following form, where I x , I y , I zare the satellite's three-axis principal inertia values, Δt is the control cycle length, and ω0′ is the satellite's orbital angular velocity:

[0067]

[0068] Then the environmental interference torque is filtered and corrected, for The first three-dimensional vector values ​​of in is the 3*1 dimensional three-axis inertial angular velocity value, given by the satellite attitude determination, K dist It is a 6*3 dimensional filter coefficient matrix, which can be designed by referring to the Kalman filter design method. is the 6*1-dimensional filter state value of this cycle, denoted by T d for The three-dimensional vector value of the back, T d This is the estimated result of the environmental disturbance torque in this period.

[0069] (2) Calculate the control quantity based on the attitude angle angular velocity and the target attitude angle angular velocity to obtain the feedback control desired torque; calculate the feedback desired control torque Where K p and K d are 3*3 dimensional control coefficients, Φ and are the three-axis Euler attitude angle and the three-axis Euler attitude angular velocity, respectively, which are given by the satellite attitude determination. sat is the 3*3 dimensional satellite inertia matrix, and × represents vector cross product calculation.

[0070] (3) Calculate the expected control torque based on the feedback control expected torque and the estimated value of the environmental disturbance torque; Calculate the expected control torque T excomp =T ex +T d .

[0071] (4) Calculate the small disturbance magnetic moment distribution according to the expected control torque and the specified magnetic control axis; first, set two of the three axes of the satellite as magnetic control axes and the other axis as the jet control axis. When setting the magnetic control axis / jet control axis, the axis with the weaker magnetic control effect should generally be set as the jet control axis. For example, the inertia of the satellite along this axis is relatively large, or the direction of the geomagnetic field is closer to this axis most of the time during the entire orbital cycle. The set magnetic control axis / jet control axis is fixed during the entire control process to ensure the continuity of magnetic control. Since the satellite sets the roll axis and pitch axis as magnetic control axes, first calculate two alternative magnetic moment values ​​M. z1 =-T cx / B y , M z2 =T cy / B x , where Tcx , T cy are the expected control torque components on the roll axis and pitch axis after torque compensation calculated in step (1), respectively, x , B y are the component values ​​of the geomagnetic induction intensity in the rolling axis and the pitch axis of the body coordinate system respectively. If M z1 With M z2 The same sign, then the yaw axis magnetic moment M z The calculation formula is M z =sgn(M z1 )min(M z1 ,M z2 ), otherwise let M z =0; then calculate the pitch axis magnetic moment M y =(T cx +M z B y ) / B z , rolling axis magnetic moment M x =(M z B x -T cy ) / B z , where B z is the component value of the geomagnetic induction intensity in the yaw axis of the body coordinate system; then the three-axis magnetic moment calculated above is written as a vector form M out =[M x M y M z ] T , for the triaxial magnetic moment M out After limiting, output M outlim , that is, if the absolute value of the magnetic moment of a certain axis does not exceed the maximum magnetic moment value allowed by the axis, then the output is based on the magnetic moment value; otherwise, the output is based on the maximum magnetic moment value allowed by the axis while retaining the positive and negative signs of the magnetic moment; finally, the output value of the magnetic control torque T is calculated mag =M outlim ×B, where B = [B x B y B z ] T It is the three-axis component representation of the geomagnetic induction intensity vector in the satellite body coordinate system.

[0072] (5) Perform phase plane control protection calculation for the specified jet control axis; for the specific algorithm, refer to page 442 of Satellite Attitude Dynamics and Control edited by Academician Tu Shancheng (Aerospace Press, 2001). The jet torque output value is T thrust , calculate the control torque output value of this cycle Used for next cycle calculation.

[0073] (7) Repeat the process throughout the satellite operation. Figure 1The low angular acceleration power spectral density optimization control process combining cooling and magnetic control is shown, thereby realizing attitude control of low angular acceleration power spectral density and ensuring that the satellite completes its scientific exploration mission safely and effectively.

[0074] The above description is only the best specific implementation mode of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by any technician familiar with the technical field within the technical scope disclosed by the present invention should be covered within the protection scope of the present invention.

[0075] The contents not described in detail in the specification of the present invention belong to the common knowledge of those skilled in the art.

Claims

1. A low angular acceleration power spectrum density optimization control method combining cooling and magnetic control, characterized in that The steps include: According to the characteristics of the orbital magnetic field and the satellite inertia distribution, the jet control axis / magnetic control axis allocation design is carried out. After the allocation, the jet control / magnetic control axis is fixed throughout the control process; According to the control torque output value of the previous cycle and the angular velocity information provided by the star-sensing attitude determination in this cycle, the environmental interference torque is filtered and estimated; The control quantity is calculated according to the angular velocity of the fixed attitude angle and the angular velocity of the target attitude angle to obtain the desired torque of feedback control; the interference torque feedforward compensation is performed to calculate the desired control torque; The magnetic moment distribution calculation is performed according to the expected control torque and the specified magnetic control axis, and the three-axis magnetic moment output is performed; the phase plane control protection calculation is performed on the specified jet control axis, and the cold air pulse width is output when the phase plane jet threshold is triggered.

