CN114291295B - Satellite double-shaft attitude measurement and control integrated method for single magnetic suspension control sensitive gyroscope - Google Patents

Abstract

The invention relates to a satellite dual-axis attitude measurement and control integrated method for a single magnetic levitation control sensitive gyroscope. The magnetic levitation control sensitive gyroscope can be used not only as an inertial actuator, but also as an inertial measurement device. Using the two-degree-of-freedom deflection of the high-speed rotating magnetic levitation rotor to change the direction of angular momentum, it can complete the exchange of two-axis angular momentum with the spacecraft and realize the two-axis attitude control of the spacecraft. According to the control produced by the Lorentz force magnetic bearing that controls the deflection of the magnetic levitation rotor The linear relationship between the torque and the control current measures the angular displacement of the maglev rotor in the stator coordinate system and the current size of the Lorentz force magnetic bearing, and realizes the measurement of the two-axis attitude angular rate of the spacecraft. This method can achieve a single maglev control sensitive gyro. The two-axis attitude angular rate measurement and attitude control of the spacecraft overcomes the shortcomings of the traditional attitude control system requiring independent actuators and sensors, and provides a new control method for spacecraft attitude measurement and control.

Description

A satellite dual-axis attitude measurement and control integrated method for a single magnetic levitation control sensitive gyroscope

technical field

The invention relates to a satellite dual-axis attitude measurement and control integrated method for a single magnetic levitation control sensitive gyroscope, which is suitable for a spacecraft attitude control system and can meet the requirements of a single magnetic levitation control sensitive gyroscope to realize two-axis attitude angular rate measurement and attitude control of the spacecraft.

technical background

The traditional spacecraft attitude control system mainly includes actuators and attitude sensors, and the attitude sensors and attitude actuators are located in different positions of the spacecraft, resulting in control dislocation. In addition, the traditional single closed-loop control of spacecraft The system bandwidth is low, and it cannot show its advantages for high-frequency spacecraft attitude maneuvers. In addition, when the attitude sensor of the spacecraft fails to work, it will lead to the paralysis of the entire attitude control system.

In order to solve the above problems, Zheng Shiqiang used the dual-frame control moment gyroscope to realize the attitude measurement and attitude control of the spacecraft, but the method he proposed cannot satisfy the attitude measurement and control of the spacecraft at the same time. Attitude angular rate measurement cannot be satisfied. When the dual-frame control moment gyro meets the attitude angular rate measurement, attitude control cannot be performed; Ren Yuan proposed a satellite single-axis measurement and control integration method based on magnetic levitation control sensitive gyroscope, but this method can only realize A single magnetic levitation control sensitive gyro controls the attitude maneuver of a single-axis satellite; Zhao Hui of Harbin Institute of Technology proposed a gyro flywheel structure, which can realize spacecraft attitude measurement and attitude control, but the rotor of this device is supported by mechanical bearings, which cannot meet the control accuracy.

The magnetic levitation control sensitive gyroscope involved in the present invention is an inertial mechanism that can realize torque output and attitude angular rate measurement. A single magnetic levitation control sensitive gyroscope can realize the integration of attitude measurement and control of two axes of the spacecraft, and realize a single magnetic levitation control. The sensitive gyroscope integrates flywheel torque output function and angular rate gyroscope attitude measurement function into one body, which provides a new control method for spacecraft attitude control system.

Contents of the invention

The problem solved by the technology of the present invention is: in order to overcome the traditional spacecraft attitude control system with complex control structure, required control components and more sensitive periods, etc., a dual-axis attitude measurement and control of spacecraft based on a single magnetic levitation control sensitive gyroscope is proposed Integrated approach. This method realizes two-axis attitude control of the spacecraft by changing the direction of the angular momentum of the rotor, and realizes the measurement of the angular velocity of the spacecraft attitude according to the linear relationship between the control torque of the Lorentz force magnetic bearing and the control current, which provides a solid foundation for the attitude control system of the spacecraft. A new method of control.

