Multi-body Coupled Attitude Control Method and System Based on Zero Force Control

Abstract

A multi-body coupled attitude control method and system based on zero-force control, which obtains the disturbing torque generated by the movement of the rotating mechanism between the satellite platform and the rotating mechanism; calculates the compensation torque according to the disturbing torque and the expected zero torque, and controls the corresponding rotating mechanism to act according to the compensation torque to offset the influence of the movement of the rotating mechanism on the control of the satellite platform. The present invention uses the rotating mechanism between the satellite platform and the payload as an intermediate medium, and controls the action of the rotating mechanism according to the compensation torque to achieve the compensation of the satellite platform, reduces the influence of the payload rotation on the control of the satellite platform, improves the attitude control accuracy and stability of the satellite platform, realizes the decoupling of the satellite platform control and the payload rotation, and can meet the satellite platform control requirements when providing different spatial orientations for multiple payloads simultaneously.

Description

Technical Field

[0001] The present invention relates to the technical field of spaceborne payload applications, and particularly to a multi-body coupled attitude control method and system based on zero-force control. Background Art

[0002] Due to the constraints of the flight orbit, space vehicles cannot meet the mission requirements of remotely sensing ground targets at any time. In order to improve the response speed to ground targets and shorten the revisit period, space vehicles often need to have the ability to adjust the attitude of remote sensing payloads to increase the remote sensing range of the payloads.

[0003] Space payloads often have high resolutions, thus posing high requirements for the pointing accuracy and stability of control. Existing main design schemes cannot solve the problems of a vehicle platform carrying multiple payloads with different space pointing requirements and the payload inertia being basically equivalent to the platform mass.

[0004] Current design schemes mainly target the following situations:

[0005] 1. The inertia of the vehicle platform is much larger than the rotating part of the payload (commonly seen in space stations), and the inertia of the payload is much smaller than the mass of the platform. Therefore, even if multiple turntable mechanisms maneuver simultaneously, it has almost no impact on the stability of the platform, which is obviously not applicable to the requirement of the satellite platform and payload having equivalent masses;

[0006] 2. Although the payload has high requirements for the pointing accuracy and stability of control, the requirements for the vehicle platform itself are not high. In this case, only the space pointing and stability of the payload need to be ensured first during design, which is obviously not applicable to multi-payload platforms because generally, all payloads have control requirements, and the control of these payloads is based on the platform dynamics. On the one hand, if the platform is unstable, it cannot satisfy multiple payloads simultaneously and ensure control to carry out tasks. On the other hand, simultaneous control of multiple payloads and the impact on the platform will also cause the platform to diverge in control due to the coupled interaction of multiple turntable mechanisms, affecting the safety of the platform;

[0007] 3. The platform-payload integration scheme. This design scheme can often only satisfy single-payload vehicles or the situation where the payloads have the same space pointing direction or a determined mutual relationship, and cannot meet the requirement of providing different space pointings for multiple payloads simultaneously. Summary of the Invention

[0008] Aiming at the deficiencies of the prior art, the present invention provides a multi-body coupled attitude control method and system based on zero-force control to solve the problem that when an existing satellite platform has multiple turntable mechanisms and carries large-inertia payloads simultaneously, it cannot ensure the high precision and stability of the attitude control of the platform and the payload.

[0009] In the first aspect, the present invention provides a multi-body coupled attitude control method based on zero-force control, including the following steps:

[0010] Obtain the disturbance torque generated by the movement of the rotating mechanism between the satellite platform and the rotating mechanism;

[0011] Calculate the compensation torque according to the disturbance torque and the desired zero torque, and control the corresponding rotating mechanism to act according to the compensation torque to offset the influence of the movement of the rotating mechanism on the satellite platform control.

[0012] Further, the specific calculation formula of the compensation torque is:

[0013]

[0014] where T e = T o - T r ; T o is the desired zero torque, T r is the disturbance torque, k p1 is the proportional coefficient of the PI controller, k I1 is the integral coefficient of the PI controller, t0 is the starting time of the movement of the rotating mechanism, t is the current time, and T c is the compensation torque of the rotating mechanism.