2. The method according to claim 1, characterized in that: The jet control axis / magnetic control axis allocation design includes setting two of the three axes of the satellite as magnetic control axes and another axis as a jet control axis, and setting the axis with an overall weaker magnetic control effect as the jet control axis. The overall weaker magnetic control effect is that the inertia of the satellite along this axis is larger than that of the other two axes, or the direction of the geomagnetic field is closer to this axis than to the other two axes most of the time during the entire orbital period.

3. The method according to claim 1, characterized in that: The environmental disturbance torque filtering is estimated as follows: First, the environmental disturbance torque is dynamically estimated, and the formula is as follows: in is the 6*1-dimensional upper periodic filter state value, is the estimated state value of this cycle in 6*1 dimension, is the 3*1 dimensional estimated control torque output value obtained by the previous cycle control calculation, A dist and B dist They are 6*6 dimensional state coefficient matrix and 6*3 dimensional output coefficient matrix respectively, in the following form, where I x , I y , I z are the satellite's three-axis principal inertia values, Δt is the control cycle length, and ω0′ is the satellite's orbital angular velocity: Then the environmental interference torque is filtered and corrected, for The first three-dimensional vector values ​​are calculated according to the following formula: in, is the 3*1 dimensional three-axis inertial angular velocity value, K dist is a 6*3 dimensional filter coefficient matrix, is the 6*1-dimensional filter state value of this cycle, denoted by T d for The three-dimensional vector value of the back, T d This is the estimated result of the environmental disturbance torque in this period.

4. The method according to claim 3, characterized in that: Calculate the feedback desired control torque Where K p and K d are 3*3 dimensional control coefficients, Φ and are the three-axis fixed-attitude Euler attitude angle and the three-axis fixed-attitude Euler attitude angular velocity, I sat is the 3*3 dimensional satellite inertia matrix, It is the 3*1 dimensional three-axis inertial angular velocity value, and × represents vector cross product calculation.

5. The method according to claim 4, characterized in that: Expected control torque T excomp =T ex +T d .

6. The method according to claim 1, characterized in that: The small perturbation magnetic moment distribution is calculated as follows: First, determine which two of the three axes of pitch, yaw and roll are magnetically controlled axes and the third axis is the jet control axis; calculate two candidate magnetic moment values ​​according to the component values ​​of the desired control torque after torque compensation in the two magnetically controlled axes, and determine the magnetic moment of the jet control axis according to whether the signs of the two candidate magnetic moment values ​​are the same; The magnetic moments of the two magnetron axes are calculated based on the magnetic moment of the jet control axis mentioned above.

7. The method according to claim 6, characterized in that: Calculate two alternative magnetic moment values ​​M i1 =-T cj / B k , M i2 =T ck / B j , j and k represent two magnetic control axes, and i represents the jet control axis; where T cj , T ck are the expected control torque after torque compensation on the magnetic control axis j and k, respectively, j , B k are the component values ​​of the geomagnetic induction intensity in the magnetic control axis j and k of the body coordinate system, respectively. If M i1 With M i2 The same sign, then the jet control axis i magnetic moment M i The calculation formula is: i =sgn(M i1 )min(M i1 ,M i2 ); otherwise, let M i =0; Then calculate the magnetic moment M of the magnetostriction axis k k =(T cj +M i B k ) / B i , magnetic moment M of magnetostriction axis j j =(M i B j -T ck ) / B i , where B i It is the component value of the geomagnetic induction intensity of the jet control axis in the body coordinate system.

8. The method according to claim 7, characterized in that: The calculated three-axis magnetic moment is written as a vector form M out =[M x M y M z ] T , for the triaxial magnetic moment M out After limiting, output M outlim , that is, if the absolute value of the magnetic moment of a certain axis does not exceed the maximum magnetic moment value allowed by the axis, then the output is based on the magnetic moment value; otherwise, the output is based on the maximum magnetic moment value allowed by the axis while retaining the positive and negative signs of the magnetic moment; calculate the output value of the magnetic control torque T mag =M outlim ×B, where B = [B x B y B z ] T It is the three-axis component representation of the geomagnetic induction intensity vector in the satellite body coordinate system.

9. The method according to claim 8, characterized in that: The jet torque output value is T thrust , calculate the control torque output value of this cycle Used for next cycle calculation.

10. A method for optimizing the power spectrum density of low angular acceleration by combining cooling and magnetic control, which is applied to gravity field measurement satellites, highly quiet scientific exploration satellites, all spacecraft requiring magnetic control or specific working modes of spacecraft.

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