The technical solution of the present invention is: use the two-degree-of-freedom deflection of the high-speed rotating magnetic levitation rotor to change the direction of angular momentum, complete the exchange of two-axis angular momentum with the spacecraft, and realize the two-axis attitude control of the spacecraft. The linear relationship between the control torque and the control current generated by the Lorentz force magnetic bearing, by measuring the angular displacement of the magnetic levitation rotor in the stator coordinate system and the magnitude of the Lorentz force magnetic bearing current, the measurement of the two-axis attitude angular rate of the spacecraft is realized, specifically Include the following steps:

(1) Establish spacecraft attitude kinematics and attitude dynamics equations based on magnetic levitation control sensitive gyroscope;

When the magnetic levitation control sensitive gyro is installed on the satellite body, the satellite rolling and yaw control can be realized by controlling the angular momentum direction of the magnetic levitation control sensitive gyro rotor. At this time, the angular momentum of the satellite can be expressed as:

H _sr =H _s + _hr (1)

Among them, H _sr represents the total angular momentum of the magnetic levitation control sensitive gyro installed on the spacecraft, H _s represents the angular momentum of the satellite body when the magnetic levitation control sensitive gyro is not working, h _r represents the angular momentum of the magnetic levitation control sensitive gyro rotor relative to the satellite body , according to the angular momentum theorem:

Among them, M represents the external torque on the satellite, ω=[ω _x ω _y ω _z ], ω _x , ω _y , ω _z represent the attitude angular velocity of the spacecraft, Denotes the differential of ω, /> h _r = [h _rx h _ry h _rz ] represents the angular momentum of the rotor in the body coordinate system, and I=[I _x I _y I _z ] ^T represents the moment of inertia of each axis of the spacecraft:

In the inertial coordinates, the deflection angular velocity and angular acceleration of the maglev rotor can be expressed as:

Among them, ω _x , ω _y , ω _z represent the attitude angular velocity of the spacecraft, ω _z represents the attitude angular acceleration of the spacecraft, /> Indicates the attitude angular velocity of the maglev rotor in the stator coordinate system, Ω indicates the rotational speed of the maglev rotor, Indicates the attitude angular acceleration of the maglev rotor in the stator coordinate system, /> represents the rotational angular acceleration of the rotor, ω _e represents the orbital angular velocity, and ω _r represents the attitude angular velocity of the maglev rotor in the inertial system, /> Indicates the attitude angular acceleration of the maglev rotor in the inertial system;

According to the rotor dynamics equation:

Among them, J _x , J _y , J _z represent the moment of inertia of the magnetic levitation rotor on their respective axes, Ω represents the rotor speed, and /> Indicates the attitude angular velocity of the rotor in the stator coordinate system, /> and /> Indicates the attitude angular acceleration of the rotor in the stator coordinate system, k _tx and k _ty indicate the torsional stiffness of the two-axis control torque output by the Lorentz force magnetic bearing, and i _x and i _y indicate the control current of the respective axes;

(2) Establish a spacecraft attitude control dynamic model

According to the maglev rotor dynamics model and the attitude dynamics model of the spacecraft, the dynamic model of the maglev control sensitive gyroscope installed on the spacecraft is obtained as follows:

Among them, ω _x , ω _y , ω _z represent the attitude angular velocity of the spacecraft, Indicates the attitude angular acceleration of the spacecraft's X-axis, Indicates the attitude angular acceleration of the spacecraft on the Z axis, M _x and M _z indicate the disturbance moments on the spacecraft on the X and Z axes, h _x , h _y and h _z indicate the angular momentum of the rotor in the body coordinate system, k _tx and k _ty represent the torsional stiffness of the two-axis control torque output by the Lorentz force magnetic bearing, i _x and i _y represent the control current of their respective axes, J _x , J _y , and J _z represent the moment of inertia of the magnetic levitation rotor on their respective axes, I _x , I _y and I _z represent the moment of inertia of each axis of the spacecraft:

According to the attitude kinematics of the spacecraft, the following formula can be obtained:

Among them, ω _x , ω _y and ω _z represent the attitude angular velocity of the spacecraft, ω ₀ represents the orbital angular velocity during the operation of the spacecraft, Indicates the yaw angle of the spacecraft, ψ indicates the roll angle of the spacecraft, /> Indicates the yaw rate of the spacecraft, /> Indicates the rolling angular velocity of the spacecraft;

Considering that the orbital angular velocity during the satellite movement is very small and the maneuvering angle of the satellite is limited, in the case of small angles, without considering the disturbance moment, combined with the attitude kinematics equation of the spacecraft, the attitude control model of the spacecraft can be expressed as:

J _x , J _y , J _z represent the moments of inertia of the maglev rotor on their respective axes, I _x , I _y and I _z represent the moments of inertia of each axis of the spacecraft, Indicates the yaw angle of the spacecraft, ψ indicates the roll angle of the spacecraft, /> Indicates the yaw rate of the spacecraft, /> Indicates the rolling angular velocity of the spacecraft, /> and /> Indicates the attitude angular velocity of the rotor in the stator coordinate system, /> and /> Indicates the attitude angular acceleration of the rotor in the stator coordinate system, k _tx and k _ty indicate the torsional stiffness of the two-axis control torque output by the Lorentz force magnetic bearing, and i _x and i _y indicate the control current of the respective axes;

According to equation (7), it can be seen that a single maglev control sensitive gyro can realize the two-axis attitude control of the spacecraft.

(3) Spacecraft attitude angular velocity measurement based on magnetic levitation control sensitive gyroscope

When the spacecraft is maneuvering, the angular momentum of the magnetic levitation rotor maneuvers together with the spacecraft, and the current controlling the maneuvering of the magnetic levitation rotor consists of two parts, one is to control the stable levitation of the magnetic levitation rotor, and the other is to control the attitude maneuver of the spacecraft.

According to the rotor dynamics equation, it can be known that:

Among them, i _rcx and i _rcy represent the control current for controlling the rotor levitation, J _r represents the radial moment of inertia of the rotor, h _z represents the angular momentum of the rotor, k _tx and k _ty represent the two-axis control torque output by the Lorentz force magnetic bearing torsional stiffness, and /> Indicates the attitude angular velocity of the rotor in the stator coordinate system, /> and /> Indicates the attitude angular acceleration of the rotor in the stator coordinate system;

When the magnetic levitation control sensitive gyro is installed on the spacecraft, the spacecraft produces an attitude maneuver, and the magnetic levitation control sensitive gyro will generate a control current, as shown in the following formula:

Among them, J _x , J _y , and J _z represent the moment of inertia of the maglev rotor on their respective axes, ω _x and ω _z represent the attitude angular velocity of the spacecraft, and /> represents the attitude angular acceleration of the spacecraft, Ω represents the rotor speed, k _tx and k _ty represent the torsional stiffness of the two-axis control torque output by the Lorentz force magnetic bearing, _isx and _isy represent the control current generated by the spacecraft attitude maneuver, where Partial current can be expressed as:

Finally, the attitude angular velocity measurement equation of the spacecraft is obtained as follows:

ω _s =N ^-1 k _t I-sχ (11)

Among them, ω _s = [ω _x ω _y ], which represents the two-axis attitude angular velocity of the spacecraft in the inertial space, I=[I _x (s) I _z (s)] represents the Laplace transform of the control current of the Lorentz force magnetic bearing, χ=[α(s) β(s)] represents the magnetic levitation rotor in the stator coordinates The Laplace transform of the attitude angular velocity under the system, s represents the Laplacian operator, and k _t represents the moment coefficient of the maglev control sensitive gyro.