[0015] Further, the specific calculation formula of the compensation torque is:

[0016]

[0017] where T e = T o - T r ; T o is the desired zero torque, T r is the disturbance torque, T q is the feedforward torque, k p1 is the proportional coefficient of the PI controller, k I1 is the integral coefficient of the PI controller, t0 is the starting time of the movement of the rotating mechanism, t is the current time, and T c is the compensation torque of the rotating mechanism.

[0018] Further, the feedforward torque T q is calculated and obtained according to the relative movement between the load and the corresponding rotating mechanism, and the specific calculation formula is:

[0019]

[0020] where I q is the inertia of the rotating mechanism, is the angular acceleration of the rotating mechanism.

[0021] In a second aspect, the present invention provides a multi-body coupled attitude control system based on zero-force control, including a payload control system, a satellite platform control system, and a turntable control system disposed between the payload control system and the satellite platform control system;

[0022] The turntable control system is configured to obtain the disturbing torque generated by the movement of the rotating mechanism between the satellite platform and the rotating mechanism; and to calculate a compensation torque according to the disturbing torque and the desired zero torque, and control the corresponding rotating mechanism to act according to the compensation torque to offset the influence of the movement of the rotating mechanism on the satellite platform control.

[0023] Further, the turntable control system includes a turntable controller, a torque sensor, and a rotating mechanism;

[0024] The torque sensor collects the disturbing torque generated by the movement of the rotating mechanism between the satellite platform and the rotating mechanism;

[0025] The turntable controller calculates a compensation torque according to the disturbing torque and the desired zero torque, and controls the corresponding rotating mechanism to act according to the compensation torque.

[0026] Further, the satellite platform control system includes a first attitude sensor, a Kalman filter, a platform controller, and a platform actuator;

[0027] The first attitude sensor collects the real-time attitude information of the satellite platform in orbit, the Kalman filter filters the real-time attitude information of the satellite platform in orbit, and the platform controller outputs a control command according to the filtered real-time attitude information of the satellite platform in orbit and its target attitude information to control the platform actuator to act, so as to realize the attitude control of the satellite platform.

[0028] Further, the first attitude sensor includes a star sensor and a first three-axis fiber optic gyroscope.

[0029] Further, the payload control system includes a second attitude sensor, a payload controller, and a payload actuator;

[0030] The second attitude sensor collects the real-time attitude information of the payload, and the payload controller outputs a control command according to the real-time attitude information of the payload and its target attitude information to control the payload actuator to act, so as to realize the pointing control of the payload.

[0031] Further, the payload actuator is a momentum wheel, and the torque of the momentum wheel is distributed by speed control. The specific formula is:

[0032] T T =-C w ·hw = -C w ·I w ·Ω w

[0033] where, T T is the torque of the momentum wheel, C w is the installation matrix of the momentum wheel, h w is the angular momentum of the momentum wheel, I w is the inertia matrix of the momentum wheel, and Ω w is the rotational speed of the momentum wheel.

[0034] Furthermore, the second attitude sensor includes an optoelectronic encoder and a second three-axis fiber optic gyroscope.

[0035] The beneficial effects of the present invention are as follows:

[0036] A multi-body coupled attitude control method and system based on zero-force control provided by the present invention uses the rotating mechanism between the satellite platform and the payload as an intermediate medium, calculates the compensation torque through the output torque of the satellite platform and the disturbance torque of the rotating mechanism, and controls the corresponding rotating mechanism to act according to the compensation torque to achieve the compensation of the satellite platform, reduces the influence of the payload rotation on the satellite platform control, improves the attitude control accuracy and stability of the satellite platform, realizes the decoupling of the satellite platform control and the payload rotation, and can meet the satellite platform control requirements when providing different spatial orientations for multiple payloads simultaneously;

[0037] The rotating mechanism, as an intermediate medium between the payload and the satellite platform, adopts a follow-up strategy, ensuring that the transmitted torque at the connection between the payload and the satellite platform main body is zero, that is, zero torque transmission, ensuring the control accuracy and control stability of the payload and the satellite platform, and simplifying the design difficulty of the multi-body platform carrying large-inertia payloads. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] In order to more clearly illustrate the technical solutions of the present invention, the drawings required for the description of the embodiments will be briefly introduced below. Obviously, the drawings in the following description are only one embodiment of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0039] Figure 1 is the control strategy block diagram of the turntable control system in the embodiment of the present invention;

[0040] Figure 2 is the control strategy block diagram of the satellite platform control system in the embodiment of the present invention;

[0041] Figure 3 is the control strategy block diagram of the payload control system in the embodiment of the present invention;

[0042] Figure 4 This is the connection relationship among the payload, turntable and satellite main body in the embodiments of the present invention. Specific embodiments

[0043] The following will clearly and completely describe the technical solutions in the present invention with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part rather than all of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the scope of protection of the present invention.

