Output constraint singularity avoidance control law for hybrid execution mechanism
By using the output constraint singular avoidance manipulation law in the hybrid actuator, finding and using singular angular momentum, the output torque error problem of the control torque gyro system in the singular state is solved, and a high-precision, error-free command torque output is achieved.
Patent Information
- Application Number
- CN202510534630.5
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-04-27
- Publication Date
- 2025-05-30
- Estimated Expiration
- 2045-04-27
AI Technical Summary
The control torque gyro system will have singular problems under certain frame angle combinations, resulting in output torque errors, and may generate torque errors when escaping the singular state.
A singular evasion manipulation law for the hybrid actuator is adopted. By finding the singular angular momentum closest to the current SGCMG system angular momentum and adding it to the optimization function, solving the Lagrangian function, a singular evasion manipulation law is established, and the torque allocation strategy is updated under consideration of the output constraints.
It realizes the singular evasion of the SGCMG system, outputs high-precision and error-free command torque, meets the actual output constraints, and is of great significance to the application of hybrid actuators.
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Figure CN120057308A_ABST
Abstract
Description
Technical Field
[0001] The invention belongs to the technical field of application of spacecraft attitude actuators, and relates to an output constraint singularity avoidance control law for hybrid actuators. Background Art
[0002] With the continuous development of the aerospace industry, the number of non-cooperative space targets such as space debris, failed satellites, and non-friendly satellites has increased rapidly, making the space operating environment increasingly complex and dangerous. Tasks such as space debris cleaning, failed satellite repair, and fuel refueling for non-cooperative space targets require spacecraft to have rapid attitude maneuvering and tracking capabilities. Attitude actuators that can output high-precision and large torques are the basis for agile satellites to achieve rapid maneuvers. Control moment gyros (CMGs) are generally used, which do not require fuel consumption, are suitable for long-term operation in orbit, can output continuous torque, and have higher control accuracy. However, there is a singularity problem. Under certain frame angle combinations, the output torque of the CMG system is in the same plane. At the same time, when the output torque capacity is limited, the CMG system often generates output torque errors in the process of escaping from the singularity. Therefore, it is of great significance to design a control law that considers output constraints to complete singularity avoidance and enable the system to output error-free command torque.
[0003] Due to the complexity of space missions, most spacecraft attitude control uses hybrid actuators, which can take advantage of the advantages of each actuator. Flywheels, as attitude control actuators commonly used in existing satellites, can use their high output accuracy and control moment gyroscopes as hybrid actuators. Flywheels can be used to assist control moment gyroscopes to avoid singular states, while providing high-precision torque for tracking control of agile satellites. Summary of the invention
[0004] The purpose of the present invention is to overcome the deficiencies in the prior art and provide an output constrained singular avoidance control law for a hybrid actuator, which can achieve singular avoidance of a SGCMG system and output a high-precision error-free command torque.
[0005] In order to achieve the purpose of the present invention, the following technical scheme is adopted to implement it.
[0006] A method for establishing an output constraint singularity avoidance control law for a hybrid actuator comprises the following steps: S1. According to the configuration of the hybrid actuator, find the angular momentum of the current SGCMG system through the command torque u and the SGCMG system frame angle δ The nearest singular angular momentum ; S2, the current SGCMG system angular momentum and the obtained singular angular momentum Add an optimization function to the distance between them, and calculate the angular momentum of the current SGCMG system Calculate the angular momentum of the SGCMG system with the influence term added , add the influence term related to the frame angular velocity, update the optimization function, construct the Lagrangian function according to the updated optimization function, and establish a singularity avoidance control law without output constraints by solving the partial derivatives of the Lagrangian function; S3. Under the condition of considering the output constraint conditions of the hybrid actuator, design the output constraint conditions as , and , and formulate the torque distribution strategies under the output constraint conditions of , and respectively; If the of RW and the of SGCMG calculated by the singularity avoidance control law in step S2 do not meet the output constraint conditions: , or , then obtain the output constraint singularity avoidance control law by updating the torque distribution strategy under this output constraint condition.