The principle of the present invention is: use the two-degree-of-freedom deflection of the high-speed rotating magnetic levitation rotor to change the angular momentum direction, complete the exchange of two-axis angular momentum with the spacecraft, and realize the two-axis attitude control of the spacecraft. The linear relationship between the control torque and the control current generated by the force magnetic bearing, by measuring the angular displacement of the magnetic levitation rotor in the stator coordinate system and the magnitude of the Lorentz force magnetic bearing current, the measurement of the two-axis attitude angular rate of the spacecraft is realized.

Compared with existing solutions, the scheme of the present invention has the main advantages of:

A single maglev control sensitive gyro can be used to complete the two-axis attitude angular rate measurement and attitude control of the spacecraft, instead of the separate actuators and attitude sensors required in the attitude control system, which simplifies the control system. The in-position control of the actuator and the sensor in the spacecraft attitude control system is realized, which avoids the shortcomings of the traditional actuator and out-of-position control in the sensitive period, and makes the control accuracy higher.

Description of drawings

Fig. 1 Diagram of control scheme of maglev rotor;

Fig. 2 Schematic diagram of the decoupling control of the maglev rotor;

Figure 3 is a schematic diagram of the installation of the magnetic levitation control sensitive gyroscope;

Figure 4 is based on the satellite dual-axis attitude angle controlled by the magnetic levitation control sensitive gyro;

Figure 5 is based on the satellite dual-axis attitude angular velocity controlled by the magnetic levitation control sensitive gyro;

Figure 6 Lorentz force magnetic bearing control current;

Fig. 7 Deflection angular displacement of the maglev rotor;

specific implementation plan

The overall control scheme of the present invention is shown in Figure 1, and the specific attitude control and attitude angular rate measurement principle block diagram is shown in Figure 2. Firstly, the attitude kinematics and attitude dynamics models of the spacecraft are established, and then two The degree of freedom deflection changes the direction of angular momentum, and can complete the exchange of two-axis angular momentum with the spacecraft to realize the two-axis attitude control of the spacecraft, using the linear relationship between the control torque and the control current generated by the Lorentz force magnetic bearing that controls the deflection of the magnetic levitation rotor , by measuring the angular displacement of the maglev rotor in the stator coordinate system and the current of the Lorentz force magnetic bearing, the measurement of the two-axis attitude angular rate of the spacecraft is realized, and the attitude angular rate measurement and attitude control of the spacecraft are realized by this method. Specifically The implementation steps are as follows:

(1) Establish spacecraft attitude kinematics and attitude dynamics equations based on magnetic levitation control sensitive gyroscope;

When the magnetic levitation control sensitive gyro is installed on the satellite body, the satellite rolling and yaw control can be realized by controlling the angular momentum direction of the magnetic levitation control sensitive gyro rotor. At this time, the angular momentum of the satellite can be expressed as:

H _sr =H _s + _hr (12)

In formula (12), H _sr represents the total angular momentum of the magnetic levitation control sensitive gyro installed on the spacecraft, H _s represents the angular momentum of the satellite body when the magnetic levitation control sensitive gyro is not working, h _r represents the magnetic levitation control sensitive gyro rotor relative to the satellite The angular momentum of the body, according to the angular momentum theorem, is:

In formula (13), M represents the external moment on the satellite, ω=[ω _x ω _y ω _z ], ω _x , ω _y , ω _z represent the attitude angular velocity of the spacecraft, Denotes the differential of ω, /> h _r = [h _rx h _ry h _rz ] represents the angular momentum of the rotor in the body coordinate system, and I=[I _x I _y I _z ] ^T represents the moment of inertia of each axis of the spacecraft:

In the inertial coordinates, the deflection angular velocity and angular acceleration of the maglev rotor can be expressed as:

In the above formula, ω _x , ω _y , ω _z represent the attitude angular velocity of the spacecraft, ω _z represents the attitude angular acceleration of the spacecraft, /> Indicates the attitude angular velocity of the maglev rotor in the stator coordinate system, Ω indicates the rotational speed of the maglev rotor, Indicates the attitude angular acceleration of the maglev rotor in the stator coordinate system, /> represents the rotational angular acceleration of the rotor, ω _e represents the orbital angular velocity, and ω _r represents the attitude angular velocity of the maglev rotor in the inertial system, /> Indicates the attitude angular acceleration of the maglev rotor in the inertial system;

According to the rotor dynamics equation:

Among them, J _x , J _y , J _z represent the moment of inertia of the magnetic levitation rotor on their respective axes, Ω represents the rotor speed, and Indicates the attitude angular velocity of the rotor in the stator coordinate system, /> and /> Indicates the attitude angular acceleration of the rotor in the stator coordinate system, k _tx and k _ty indicate the torsional stiffness of the two-axis control torque output by the Lorentz force magnetic bearing, and i _x and i _y indicate the control current of the respective axes;

(2) Establish a spacecraft attitude control dynamic model

According to the maglev rotor dynamics model and the attitude dynamics model of the spacecraft, the dynamic model of the maglev control sensitive gyroscope installed on the spacecraft is obtained as follows:

In the above formula, ω _x , ω _y , ω _z represent the attitude angular velocity of the spacecraft, Indicates the attitude angular acceleration of the spacecraft's X-axis, Indicates the attitude angular acceleration of the spacecraft on the Z axis, M _x and M _z indicate the disturbance moments on the spacecraft on the X and Z axes, h _x , h _y and h _z indicate the angular momentum of the rotor in the body coordinate system, k _tx and k _ty represent the torsional stiffness of the two-axis control torque output by the Lorentz force magnetic bearing, i _x and i _y represent the control current of their respective axes, J _x , J _y , and J _z represent the moment of inertia of the magnetic levitation rotor on their respective axes, I _x , I _y and I _z represent the moment of inertia of each axis of the spacecraft:

According to the attitude kinematics of the spacecraft, the following formula can be obtained:

In formula (17), ω _x , ω _y and ω _z represent the attitude angular velocity of the spacecraft, ω ₀ represents the orbital angular velocity during the operation of the spacecraft, Indicates the yaw angle of the spacecraft, ψ indicates the roll angle of the spacecraft, /> Indicates the yaw rate of the spacecraft, /> Indicates the rolling angular velocity of the spacecraft;

Considering that the orbital angular velocity during the satellite movement is very small and the maneuvering angle of the satellite is limited, in the case of small angles, without considering the disturbance moment, combined with the attitude kinematics equation of the spacecraft, the attitude control model of the spacecraft can be expressed as:

J _x , J _y , J _z represent the moments of inertia of the maglev rotor on their respective axes, I _x , I _y and I _z represent the moments of inertia of each axis of the spacecraft, Indicates the yaw angle of the spacecraft, ψ indicates the roll angle of the spacecraft, /> Indicates the yaw rate of the spacecraft, /> Indicates the rolling angular velocity of the spacecraft, /> and /> Indicates the attitude angular velocity of the rotor in the stator coordinate system, /> and /> Indicates the attitude angular acceleration of the rotor in the stator coordinate system, k _tx and k _ty indicate the torsional stiffness of the two-axis control torque output by the Lorentz force magnetic bearing, and i _x and i _y indicate the control current of the respective axes;

According to equation (18), it can be seen that a single maglev control sensitive gyro can realize the two-axis attitude control of the spacecraft.

(3) Spacecraft attitude angular velocity measurement based on magnetic levitation control sensitive gyroscope

When the spacecraft is maneuvering, the angular momentum of the magnetic levitation rotor maneuvers together with the spacecraft, and the current controlling the maneuvering of the magnetic levitation rotor consists of two parts, one is to control the stable levitation of the magnetic levitation rotor, and the other is to control the attitude maneuver of the spacecraft.