[0044] The following will specifically describe the technical solutions of the present application with specific embodiments. These specific embodiments can be combined with each other, and the same or similar concepts or processes may not be repeated in some embodiments.

[0045] For the aircraft to be oriented towards the ground, the pointing of the payload is achieved through a rotating mechanism. The aircraft (such as a small satellite) is small in size and light in weight, and is easily affected by the rotation of the payload. The rotating mechanisms of the on-board payloads (space turntables, scanning mirrors, solar panels, etc.) have relatively large masses relative to the small satellite. The rotation of the payload will cause large fluctuations in the moment of inertia of the small satellite, seriously affecting the operation stability and attitude control of the satellite itself. The existence of the disturbing torque of the rotating mechanism and vibrations will also seriously interfere with the operation of the satellite body, causing deviations in the satellite attitude and reducing the accuracy of the rotation detection sensor; limited by the hardware system bandwidth of the satellite platform control system and the turntable control system itself, relying solely on the adaptation of the rotating mechanism and the satellite platform to eliminate this influence has poor effects. Based on this, the present invention calculates the compensation torque according to the output torque of the satellite platform and the disturbing torque of the rotating mechanism, and controls the corresponding rotating mechanism (such as the turntable) to act according to the compensation torque to offset the influence of the movement of the rotating mechanism on the satellite platform, realizing the decoupling of satellite platform control and payload rotation.

[0046] An attitude control method for multi-body coupling based on zero-force control provided by an embodiment of the present invention, wherein the multi-body coupling attitude control system includes a payload control system, a satellite platform control system, and a turntable control system provided between the payload control system and the satellite platform control system. The specific control method includes the following steps:

[0047] Step 1: Obtain the disturbing torque generated by the movement of the rotating mechanism between the satellite platform and the rotating mechanism.

[0048] Step 2: Calculate the compensation torque according to the disturbing torque in Step 1 and the expected zero torque, and control the corresponding rotating mechanism to act according to the compensation torque to offset the influence of the movement of the rotating mechanism on the satellite platform control.

[0049] In a specific embodiment of the present invention, asFigure 1 As shown in Figure 1 , the turntable control system includes a turntable controller, a torque sensor, and a rotating mechanism; the torque sensor collects the disturbing torque generated by the movement of the rotating mechanism between the satellite platform and the rotating mechanism and sends it to the turntable controller. The turntable controller calculates the compensation torque according to the disturbing torque and the expected zero torque. The specific calculation formula is:

[0050]

[0051] where T e = T o - T r ; T o is the expected zero torque, which is 0; T r is the disturbing torque; k p1 is the proportional coefficient of the PI controller; k I1 is the integral coefficient of the PI controller; t0 is the starting time of the movement of the rotating mechanism; t is the current time; T c is the compensation torque of the rotating mechanism.

[0052] If only relying on the disturbing torque T r for feedback control, the control response speed will be slow and the tracking error will be large due to the lag effect of the turntable controller. Therefore, in another specific embodiment of the present invention, the specific calculation formula of the compensation torque is:

[0053]

[0054] where T q is the feedforward torque. The feedforward torque T q is calculated and obtained according to the relative movement between the load and the corresponding rotating mechanism. The specific calculation formula is:

[0055]

[0056] where I q is the inertia of the corresponding rotating mechanism, is the angular acceleration of the corresponding rotating mechanism. When performing the motion planning of the load pointing based on the known current pointing of the satellite platform (i.e., the spatial attitude reference established by the satellite platform) and the expected pointing of the mission target load, the angular velocity and angular acceleration of the rotating mechanism can be obtained, and the angular acceleration of the rotating mechanism is used as the input of the control feedforward.

[0057] Adding a feedforward part in the calculation of the compensation torque can greatly improve the response speed of the control system, reduce the tracking error in the follow-up process of the rotating mechanism, and improve the stability of the control.