[0007] As a preferred solution of the present invention, the searching process of the singular angular momentum includes the following steps: S11. Establish a spacecraft reference frame according to the configuration of the hybrid actuator to obtain the system matrix of the hybrid actuator; S12. Combine the gimbal angles of each SGCMG into the gimbal angle set of the SGCMG system, and obtain the singular angular momentum closest to the th SGCMG gimbal angle through the commanded torque u and the SGCMG system gimbal angle δ: S13. Add up the singular angular momenta closest to all SGCMG gimbal angles , which is the singular angular momentum corresponding to the SGCMG system: ; ; In the formula, is the gimbal angle of the th SGCMG; are the two singular gimbal angles corresponding to the commanded torque respectively, is the control torque; is the The angular momentum direction of the rotor of an SGCMG; For the nearest rotor singular angular momentum direction corresponding to the gimbal angle of the th SGCMG;
[0008] As a preferred solution of the present invention, the specific process of obtaining the nearest singular angular momentum to the gimbal angle of the th SGCMG includes the following steps: S121. In the coordinate system definition of the SGCMG, is the unit vector of the installation direction of the th SGCMG gimbal, is the unit vector of the rotor angular velocity direction, is the unit vector in the opposite direction of the gyro output torque; S122. Considering the th SGCMG, if the control torque is , and the command torque is set as , then is considered as the output torque direction, and the output torque of the SGCMG system satisfies ; S123. Since the gimbal axis is fixed, is constrained in the vertical plane. If the SGCMG is in a singular state, is simultaneously located in the vertical plane. At this time, coincides with the intersection line of these two planes, has two choices, which are respectively , The corresponding control torque gyro gimbal angle is the singular gimbal angle ; S124. Define as the angular momentum direction of the rotor of the th SGCMG corresponding to the singular gimbal angle , divide the vertical plane into two parts, compare the included angle between and the singular rotor angular momentum . The smaller included angle of is corresponding to the nearest singular angular momentum direction.
[0009] As a preferred solution of the present invention, the specific process of constructing a singular avoidance control law without output constraints: S21. The current angular momentum of the SGCMG system The distance to the singular angular momentum is added to the optimization function; where: the optimization function is: ; In the formula, is the gimbal angle and the derivative of the flywheel angular velocity; is the Jacobian matrix of the SGCMG system; is the moment of inertia of the flywheel; , is the weight matrix; is the current angular momentum of the SGCMG system; is the system matrix; where: the coefficients in the weight matrix are: ; In the formula, is the magnitude of the rotor angular momentum of each SGCMG, are respectively the maximum gimbal angular velocity of the SGCMG and the maximum rotational angular acceleration of the RW; S22. According to the current angular momentum of the SGCMG system in step S21, calculate the angular momentum of the SGCMG system with the influence term added, and add the influence term related to the gimbal angular velocity to update the optimization function; where: the formula for calculating the angular momentum of the SGCMG system is: ; In the formula, is the system angular momentum with the influence term added; is the gimbal angular velocity of the th SGCMG; is the output torque direction of the th SGCMG; is a very small positive constant; The updated optimization function is: ; Denote ; S23. According to the updated optimization function obtained in step S22, establish the Lagrangian function , and by solving the partial derivatives of the Lagrangian function , obtain the singularity avoidance control law without output constraints; where: the Lagrangian function is: ; In the formula, is the Lagrange multiplier; By solving the Lagrangian function The partial derivatives are obtained as follows: ; In the formula, is the coefficient matrix, is the constant matrix, and the form is as follows: ; ; The relationship between the coefficients in the matrix and the system matrix is: ; ; In the formula, the system matrix ; is the element in the rd row and th column of the system matrix ; Solve the Lagrange multiplier: ; ; In the formula, , ; is the element in the th row and th column of the matrix , is the element in the th row and th column of the matrix , are respectively the component magnitudes of along each axis in the body coordinate system; The obtained singularity avoidance control law without output constraints is: ; In the formula, is the coefficient matrix, is the constant matrix, is the obtained Lagrange multiplier.
