Low angle acceleration power spectral density optimization control method combining cold air and magnetic control

Abstract

The low-angle acceleration power spectrum density optimization control method combined with cold gas and magnetic control first performs jet control axis / magnetic control axis distribution design according to the characteristics of the orbit magnetic field and the inertia distribution characteristics of the satellite, adopts the jet control / magnetic control axis fixed setting mode, so as to guarantee the continuity of the magnetic control to the maximum extent and reduce the switching disturbance. Secondly, the disturbance torque filtering estimation is performed, and the disturbance torque feedforward compensation is performed when the expected control torque is calculated, so as to enhance the disturbance suppression ability of the control through the feedback and feedforward combined control. The direction of the cold gas control is subjected to the jet phase plane protection calculation, and the cold gas pulse width output is performed when necessary. The direction of the magnetic control is subjected to the small disturbance magnetic moment distribution calculation according to the geomagnetic field information and the expected control torque, and the three-axis magnetic moment output is performed.

Description

Technical Field

[0001] This invention relates to the field of spacecraft attitude control, particularly a low-angular acceleration power spectral density optimization control method combining cold gas and magnetic control. It is applicable to all spacecraft employing a combination of magnetic control and thrust control to achieve high-precision three-axis attitude stability, such as gravity field measurement satellites and high-quietness scientific exploration satellites. This method can also be applied to all other spacecraft requiring magnetic control or specific spacecraft operating modes. Background Technology

[0002] Satellites used for precision gravity field measurement missions are equipped with payloads including ultra-high-precision electrostatic levitation accelerometers. To minimize the impact of satellite disturbances on accelerometer measurements, attitude control must meet low angular acceleration power spectral density requirements. The attitude control system is designed to exclude rotating and wobbling components such as momentum wheels and liquid fuel, employing a cold gas thruster and a continuous voltage magnetic torque converter as the attitude control actuators, and using optimized propellant consumption control methods to ensure the satellite can operate normally and meet its design life requirements. However, existing control methods cannot meet the low angular acceleration power spectral density requirements. Summary of the Invention

[0003] The technical problem solved by this invention is to overcome the shortcomings of the prior art and design a low-angle acceleration power spectral density optimization control method that combines cold air and magnetic control, which achieves a very good attitude control effect of low-angle acceleration power spectral density.

[0004] The technical solution of this invention is: a low-angular acceleration power spectral density optimization control method combining cold air and magnetic control, comprising the following steps:

[0005] Based on the characteristics of the orbital magnetic field and the satellite's inertia distribution, the jet control axis / magnetic control axis allocation design is carried out, and the jet control / magnetic control axis is fixed throughout the entire control process after allocation;

[0006] Based on the control torque output value of the previous cycle and the angular velocity information provided by the star-sensor attitude determination in this cycle, the environmental disturbance torque is filtered and estimated.

[0007] The control quantity is calculated based on the attitude fixed angle and angular velocity and the target attitude angle and angular velocity to obtain the desired feedback control torque; the desired control torque is calculated by performing disturbance torque feedforward compensation.

[0008] The magnetic moment distribution is calculated based on the desired 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 gas 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 jet control axis, and setting the axis with a generally weaker magnetic control effect as the jet control axis. The generally weaker magnetic control effect means that the satellite's inertia along this axis is relatively large compared to the other two axes, or that the direction of the geomagnetic field is closer to this axis than the other two axes for most of the time during the entire orbital period.

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

[0011] First, the environmental disturbance torque is dynamically estimated, as shown in the following formula:

[0012]

[0013] in The state values ​​are 6*1 dimensional upper-periodic filters. For the estimated state values ​​of the current period in 6*1 dimension, A is the 3*1 dimension estimated control torque output value obtained from the previous cycle control calculation. dist and B dist These are a 6*6 dimensional state coefficient matrix and a 6*3 dimensional output coefficient matrix, respectively, in the following form, where I x I y I z These represent the satellite's three-axis principal inertia values, Δt is the control period length, and ω0′ is the satellite's orbital angular velocity.

[0014]

[0015]

[0016] Then, the environmental disturbance torque is filtered and corrected, and the result is recorded. for The first three dimensions of the vector are calculated using the following formula:

[0017]

[0018] in, K represents the 3*1 dimensional triaxial inertial angular velocity value. dist It is a 6*3 dimensional filter coefficient matrix. Let T be the 6*1 dimensional current-cycle filtered state value. d for The last three-dimensional vector value, T d This is the current period estimate of the environmental disturbance torque.