[0058] The turntable controller outputs a control command according to T c to control the action of the rotating mechanism, so that the torque generated by the rotating mechanism is Tc , to offset the influence of the movement of the rotating mechanism on the attitude of the satellite platform for earth orientation, and to achieve the decoupling of the satellite platform control and the payload rotation. For multiple rotating mechanisms, each rotating mechanism is controlled according to the corresponding compensation torque, so as to meet the satellite platform control requirements when providing different spatial orientations for multiple payloads simultaneously. In this embodiment, the movement of the rotating mechanism is driven by a brushless motor.

[0059] In a specific embodiment of the present invention, as Figure 2 shown, the satellite platform control system includes a first attitude sensor, a Kalman filter, a platform controller, and a platform actuator; the first attitude sensor collects the real-time attitude information of the satellite platform in orbit, the Kalman filter filters and estimates the real-time attitude information of the satellite platform in orbit, and the platform controller outputs a control instruction according to the filtered real-time attitude information of the satellite platform in orbit and its target attitude information θ ref_s to control the action of the platform actuator and achieve the attitude control of the satellite platform.

[0060] In a specific embodiment of the present invention, the first attitude sensor includes a star sensor and a first three-axis fiber optic gyroscope. The star sensor and the first three-axis fiber optic gyroscope are fixedly installed on the platform surface of the satellite platform. The first three-axis fiber optic gyroscope senses the angular velocity of the satellite platform, and the star sensor senses the azimuth of the satellite platform and provides measurement information for the first three-axis fiber optic gyroscope. The Kalman filter filters and estimates the measured attitude information of the first three-axis fiber optic gyroscope and the star sensor. The platform controller obtains the torque T of the platform actuator according to the measured attitude information and its target attitude information θ ref_s , and issues a control instruction according to the torque T of the platform actuator s to make the platform actuator generate a torque T under this control instruction s , and the specific formula is: s T

[0061] T s =-k p2 ·sgn(q0)·I·q v -k d2 ·I·ω + ω×H (4)

[0062] where, T s is the torque information output by the satellite platform, k p2 is the proportional coefficient of the PD controller, k d2 is the differential coefficient of the PD controller, sgn() is the sign function, and q0 is the scalar part of the error quaternion; q0 is obtained through the target attitude θ ref_sWith the actual attitude It is obtained through calculation, and its calculation method is the prior art; q v Is the vector part of the error quaternion, q v Through the target attitude θ ref_s With the actual attitude It is obtained through calculation, and its calculation method is the prior art; I is the inertia matrix of the star body (representing the mass characteristics of the star body), ω is the angular velocity of the star body, ω is detected and obtained by the angular velocity measurement sensor, and H is the angular momentum of the star body. Figure 2 Among them, the reaction wheel is the platform actuator, that is, the actuator of the torque T s Of the actuator.

[0063] In a specific embodiment of the present invention, as Figure 3 Shown, the payload control system includes a second attitude sensor, a payload controller, and a payload actuator; the second attitude sensor collects the real-time attitude information of the payload, and the payload controller outputs a control command according to the real-time attitude information of the payload and its target attitude information to control the action of the payload actuator, so as to realize the pointing control of the payload.

[0064] In a specific embodiment of the present invention, the second attitude sensor includes an optical encoder and a second three-axis fiber optic gyroscope. The optical encoder and the second three-axis fiber optic gyroscope are fixedly installed on the payload. The second three-axis fiber optic gyroscope senses the rotational angular rate of the payload, and the optical encoder senses the relative rotation angle information of the payload. The payload controller obtains the torque T Of the payload actuator according to the measured attitude information θ ref_T And issues a control command according to the torque T T Of the payload actuator, so that the payload actuator generates a torque T T Under this control command. In this embodiment, the payload actuator is a momentum wheel, and the torque of the momentum wheel is realized by controlling the rotational speed of the momentum wheel. The specific distribution formula is: T T

[0065] T T =-C w ·h w =-C w ·I w ·Ω w (5)

[0066] Among them, T T Is the torque of the momentum wheel, C w Is the installation matrix of the momentum wheel, h w Is the angular momentum of the momentum wheel, I w Is the inertia matrix of the momentum wheel, Ω w Is the rotational speed of the momentum wheel.