[0010] As a preferred embodiment of the present invention, when the of RW calculated by the singularity avoidance control law in step S23 does not satisfy the output constraint condition: Update process of the torque distribution strategy under the output constraint condition: When the of RW calculated by the singularity avoidance control law in step S23 exceeds the output constraint condition: ; In the formula, is the torque acting on the RW system calculated by the singularity avoidance control law in step S23, are respectively the maximum output angular acceleration of the th RW and the output angular acceleration obtained by the singularity avoidance control law in step S23; Solve the output frame angular velocity of the SGCMG with the remaining commanded torque , and the optimization function becomes: ; In the formula, is the weight matrix of the SGCMG; Take the partial derivative of the Lagrangian function to obtain: ; In the formula, the system matrix and the constant matrix are updated to: ; ; Let , , substitute into step S23 to get , then the updated singularity avoidance control law is: ; In the formula, is the updated coefficient matrix, is the updated constant matrix, is the updated Lagrange multiplier; If the frame angular velocity obtained from the above formula is greater than the maximum value of the frame angular velocity, the output frame angular velocity of the SGCMG is updated to: ; In the formula, is the torque acting on the SGCMG system calculated by the updated singularity avoidance control law, are respectively the maximum output frame angular velocity of the th SGCMG and the output frame angular velocity obtained by the updated singularity avoidance control law.
[0011] As a preferred solution of the present invention, when the of the SGCMG calculated by the singularity avoidance control law in step S23 does not satisfy the output constraint condition: When Update process of the torque distribution strategy under the output constraint condition: When the of the SGCMG calculated by the singularity avoidance manipulation law in step S23 exceeds the output constraint condition: ; In the formula, is the torque acting on the SGCMG system calculated by the singularity avoidance manipulation law in step S23, are respectively the maximum output frame angular velocity of the th SGCMG and the output frame angular velocity obtained by the singularity avoidance manipulation law in step S23; The rotor rotational angular acceleration of the RW can be obtained using the remaining command torque as: ; If the obtained rotational angular acceleration is greater than the maximum value of the rotational angular acceleration, a torque error will occur at this time, and the rotor rotational angular acceleration of the RW is updated to: ; In the formula, is the torque acting on the RW system calculated after updating the rotor rotational angular acceleration, are respectively the maximum output angular acceleration of the th RW and the output angular acceleration obtained after updating the rotor rotational angular acceleration.
[0012] As a preferred solution of the present invention, when the of the RW and the of the SGCMG calculated by the singularity avoidance manipulation law in step S23 do not satisfy their respective output constraint conditions: , Update process of the torque distribution strategy under the output constraint condition: If the of the RW and the of the SGCMG calculated by the singularity avoidance manipulation law in step S23 exceed their respective output constraint conditions: , then update the system parameters to: ; In the formula, is the torque acting on the SGCMG system calculated by the singularity avoidance manipulation law in step S23, is the torque acting on the RW system calculated by the singularity avoidance manipulation law in step S23, are respectively the maximum output frame angular velocity of the th SGCMG and the output frame angular velocity obtained by the singularity avoidance manipulation law in step S23, are respectively the maximum output angular acceleration of the th RW and the output angular acceleration obtained by the singularity avoidance control law in step S23.
[0013] Beneficial effects: 1. Based on the hybrid actuator, considering the ability of the actuator system to output torque without error, the distance between the SGCMG system and the singular state is defined and added to the optimization index in the control law, which has strong applicability; 2. The weighted coefficient is introduced to consider the output ability of each actuator and make full use of its output torque ability; 3. Considering the output ability constraint of the actuator, the singularity avoidance control law is updated to satisfy the actual limitation while outputting the command torque without error, which has important practical significance; 4. The singularity avoidance of the SGCMG system is realized, and the command torque with high precision can be output. Considering the actual output constraint, the angular momentum trajectory of the system is optimized in real time, which has certain reference significance for the application of the hybrid actuator. Description of the Drawings
[0014] Figure 1 is the overall workflow diagram of the present invention; Figure 2 is the workflow diagram of the output constraint singularity avoidance control law of the present invention; Figure 3 is the schematic diagram of the hybrid actuator configuration of the present invention; Figure 4 is the schematic diagram of the singular angular momentum of the present invention; Figure 5 is the schematic diagram of the singular angular momentum closest to the system angular momentum of the present invention. Detailed Embodiment
[0015] The present invention will be further described according to the embodiments and the drawings.