[0019] Preferably, the expected control torque is calculated based on feedback. Where K p and K dAll are 3*3 dimension control coefficients, Φ and These are the three-axis fixed-attitude Euler attitude angle and the three-axis fixed-attitude Euler attitude angular velocity, respectively. sat It is a 3*3 satellite inertia matrix. The value represents the 3*1 dimensional triaxial inertial angular velocity, and × indicates the vector cross product calculation.

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

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

[0022] First, determine which two of the three axes (pitch, yaw, and roll) are magnetic control axes, and which third axis is the jet control axis. Based on the component values ​​of the desired control torque after torque compensation in the two magnetic control axes, calculate two candidate magnetic moment values. Determine the magnetic moment of the jet control axis based on whether the signs of the two candidate magnetic moment values ​​are the same.

[0023] Calculate the magnetic moments of the two magnetic control axes based on the magnetic moments of the jet control axes mentioned above.

[0024] Preferably, two candidate 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 These represent the calculated values ​​of the desired control torque after torque compensation in the j and k components of the magnetic control axis, respectively. j B k Let M be the components of the geomagnetic induction intensity along the magnetostriction axes j and k in the body coordinate system. i1 With M i2 If the signs are the same, then the magnetic moment M of the jet control axis i is... i The calculation formula is: M i =sgn(M i1 min(M) i1 M i2 Otherwise, let M i =0;

[0025] Then calculate the magnetic moment M of the magnetically controlled axis k. k =(T cj +M i B k ) / B i Magnetic control axis j magnetic moment M j =(M i B j -Tck ) / B i B i This represents the component value of the geomagnetic induction intensity along the jet control axis in the body coordinate system.

[0026] Preferably, the calculated triaxial magnetic moment is written in vector form M. out =[M x M y M z ] T Regarding the triaxial magnetic moment M out Output M after amplitude limiting outlim That is, if the absolute value of the magnetic moment of a certain axis does not exceed the maximum allowable magnetic moment value of that axis, then the output is based on that magnetic moment value; otherwise, the output is based on the maximum allowable magnetic moment value of that axis while retaining the sign of the magnetic moment; calculate the magnetic control torque output value T. mag =M outlim ×B, where B=[B x B y B z ] T This represents the three-axis components of the geomagnetic induction intensity vector in the satellite's body coordinate system.

[0027] Preferably, the jet torque output value is denoted as T. thrust Calculate the control torque output value for this cycle. Used for calculation in the next cycle.

[0028] A low-angular acceleration power spectral density optimization control method combining cold gas and magnetic control is proposed for application in gravity field measurement satellites and high-quietness scientific exploration satellites, as well as all spacecraft requiring magnetic control or specific operating modes of spacecraft.

[0029] The advantages of this invention compared to the prior art are:

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

[0031] (2) This invention improves the satellite attitude control accuracy and optimizes the satellite angular acceleration power spectral density by filtering and estimating the satellite environmental interference torque and feeding forward compensation, and enhances the disturbance suppression capability through feedback and feedforward joint control, while reducing the consumption of thrust working fluid.

[0032] (3) The present invention is based on magnetic control and thruster to achieve high-precision satellite attitude control with low working fluid consumption. When other actuators such as momentum wheel or CMG fail and cannot be used, or when other actuators are not used or configured due to low power consumption or low cost requirements, low angular acceleration spectral density satellite attitude control can still be achieved, which greatly improves the reliability of satellite operation and extends the service life of satellite. Attached Figure Description

[0033] Figure 1 This is a flowchart of the low-angle acceleration power spectral density optimization control method combining cold air and magnetic control of the present invention; Detailed Implementation

[0034] A method for optimizing the low-angular acceleration power spectral density by combining cooling gas and magnetic control includes the following steps:

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

[0036] Two of the satellite's three axes are set as magnetic control axes, and the third axis is set as a 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 satellite's inertia along this axis is relatively large, or the direction of the Earth's magnetic field is closer to this axis for most of the time during the entire orbital period. The set magnetic control axis / jet control axis remains unchanged throughout the entire control process to ensure the continuity of magnetic control.