[0067] The satellite platform control system establishes a three-axis attitude reference coordinate, providing a dynamic basis for the control of each rotating mechanism. When the payload needs to adjust its current spatial orientation, the payload control system calculates the control commands for the momentum wheels based on the three-axis attitude reference coordinate established by the satellite platform, achieving high-precision pointing control of the payload. According to the disturbing torque collected by the torque sensor, the turntable controller calculates the compensation torque and controls the rotating mechanism based on the compensation torque, achieving zero-torque transmission between the satellite platform and the payload.

[0068] An embodiment of the present invention further provides a multi-body coupled attitude control system based on zero-force control, including a payload control system, a satellite platform control system, and a turntable control system provided between the payload control system and the satellite platform control system. As Figure 4 shown, the satellite platform is connected to the rotating mechanism through a connecting support structure, and the rotating mechanism establishes a control connection between the satellite platform and the payload.

[0069] In a specific embodiment of the present invention, as Figure 1 shown, the turntable control system includes a turntable controller, a torque sensor, and a rotating mechanism; the torque sensor collects the disturbing torque generated by the movement of the rotating mechanism between the satellite platform and the rotating mechanism and sends it to the turntable controller. The turntable controller calculates the compensation torque according to the disturbing torque and the expected zero torque, and the specific formula is shown in Equation (1) or (2). The turntable controller controls the action of the rotating mechanism according to the output control command of T c to make the torque generated by the rotating mechanism be T c , so as to offset the influence of the movement of the rotating mechanism on the attitude of the satellite platform facing the ground, realizing the decoupling of the satellite platform control and the payload rotation.

[0070] In a specific embodiment of the present invention, as Figure 2 shown, the satellite platform control system includes a star sensor, a first three-axis fiber optic gyroscope, a Kalman filter, a platform controller, and a platform actuator; the star sensor and the first three-axis fiber optic gyroscope are fixedly installed on the platform surface of the satellite platform. The first three-axis fiber optic gyroscope senses the angular velocity of the satellite platform, and the star sensor senses the azimuth of the satellite platform, providing measurement information for the first three-axis fiber optic gyroscope; the Kalman filter filters and estimates the measured attitude information of the first three-axis fiber optic gyroscope and the star sensor. The platform controller obtains the torque T of the platform actuator according to the measured attitude information θ ref_s and its target attitude information s , and issues a control command according to the torque T s of the platform actuator, so that the platform actuator generates a torque T s under this control command., the specific formula is shown in Equation (4) to achieve real-time control of the satellite platform attitude.

[0071] In a specific embodiment of the present invention, as Figure 3 shown, the payload control system includes an optoelectronic encoder, a second three-axis fiber optic gyroscope, a payload controller, and a payload actuator; the optoelectronic encoder and the second three-axis fiber optic gyroscope are fixedly installed on the payload, the second three-axis fiber optic gyroscope senses the rotational angular velocity of the payload, and the optoelectronic encoder senses the relative rotation angle information of the payload; the payload controller obtains the torque T of the payload actuator according to the measured attitude information and its target attitude information θ ref_T and issues a control command according to the torque T of the payload actuator, so that the payload actuator generates the torque T under this control command T to achieve the pointing control of the payload. T T

[0072] Although the preferred embodiments of the present invention have been described, those skilled in the art can make additional changes and modifications once they learn the basic creative concept. Therefore, the appended claims are intended to be construed to include the preferred embodiments and all changes and modifications falling within the scope of the present invention. Obviously, those skilled in the art can make various changes and variations to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalent technologies, the present invention is also intended to include these modifications and variations.​​

Claims

1. A multi-body coupling attitude control method based on zero-force control, characterized in that: The following steps are involved: Obtaining the disturbance torque between the satellite platform and the rotating mechanism caused by the movement of the rotating mechanism; Calculating a compensation torque according to the disturbance torque and the desired zero torque, and controlling a corresponding rotation mechanism action according to the compensation torque to offset the influence of the rotation mechanism motion on the control of the satellite platform; Here, the desired zero moment is 0.