[0016] As an embodiment of the present invention, as Figure 1 shown, a method for establishing an output constraint singularity avoidance control law for a hybrid actuator includes the following steps: S1. According to the configuration of the hybrid actuator, find the singular angular momentum closest to the current SGCMG system angular momentum through the command torque u and the SGCMG system frame angle δ; where: the singular angular momentum is: : ; ; In the formula, is the frame angle of the th SGCMG; are respectively the command torque The two corresponding singular frame angles are control torques; is the th rotor angular momentum direction of the SGCMG corresponding to the singular frame angle; is the th rotor singular angular momentum direction closest to the frame angle of the th SGCMG; is the singular angular momentum closest to the current SGCMG system angular momentum S2. According to the current SGCMG system angular momentum in step S1 and the obtained singular angular momentum , establish a singular avoidance control law without output constraints, including the following steps: S21. Incorporate the distance between the current SGCMG system angular momentum in step S1 and the obtained singular angular momentum into the optimization function; where: the optimization function is: ; In the formula, is the frame angle and the derivative of the flywheel angular velocity; is the Jacobian matrix of the SGCMG system; is the moment of inertia of the flywheel; , is the weight matrix; is the current SGCMG system angular momentum; is the system matrix; where: the coefficients in the weight matrix are: ; In the formula, is the magnitude of the rotor angular momentum of each SGCMG, are respectively the maximum frame angular velocity of the SGCMG and the maximum rotational angular acceleration of the RW; S22. Calculate the SGCMG system angular momentum with the influence term added according to the current SGCMG system angular momentum in step S21 , and add the influence term related to the frame angular velocity to update the optimization function; where: the calculation formula for the SGCMG system angular momentum is: ; In the formula, is the system angular momentum with the influence term added; is the th frame angular velocity of the th SGCMG; Output torque direction of a SGCMG; is a very small positive constant; The updated optimization function is: ; Denote ; S23. Based on the updated optimization function obtained in step S22, establish the Lagrangian function , and by solving the partial derivatives of the Lagrangian function , obtain the singularity avoidance control law without output constraints; where: the Lagrangian function is: ; In the formula, is the Lagrange multiplier; The singularity avoidance control law without output constraints is: ; In the formula, is the coefficient matrix, is the constant matrix, is the obtained Lagrange multiplier; S3. Considering the output constraint conditions of the hybrid actuator, design the output constraint conditions as , and , and respectively formulate the , and torque distribution strategies under the output constraint conditions; If the of RW and the of SGCMG calculated by the singularity avoidance control law in step S2 satisfy the output constraint conditions: , or , then obtain the output constraint singularity avoidance control law through the torque distribution strategy under this output constraint condition; If the of RW and the of SGCMG calculated by the singularity avoidance control law in step S2 do not satisfy the output constraint conditions: , or , then update the torque distribution strategy under this output constraint condition, as shown in Figure 2 ; where: When the of RW calculated by the singularity avoidance control law in step S23 does not satisfy the output constraint condition: , Update process of torque distribution strategy under output constraints: When the of RW calculated by the singularity avoidance control law in step S23 exceeds the output constraints: ; wherein, is the torque acting on the RW system calculated by the singularity avoidance control law in step S23, are the maximum output angular acceleration of the th RW and the output angular acceleration obtained by the singularity avoidance control law in step S23, respectively; Solve the output gimbal angular velocity of SGCMG with the remaining commanded torque , and the optimization function becomes: ; wherein, is the weight matrix of SGCMG; Take the partial derivative of the Lagrangian function to obtain: ; wherein, the system matrix and the constant matrix are updated to: ; ; Let , , substitute into step S23 to get , then the updated singularity avoidance control law is: ; wherein, is the updated coefficient matrix, is the updated constant matrix, is the updated Lagrange multiplier; If the gimbal angular velocity obtained from the above formula is greater than the maximum gimbal angular velocity, the output gimbal angular velocity of SGCMG is updated to: ; wherein, is the torque acting on the SGCMG system calculated by the updated singularity avoidance control law, are the maximum output gimbal angular velocity of the th SGCMG and the output gimbal angular velocity obtained by the updated singularity avoidance control law, respectively.