[0037] (2) Based on the control torque output value of the previous cycle and the angular velocity information provided by the star-sensor attitude determination in this cycle, the environmental disturbance torque is filtered and estimated;

[0038] First, the environmental disturbance torque is dynamically estimated, as shown in the following formula:

[0039]

[0040] in The state values ​​are 6*1 dimensional upper-period filters, and the initial value can be [000000]. T , For the estimated state values ​​of the current period in 6*1 dimension, The output value of the 3*1 dimension control torque in the previous cycle is calculated from the control of the previous cycle, A. dist and B dist These are a 6*6 dimensional state coefficient matrix and a 6*3 dimensional output coefficient matrix, respectively, in the following form, where I x I y I z These represent the satellite's three-axis principal inertia values, Δt is the control period length, and ω0′ is the satellite's orbital angular velocity.

[0041]

[0042] Then, the environmental disturbance torque is filtered and corrected, and the result is recorded. for The first three dimensions of the vector are calculated using the following formula:

[0043]

[0044] in The values ​​are 3*1 dimensional three-axis inertial angular velocities, provided by satellite attitude determination, K. dist The filter coefficient matrix is ​​6*3 dimensional; the Kalman filter design method can be referenced for its design. Let T be the 6*1 dimensional current-cycle filtered state value. d for The last three-dimensional vector value, T d This is the current period estimate of the environmental disturbance torque.

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

[0046] Calculate the expected control torque feedback Where K p and K d All are 3*3 dimension control coefficients, Φ and These are the three-axis attitude-fixed Euler attitude angles and the three-axis attitude-fixed Euler attitude angular velocities, respectively, provided by satellite attitude determination. sat This is a 3*3 satellite inertia matrix, where × indicates the vector cross product calculation.

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

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

[0049] First, set two of the satellite's three axes as magnetic control axes and the third as a 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 satellite's inertia along this axis is relatively large, or the direction of the Earth's magnetic field is closer to this axis for most of the entire orbital period. The set magnetic control axis / jet control axis remains unchanged throughout the entire control process to ensure the continuity of magnetic control.

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

[0051] First, calculate the two candidate magnetic moment values ​​M. x1 =-T cy / B z M x2 =T cz / B y T cy T cz The values ​​of the desired control torque after torque compensation calculated in step (1) are the pitch axis and yaw axis components, respectively. y B z These are the components of the geomagnetic induction intensity along the pitch and yaw axes of the body coordinate system, respectively. If M x1 With M x2 If the signs are the same, then the magnetic moment M of the rolling shaft is... x The calculation formula is: M 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 B x This represents the component value of the geomagnetic induction intensity along 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 the two candidate magnetic moment values ​​M. z1 =-T cx / B y M z2 =T cy / B x T cx T cy The components of the desired control torque after torque compensation calculated in step (1) are B, respectively, along the roll axis and pitch axis. x B y Let M be the components of the geomagnetic induction intensity along the roll and pitch axes of the body coordinate system, respectively. z1 With M z2 If the signs are the same, then the yaw axis magnetic moment M z The calculation formula is M z =sgn(M z1min(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 shaft magnetic moment M x =(M z B x -T cy ) / B z B z This represents the component of the geomagnetic induction intensity along the yaw axis in the body coordinate system.

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

[0057] First, calculate the two candidate magnetic moment values ​​M. y1 =T cx / B z M y2 =-T cz / B x T cx T cz The values ​​of the desired control torque after torque compensation calculated in step (1) are the components of the rolling axis and the yaw axis, respectively. x B z These are the components of the geomagnetic induction intensity along the rolling axis and yaw axis of the body coordinate system, respectively. If M y1 With M y2 If the signs are the same, 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 shaft 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 B y This represents the component of the geomagnetic induction intensity along the pitch axis of the body coordinate system.

[0059] Then, the calculated triaxial magnetic moment is written in vector form M.out =[M x M y M z ] T Regarding the triaxial magnetic moment M out Output M after amplitude limiting outlim That is, if the absolute value of the magnetic moment of a certain axis does not exceed the maximum allowable magnetic moment value of that axis, then the output is based on that magnetic moment value; otherwise, the output is based on the maximum allowable magnetic moment value of that axis while retaining the sign of the magnetic moment.

[0060] Finally, the magnetic control torque output value T is calculated. mag =M outlim ×B, where B=[B x B y B z ] T This represents the three-axis components of the geomagnetic induction intensity vector in the satellite's body coordinate system.