2. The multi-body coupling attitude control method based on zero-force control according to claim 1, characterized in that: The specific calculation formula of the compensation torque is: Among them, T e =T o -T r , T o is the desired zero moment, T r is the disturbance torque, k p1 is the proportional coefficient of the PI controller, k I1 is the integral coefficient of the PI controller, t0 is the starting time of the rotating mechanism, t is the current time, T c is the compensation torque of the rotating mechanism.

3. The multi-body coupling attitude control method based on zero-force control according to claim 1, characterized in that: The specific calculation formula of the compensation torque is: Among them, T e =T o -T r , T o is the desired zero torque, T r is the disturbance torque, T q is the feedforward torque, k p1 is the proportional coefficient of the PI controller, k I1 is the integral coefficient of the PI controller, t0 is the starting time of the rotating mechanism, t is the current time, T c is the compensation torque of the rotating mechanism.

4. The multi-body coupling attitude control method based on zero-force control according to claim 3, characterized in that: The feedforward torque T q It is calculated based on the relative motion between the load and the corresponding rotating mechanism. The specific calculation formula is: Among them, I q is the inertia of the rotating mechanism, is the angular acceleration of the rotating mechanism.

5. A multi-body coupled attitude control system based on zero-force control, comprising a payload control system, a satellite platform control system, and a turntable control system disposed between the payload control system and the satellite platform control system; characterized in that: The turntable control system is used to obtain the disturbance torque between the satellite platform and the rotation mechanism due to the movement of the rotation mechanism; and is used to calculate the compensation torque based on the disturbance torque and the desired zero torque, and control the corresponding rotation mechanism action according to the compensation torque to offset the influence of the rotation mechanism movement on the control of the satellite platform; Here, the desired zero moment is 0.

6. The multi-body coupling attitude control system based on zero-force control according to claim 5, characterized in that: The turntable control system includes a turntable controller, a torque sensor and a rotation mechanism; The torque sensor collects the disturbance torque between the satellite platform and the rotating mechanism due to the movement of the rotating mechanism; The turntable controller calculates a compensation torque according to the disturbance torque and the desired zero torque, and controls the corresponding rotation mechanism action according to the compensation torque.

7. The multi-body coupling attitude control system based on zero-force control according to claim 6, characterized in that: The specific calculation formula of the compensation torque is: Among them, T e =T o -T r , T o is the desired zero torque, T r is the disturbance torque, k p1 is the proportional coefficient of the PI controller, k I1 is the integral coefficient of the PI controller, t0 is the starting time of the rotating mechanism, t is the current time, T c is the compensation torque of the rotating mechanism.

8. The multi-body coupling attitude control system based on zero-force control according to claim 6, characterized in that: The specific calculation formula of the compensation torque is: Among them, T e =T o -T r , T o is the desired zero moment, T r is the disturbance torque, T q is the feedforward torque, k p1 is the proportional coefficient of the PI controller, k I1 is the integral coefficient of the PI controller, t0 is the starting time of the rotating mechanism, t is the current time, T c is the compensation torque of the rotating mechanism.

9. The multi-body coupling attitude control system based on zero-force control according to any one of claims 5 to 8, characterized in that: The satellite platform control system includes a first attitude sensor, a Kalman filter, a platform controller and a platform actuator; The first attitude sensor collects real-time attitude information of the satellite platform on orbit, the Kalman filter filters the real-time attitude information of the satellite platform on orbit, and the platform controller outputs control instructions based on the filtered real-time attitude information of the satellite platform on orbit and its target attitude information to control the action of the platform actuator to achieve attitude control of the satellite platform.

10. The multi-body coupling attitude control system based on zero-force control according to any one of claims 5 to 8, characterized in that: The load control system includes a second attitude sensor, a load controller and a load actuator; The second attitude sensor collects real-time attitude information of the payload, and the payload controller outputs control instructions based on the real-time attitude information of the payload and its target attitude information to control the action of the payload actuator, thereby achieving directional control of the payload; The load actuator is a momentum wheel, and the torque of the momentum wheel is distributed by speed control. The specific formula is: T T =-C w ·h w =-C w ·I w ·Ω w Among them, T T is the torque of the momentum wheel, C w is the installation matrix of the momentum wheel, h w is the angular momentum of the momentum wheel, I w is the inertia matrix of the momentum wheel, Ω w is the speed of the momentum wheel.

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