[0017] As a preferred embodiment of the present invention, when the of the SGCMG calculated by the singularity avoidance manipulation law in step S23 does not satisfy the output constraint condition: Update process of the torque distribution strategy under the output constraint condition: When the of the SGCMG calculated by the singularity avoidance manipulation law in step S23 exceeds the output constraint condition: , the system parameters are updated to: ; In the formula, is the torque acting on the SGCMG system calculated by the singularity avoidance manipulation law in step S23, are respectively the maximum output frame angular velocity of the th SGCMG and the output frame angular velocity obtained by the singularity avoidance manipulation law in step S23; The rotor rotational angular acceleration of the RW can be obtained with the remaining command torque as: ; If the obtained rotational angular acceleration is greater than the maximum value of the rotational angular acceleration, a torque error will occur at this time, and the rotor rotational angular acceleration of the RW is updated to: ; In the formula, is the torque acting on the RW system calculated after updating the rotor rotational angular acceleration, are respectively the maximum output angular acceleration of the th RW and the output angular acceleration obtained after updating the rotor rotational angular acceleration.
[0018] As a preferred embodiment of the present invention, when the of the RW and the of the SGCMG calculated by the singularity avoidance manipulation law in step S23 do not satisfy their respective output constraint conditions: when, Update process of the torque distribution strategy under the output constraint condition: If the of the RW and the of the SGCMG calculated by the singularity avoidance manipulation law in step S23 exceed their respective output constraint conditions: , the system parameters are updated to: ; In the formula, The torque acting on the SGCMG system calculated by the singularity avoidance control law in step S23 The torque acting on the RW system calculated by the singularity avoidance control law in step S23 are respectively the maximum output gimbal angular velocity of the th SGCMG and the output gimbal angular velocity obtained by the singularity avoidance control law in step S23, and are respectively the maximum output angular acceleration of the
[0019] th RW and the output angular acceleration obtained by the singularity avoidance control law in step S23.
[0019] After completing the configuration of the hybrid actuator, considering the commanded torque at a certain moment during the satellite maneuver and the gimbal angle combination of the SGCMG system at this time, the angular momentum of the system at this moment and the singular angular momentum closest to it are obtained; the distance between the system and the singular state is added to the optimization index to design the singularity avoidance control law without output constraints; if the output command obtained by the solution exceeds the output constraint, the commanded torque is redistributed to obtain the updated singularity avoidance control law; finally, the gimbal angular velocity and the flywheel rotational angular acceleration command at this moment are obtained, and the angular momentum trajectory of the system during the maneuver is optimized so that the hybrid actuator can output the commanded torque without error for a long time.
[0020] As an embodiment of the present invention, as Figures 3 to 5 shown, the process of finding the singular angular momentum includes the following steps: S11. According to the configuration of the hybrid actuator, a spacecraft reference frame is established to obtain the system matrix of the hybrid actuator, as Figure 3 shown; S12. The gimbal angles of each SGCMG are combined into the gimbal angle set of the SGCMG system, and the singular angular momentum closest to the gimbal angle of the th SGCMG is obtained through the commanded torque u and the gimbal angle δ of the SGCMG system; among them: the specific process of obtaining the singular angular momentum is as Figure 4 and Figure 5 shown, and includes the following steps: S121. In the coordinate system definition of the control moment gyro, is the unit vector of the installation direction of the gimbal of the th SGCMG, is the unit vector of the rotor angular velocity direction, is the unit vector in the opposite direction of the gyro output torque; S122. Considering the A SGCMG, if the control torque is , assuming the command torque , then it is considered that is the output torque direction, and the output torque of the SGCMG system satisfies ; S123. Since the gimbal axis is fixed, is constrained in the vertical plane. If the SGCMG is in a singular state, is simultaneously located in the vertical plane. At this time, coincides with the intersection line of these two planes. At this time, has two choices, which are respectively , The corresponding control moment gyro gimbal angle is the singular gimbal angle , as shown in Figure 4 ; S124. Define as the direction of the -th SGCMG rotor angular momentum corresponding to the singular gimbal angle, divides the vertical plane into two parts. Compare the angle between and the singular rotor angular momentum . The smaller angle is the corresponding closest singular angular momentum direction, as shown in Figure 5 ; S13. Add up the closest singular rotor angular momenta corresponding to all SGCMG gimbal angles , which is the singular angular momentum corresponding to the SGCMG system: ; ; In the formula, is the gimbal angle of the -th SGCMG; are respectively the two singular gimbal angles corresponding to the command torque , is the control torque; is the direction of the -th SGCMG rotor angular momentum corresponding to the singular gimbal angle; is the closest rotor singular angular momentum direction corresponding to the gimbal angle of the -th SGCMG; is the closest singular angular momentum of the SGCMG system.