According to the rotor dynamics equation, it can be known that:

In equation (18), i _rcx and i _rcy represent the control current for controlling the rotor levitation, J _r represents the radial moment of inertia of the rotor, h _z represents the angular momentum of the rotor, k _tx and k _ty represent the output of the Lorentz force magnetic bearing. The torsional stiffness of the axis controlling the moment, and /> Indicates the attitude angular velocity of the rotor in the stator coordinate system, /> and /> Indicates the attitude angular acceleration of the rotor in the stator coordinate system;

When the magnetic levitation control sensitive gyro is installed on the spacecraft, the spacecraft produces an attitude maneuver, and the magnetic levitation control sensitive gyro will generate a control current, as shown in the following formula:

In equation (20), J _x , J _y , and J _z represent the moment of inertia of the maglev rotor on their respective axes, ω _x and ω _z represent the attitude angular velocity of the spacecraft, and /> represents the attitude angular acceleration of the spacecraft, Ω represents the rotor speed, k _tx and k _ty represent the torsional stiffness of the two-axis control torque output by the Lorentz force magnetic bearing, _isx and _isy represent the control current generated by the spacecraft attitude maneuver, where Partial current can be expressed as:

Finally, the attitude angular velocity measurement equation of the spacecraft is obtained as follows:

ω _s =N ^-1 k _t I-sχ (22)

In the above formula, ω _s = [ω _x ω _y ], which means the two-axis attitude angular velocity of the spacecraft in the inertial space, I=[I _x (s) I _z (s)] represents the Laplace transform of the control current of the Lorentz force magnetic bearing, χ=[α(s) β(s)] represents the magnetic levitation rotor in the stator coordinates The Laplace transform of the attitude angular velocity under the system, s represents the Laplacian operator, and k _t represents the moment coefficient of the maglev control sensitive gyro.

The contents not described in detail in the present application belong to the prior art known to those skilled in the art.

Claims (5)

1. A satellite double-shaft attitude measurement and control integrated method of a single magnetic suspension control sensitive gyroscope is characterized by comprising the following steps of: the magnetic suspension control sensitive gyroscope can be used for realizing the attitude measurement and attitude control of two shafts of a spacecraft, the two-degree-of-freedom deflection of a high-speed rotating magnetic suspension rotor is utilized for changing the angular momentum direction, the high-speed rotating magnetic suspension rotor can exchange the angular momentum of the two shafts with the spacecraft, the attitude control of the two shafts of the spacecraft is realized, the linear relation between the control moment and the control current generated by a lorentz force magnetic bearing for controlling the deflection of the magnetic suspension rotor is utilized for measuring the angular displacement and the lorentz force magnetic bearing current of the magnetic suspension rotor under a stator coordinate system, and the measurement of the attitude angular rate of the two shafts of the spacecraft is realized, and the method specifically comprises the following steps:

(1) Establishing spacecraft attitude kinematics and attitude dynamics equations based on a magnetic suspension control sensitive gyroscope;

when the magnetic suspension control sensitive gyroscope is mounted on the satellite body, the rolling and yaw control of the satellite are realized by controlling the angular momentum direction of the rotor of the magnetic suspension control sensitive gyroscope, and the angular momentum of the satellite is expressed as:

H _sr ＝H _s +h _r (1)

wherein H is _sr Representing the total angular momentum of the magnetically levitated control sensitive gyroscope mounted on the spacecraft, H _s The angular momentum h of the satellite body when the magnetic suspension control sensitive gyroscope does not work is represented _r The angular momentum of the magnetic suspension control sensitive gyro rotor relative to the satellite body is expressed, and according to the angular momentum theorem, the angular momentum comprises:

wherein M represents the external moment applied to the satellite, ω= [ ω ] _x ω _y ω _z ],ω _x 、ω _y 、ω _z Represents the angular velocity of the attitude of the spacecraft,represents the differentiation of ω, ++>h _r ＝[h _rx h _ry h _rz ]Representing the angular momentum of the rotor in the body coordinate system, i= [ I ] _x I _y I _z ] ^T Representing the moment of inertia of each axis of the spacecraft:

under inertial coordinates, the yaw angular velocity and the angular acceleration of the magnetically levitated rotor are expressed as:

wherein omega _x 、ω _y 、ω _z Represents the angular velocity of the attitude of the spacecraft,representing attitude angular acceleration of spacecraft，/>The attitude angular velocity of the magnetic suspension rotor under the stator coordinate system is represented, omega represents the rotating speed of the magnetic suspension rotor,representing the attitude angular acceleration of the magnetic levitation rotor in the stator coordinate system,/->Indicating angular acceleration, ω of rotor rotation _e Represents the angular velocity, ω of the track _r Representing the attitude angular velocity of the magnetic levitation rotor under inertial system,/->Representing the attitude angular acceleration of the magnetic levitation rotor under an inertial system;

from the rotor dynamics equation:

wherein J is _x ，J _y ，J _z Respectively represent the rotational inertia of the magnetic suspension rotor on the respective shaft, wherein omega represents the rotor rotating speed,and->Representing the angular velocity of the rotor in the stator coordinate system,/->And->Representing the angular acceleration, k, of the rotor in the stator coordinate system _tx And k _ty The torsional rigidity of the output two-axis control moment of the Lorentz force magnetic bearing is represented, i _x And i _y Representing the control current of the respective axes;

(2) Establishing a spacecraft attitude control dynamics model

According to the magnetic suspension rotor dynamics model and the spacecraft attitude dynamics model, the dynamics model of the magnetic suspension control sensitive gyroscope mounted on the spacecraft is obtained as shown in the following formula:

wherein omega _x 、ω _y 、ω _z Represents the angular velocity of the attitude of the spacecraft,represents the attitude angular acceleration of the spacecraft X-axis, < >>Represents the attitude angular acceleration of the Z axis of the spacecraft, M _x And M _z Represents the disturbance moment applied to the spacecraft in the X axis and the Z axis, h _x 、h _y And h _z Representing angular momentum, k, of the rotor in the body coordinate system _tx And k _ty The torsional rigidity of the output two-axis control moment of the Lorentz force magnetic bearing is represented, i _x And i _y Representing control current of respective axes, J _x ，J _y ，J _z Respectively represent the rotational inertia of the magnetic suspension rotor on the respective shaft, I _x 、I _y And I _z Representing the moment of inertia of each axis of the spacecraft:

the following formula is obtained according to the attitude kinematics of the spacecraft:

wherein omega _x 、ω _y And omega _z Representing the angular velocity, ω, of the attitude of a spacecraft ₀ Representing the orbital angular velocity during operation of the spacecraft,representing yaw angle of spacecraft, ψ represents roll angle of spacecraft, +.>Representing yaw rate of spacecraft, +.>Representing the roll angular velocity of the spacecraft;

considering that the orbit angular velocity in the satellite motion process is very small and the satellite maneuvering angle is limited, under the condition of small angle and without considering the disturbance moment, combining with the attitude kinematic equation of the spacecraft, the model of spacecraft attitude control is expressed as:

wherein J is _x ，J _y ，J _z Respectively represent the rotational inertia of the magnetic suspension rotor on the respective shaft, I _x 、I _y And I _z Representing the moment of inertia of each axis of the spacecraft,representing yaw angle of spacecraft, ψ represents roll angle of spacecraft, +.>Representing yaw rate of spacecraft, +.>Representing the roll angular velocity of a spacecraft, +.>And->Representing the angular velocity of the rotor in the stator coordinate system,/->And->Representing the angular acceleration, k, of the rotor in the stator coordinate system _tx And k _ty The torsional rigidity of the output two-axis control moment of the Lorentz force magnetic bearing is represented, i _x And i _y Representing the control current of the respective axes;

so that the single magnetic suspension control sensitive gyroscope can realize the two-axis attitude control of the spacecraft;