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

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

[0063] Let the jet torque output value be T. thrust Calculate the control torque output value for this cycle. Used for calculation in the next cycle.

[0064] Example 1:

[0065] Taking a low-Earth orbit satellite with an orbital inclination of around 90 degrees as an example, such as 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-sensor attitude determination in this cycle, the environmental disturbance torque is filtered and estimated; firstly, the environmental disturbance torque is dynamically estimated. in The state values ​​are 6*1 dimensional upper-period filters, and the initial value can be [000000]. T , For the estimated state values ​​of the current period in 6*1 dimension, The 3*1 dimension control torque output value is calculated from the previous cycle control, A. dist and B dist These are a 6*6 dimensional state coefficient matrix and a 6*3 dimensional output coefficient matrix, respectively, in the following form, where I x I y I zThese represent the satellite's three-axis principal inertia values, Δt is the control period length, and ω0′ is the satellite's orbital angular velocity.

[0067]

[0068] Then, the environmental disturbance torque is filtered and corrected, and the result is recorded. for Calculate the first three dimensions of the vector values. in The values ​​are 3*1 dimensional three-axis inertial angular velocities, provided by satellite attitude determination, K. dist The filter coefficient matrix is ​​6*3 dimensional; the Kalman filter design method can be referenced for its design. Let T be the 6*1 dimensional current-cycle filtered state value. d for The last three-dimensional vector value, T d This is the current period estimate of the environmental disturbance torque.

[0069] (2) Calculate the control quantity based on the attitude angle angular velocity and the target attitude angle angular velocity to obtain the desired feedback control torque; calculate the desired feedback control torque. Where K p and K d All are 3*3 dimension control coefficients, Φ and These are the three-axis Euler attitude angles and the three-axis Euler attitude angular velocities, respectively, provided by the satellite attitude determination system. sat This is a 3*3 satellite inertia matrix, where × indicates the vector cross product calculation.

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

[0071] (4) Calculate the small disturbance magnetic moment allocation based on the desired control torque and the specified magnetic control axis; first, set two of the satellite's three axes as magnetic control axes and the other as a 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, when the satellite's inertia along this axis is relatively large, or when the direction of the geomagnetic field is closer to this axis for most of the entire orbital period; the set magnetic control axis / jet control axis remains fixed throughout the 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 the two alternative magnetic moment values ​​M. z1 =-T cx / B y M z2 =T cy / B x Tcx T cy The components of the desired control torque after torque compensation calculated in step (1) are B, respectively, along the roll axis and pitch axis. x B y Let M be the components of the geomagnetic induction intensity along the roll and pitch axes of the body coordinate system, respectively. z1 With M z2 If the signs are the same, 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 shaft magnetic moment M x =(M z B x -T cy ) / B z B z Let M be the component of the geomagnetic induction intensity along the yaw axis in the body coordinate system; then, the calculated triaxial magnetic moment is written in vector form as M. out =[M x M y M z ] T Regarding the triaxial magnetic moment M out Output M after amplitude limiting outlim That is, if the absolute value of the magnetic moment of a certain axis does not exceed the maximum allowable magnetic moment value of that axis, then the output is based on that magnetic moment value; otherwise, the maximum allowable magnetic moment value of that axis is output while retaining the sign of the magnetic moment. Finally, the magnetic control torque output value T is calculated. mag =M outlim ×B, where B=[B x B y B z ] T This represents the three-axis components of the geomagnetic induction intensity vector in the satellite's body coordinate system.

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

[0073] (7) Repeat the process throughout the entire operation of the satellite. Figure 1The diagram illustrates a low-angular acceleration power spectral density optimization control process that combines cold air and magnetocontrol, thereby achieving attitude control of low-angular acceleration power spectral density and ensuring that the satellite can safely and effectively complete its scientific exploration mission.

[0074] The above description is only the best specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the protection scope of the present invention.

[0075] The contents not described in detail in this specification are common knowledge to those skilled in the art.