[0021] As an embodiment of the present invention, the specific construction process of the singularity avoidance control law without output constraints is as follows: Based on the updated optimization function obtained in step S22, a Lagrangian function is established , and its expression is: ; In the formula, is the Lagrange multiplier; Take the partial derivatives of the Lagrangian function to obtain: ; In the formula, is the coefficient matrix, is a constant matrix, and its form is as follows: ; ; The coefficients in the matrix are related to the system matrix as follows: ; ; In the formula, the system matrix ; is the th row and th column element of the system matrix ; Solve for the Lagrange multiplier: ; ; In the formula, , ; is the th row and th column element of the matrix , is the th row and th column element of the matrix , are the magnitudes of the components of along each axis in the body coordinate system; The obtained singularity avoidance control law without output constraints is: .
[0022] In the formula, is the coefficient matrix, is the constant matrix, is the obtained Lagrange multiplier.
[0023] The preferred embodiments of the embodiments of the present application have been described above with reference to the accompanying drawings. This does not limit the scope of the rights of the embodiments of the present application. Any modifications, equivalent substitutions, and improvements made by those skilled in the art without departing from the scope and essence of the embodiments of the present application shall fall within the scope of the rights of the embodiments of the present application.
Claims
1. An output-constrained singularity avoidance control law for a hybrid actuator, characterized in that: The method for establishing the output constraint singularity avoidance control law comprises the following steps: S1. According to the configuration of the hybrid actuator, find the angular momentum of the current SGCMG system through the command torque u and the SGCMG system frame angle δ Recent singular angular momentum ; S2, the current SGCMG system angular momentum and the obtained singular angular momentum The distance between them is added to the optimization function, and the angular momentum of the current SGCMG system is Calculation of the angular momentum of the SGCMG system with the influence term added , and add the influence term related to the frame angular velocity, update the optimization function, construct the Lagrangian function according to the updated optimization function, and establish the singular avoidance control law without output constraints by solving the partial derivatives of the Lagrangian function; S3. Considering the output constraints of the hybrid actuator, the output constraints are designed as , and , and formulate , and Torque allocation strategy under output constraints; If the RW calculated by the singular avoidance maneuvering law in step S2 and SGCMG Output constraints are not met: , or , then by updating the torque distribution strategy under the output constraint condition, the output constraint singularity avoidance control law is obtained.
2. The output constraint singularity avoidance control law for hybrid actuators according to claim 1, characterized in that: The singular angular momentum The search process includes the following steps: S11. According to the configuration of the hybrid actuator, establish the spacecraft reference system to obtain the system matrix of the hybrid actuator ; S12. Combine the frame angles of each SGCMG into a frame angle set of the SGCMG system , and the command torque u and the SGCMG system frame angle δ are used to obtain SGCMG frame corners The nearest singular angular momentum: S13. All SGCMG frame corners The corresponding singular rotor angular momentum of the nearest singular rotor is added together to obtain the singular angular momentum of the SGCMG system: ； ； In the formula, For the The frame angle of SGCMG; The command torque The corresponding two singular frame angles, is the control torque; is the first angle corresponding to the singular frame angle The direction of the angular momentum of the SGCMG rotor; For the The frame angle of each SGCMG corresponds to the direction of the closest rotor singular angular momentum; is the nearest singular angular momentum of the SGCMG system.