(3) Spacecraft attitude angular velocity measurement based on magnetic suspension control sensitive gyroscope

When the spacecraft is maneuvered, the angular momentum of the magnetic suspension rotor maneuvers along with the spacecraft, the current for controlling the magnetic suspension rotor maneuver consists of two parts, one part is used for controlling the stable suspension of the magnetic suspension rotor, and the other part is used for controlling the attitude maneuver of the spacecraft;

from the rotor dynamics equation, it can be seen that:

wherein i is _rcx And i _rcy Representing control current for controlling rotor levitation, J _r Represents the radial moment of inertia of the rotor, h _z Representing angular momentum, k, of the rotor _tx And k _ty The torsional rigidity of the lorentz force magnetic bearing for outputting the control moment of the two shafts is represented,and->Representing the angular velocity of the rotor in the stator coordinate system,/->And->Representing the attitude angular acceleration of the rotor under a stator coordinate system;

when the magnetic suspension control sensitive gyroscope is mounted on a spacecraft, the spacecraft generates attitude maneuver, and the magnetic suspension control sensitive gyroscope generates control current as shown in the following formula:

wherein J is _x ，J _y ，J _z Respectively represent the rotational inertia omega of the magnetic suspension rotor on the respective shaft _x And omega _z Represents the angular velocity of the attitude of the spacecraft,and->Representing the attitude angular acceleration of the spacecraft, Ω representing the rotor speed, k _tx And k _ty The torsional rigidity of the output two-axis control moment of the Lorentz force magnetic bearing is represented, i _sx And i _sy Representing a control current generated by attitude maneuver of the spacecraft, the partial current being expressed as:

finally, an attitude angular velocity measurement equation of the spacecraft is obtained, wherein the equation is shown as follows:

ω _s ＝N ^-1 k _t I-sχ (11)

wherein omega _s ＝[ω _x ω _y ]Represents the two-axis attitude angular velocity of the spacecraft in the inertial space,I＝[I _x (s)I _z (s)]laplacian transformation of control current representing Lorentz force magnetic bearing, χ= [ α(s) β(s)]Laplacian transformation representing the angular velocity of a magnetically levitated rotor in a stator coordinate system, s representing the Laplacian, k _t And the moment coefficient of the magnetic suspension control sensitive gyroscope is represented.

2. The integrated satellite double-shaft attitude measurement and control method of the single magnetic suspension control sensitive gyroscope according to claim 1, which is characterized in that: the angular displacement of the magnetic suspension rotor under the magnetic suspension control sensitive gyroscope stator coordinate system is required to be measured, and the attitude angular speed and the angular acceleration of the magnetic suspension rotor are obtained through differentiation.

3. The integrated satellite double-shaft attitude measurement and control method of the single magnetic suspension control sensitive gyroscope according to claim 1, which is characterized in that: the total control current of the Lorentz force magnetic bearing comprises two parts, wherein one part of control current is used for realizing stable control of the magnetic suspension rotor, the other part of control current is used for realizing movement of the magnetic suspension rotor under an inertial system, and the other part of control current is used for realizing attitude control and attitude angular rate measurement of the spacecraft.

4. The integrated satellite double-shaft attitude measurement and control method of the single magnetic suspension control sensitive gyroscope according to claim 1, which is characterized in that: it is necessary to measure the control current of the lorentz force magnetic bearing.

5. The integrated satellite double-shaft attitude measurement and control method of the single magnetic suspension control sensitive gyroscope according to claim 1, which is characterized in that: the magnetic suspension control sensitive gyroscope is used for carrying out attitude control on the spacecraft, and an additional attitude sensor is not needed, so that the traditional control system is simplified.