Claims

1. A method for optimizing the low-angular acceleration power spectral density by combining cold air and magnetic control, characterized in that... Includes the following steps: Based on the characteristics of the orbital magnetic field and the satellite's inertia distribution, the jet control axis / magnetic control axis allocation design is carried out, and the jet control / magnetic control axis is fixed throughout the entire control process after allocation; Based on the control torque output value of the previous cycle and the angular velocity information provided by the star-sensor attitude determination in this cycle, the environmental disturbance torque is filtered and estimated. The control quantity is calculated based on the attitude fixed angle and angular velocity and the target attitude angle and angular velocity to obtain the desired feedback control torque; the desired control torque is calculated by performing disturbance torque feedforward compensation. Magnetic moment distribution calculation is performed based on the desired control torque and the specified magnetic control axis, and three-axis magnetic moment output is performed; phase plane control protection calculation is performed on the specified jet control axis, and cold gas pulse width is output when the phase plane jet threshold is triggered; The environmental disturbance torque filtering estimation is as follows: First, the environmental disturbance torque is dynamically estimated, as shown in the following formula: in The state values ​​are 6*1 dimensional upper-periodic filters. For the estimated state values ​​of the 6*1 dimensional current period, A is the 3*1 dimension estimated control torque output value obtained from the previous cycle control calculation. dist and B dist These are a 6*6 dimensional state coefficient matrix and a 6*3 dimensional output coefficient matrix, respectively, in the following form, where I x I y I z These represent the satellite's three-axis principal inertia values, Δt is the control period length, and ω0′ is the satellite's orbital angular velocity. Then, the environmental disturbance torque is filtered and corrected, and the result is recorded. for The first three dimensions of the vector are calculated using the following formula: in, K represents the 3*1 dimensional triaxial inertial angular velocity value. dist It is a 6*3 dimensional filter coefficient matrix. Let T be the 6*1 dimensional current-cycle filtered state value. d for The last three-dimensional vector value, T d This is the current period estimate of the environmental disturbance torque.

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 and the other as the jet control axis. The axis with the weaker overall magnetic control effect is set as the jet control axis. The weaker overall magnetic control effect means that the satellite's inertia along this axis is relatively large compared to the other two axes, or that the direction of the geomagnetic field is closer to this axis than the other two axes for most of the time during the entire orbital period.

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

4. The method according to claim 3, characterized in that: Desired control torque T excomp =T ex +T d T ex To provide feedback control for the desired torque.

5. The method according to claim 1, characterized in that: The calculation of the magnetic moment distribution under small disturbances is as follows: First, determine which two of the three axes (pitch, yaw, and roll) are magnetic control axes, and which third axis is the jet control axis. Based on the component values ​​of the desired control torque after torque compensation in the two magnetic control axes, calculate two candidate magnetic moment values. Determine the magnetic moment of the jet control axis based on whether the signs of the two candidate magnetic moment values ​​are the same. Calculate the magnetic moments of the two magnetic control axes based on the magnetic moments of the jet control axes mentioned above.

6. The method according to claim 5, characterized in that: Calculate the two candidate 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 These represent the calculated values ​​of the desired control torque after torque compensation in the j and k components of the magnetic control axis, respectively. j B k Let M be the components of the geomagnetic induction intensity along the magnetostriction axes j and k in the body coordinate system. i1 With M i2 If the signs are the same, then the magnetic moment M of the jet control axis i is... i The calculation formula is: M i =sgn(M i1 min(M) i1 M i2 Otherwise, let M i =0; Then calculate the magnetic moment M of the magnetically controlled axis k. k =(T cj +M i B k ) / B i Magnetic control axis j magnetic moment M j =(M i B j -T ck ) / B i B i This represents the component value of the geomagnetic induction intensity along the jet control axis in the body coordinate system.

7. The method according to claim 6, characterized in that: The calculated triaxial magnetic moment is written in vector form M. out =[M x M y M z ] T Regarding the triaxial magnetic moment M out Output M after amplitude limiting outlim That is, if the absolute value of the magnetic moment of a certain axis does not exceed the maximum allowable magnetic moment value of that axis, then the output is based on that magnetic moment value; otherwise, the maximum allowable magnetic moment value of that axis is output while retaining the sign of the magnetic moment. Calculate the magnetic control torque output value T. mag =M outlim ×B, where B=[B x B y B z ] T This represents the three-axis components of the geomagnetic induction intensity vector in the satellite's body coordinate system.

8. The method according to claim 7, characterized in that: Let the jet torque output value be T. thrust Calculate the control torque output value for this cycle. Used for calculation in the next cycle.

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