3. The output constraint singularity avoidance control law for hybrid actuator according to claim 2, characterized in that: Get the SGCMG frame corners The specific process of the nearest singular angular momentum includes the following steps: S121. In the coordinate system definition of SGCMG, For the The unit vector of the SGCMG frame installation direction, is the unit vector in the direction of the rotor angular velocity, is the unit vector in the opposite direction of the gyro output torque; S122. Consider SGCMG, if the control torque is , let the command torque , then it is believed that is the output torque direction, and the output torque of the SGCMG system satisfies ; S123, because the frame axis is fixed, Constrained in If the SGCMG is in a singular state, Also located in The vertical plane, at this time coincides with the intersection of these two planes, There are two options: , The corresponding control moment gyro frame angle is the singular frame angle ; S124. Definition For the odd frame angle The corresponding The direction of the SGCMG rotor angular momentum, Will The vertical plane is divided into two parts, comparing and singular rotor angular momentum The angle of for The corresponding distance is the direction of the singular angular momentum that is closest.
4. The output constraint singularity avoidance control law for a hybrid actuator according to claim 2, characterized in that: The specific process of constructing the singular avoidance manipulation law without output constraints is as follows: S21, the current SGCMG system angular momentum and singular angular momentum The distance between them is added into the optimization function; where the optimization function is: ； In the formula, is the frame angle and the derivative of the flywheel angular velocity; is the Jacobian matrix of the SGCMG system; is the moment of inertia of the flywheel; , is the weight matrix; is the current angular momentum of the SGCMG system; is the system matrix; where: the coefficients in the weight matrix are: ； In the formula, is the rotor angular momentum of each SGCMG, are the maximum frame angular velocity of SGCMG and the maximum rotational angular acceleration of RW, respectively; S22, according to the current SGCMG system angular momentum in step S21 Calculation of the angular momentum of the SGCMG system with the influence term added , and add the influence term related to the frame angular velocity to update the optimization function; where: SGCMG system angular momentum The calculation formula is: ； In the formula, is the system angular momentum after adding the influence term; For the The frame angular velocity of each SGCMG; For the The output torque direction of each SGCMG; is a very small positive constant; The updated optimization function is: ； remember ; S23, establishing a Lagrangian function according to the updated optimization function obtained in step S22 , by solving the Lagrangian function The partial derivative of , we get the singular avoidance control law without output constraints; where: Lagrangian function for: ； In the formula, is the Lagrange multiplier; By solving the Lagrangian function The partial derivative of , we get: ； In the formula, is the coefficient matrix, is a constant matrix in the following form: ； ； Coefficients in matrices and system matrices The relationship is: ； ； In the formula, the system matrix ; is the system matrix No. Line Elements of a column; Solve for the Lagrange multipliers: ； ； In the formula, , ; For the matrix No. Line The elements of the column, For the matrix No. Line The elements of the column, They are The magnitude of the components along each axis in the body coordinate system; The obtained singular avoidance control law without output constraints is: ； In the formula, is the coefficient matrix, is a constant matrix, To obtain the Lagrange multiplier.
5. The output constraint singularity avoidance control law for hybrid actuators according to claim 4, characterized in that: When the RW calculated by the singular avoidance maneuvering law in step S23 Output constraints are not met: hour, The updating process of the torque distribution strategy under output constraints: When the RW calculated by the singular avoidance maneuvering law in step S23 Output constraints exceeded: , then update the system parameters as: ； In the formula, The torque acting on the RW system is calculated by the singular avoidance maneuvering law in step S23, Respectively The maximum output angular acceleration of each RW and the output angular acceleration obtained by the singular avoidance control law in step S23; Use the remaining command torque to solve the output frame angular velocity of the SGCMG , the optimization function becomes: ； In the formula, is the weight matrix of SGCMG; For the Lagrangian function Taking partial derivatives we get: ； In the formula, the system matrix and constant matrix Updated to: ； ； make , , substituted into step S23 to obtain , then the updated singular avoidance control law is: ； In the formula, is the updated coefficient matrix, is the updated constant matrix, is the updated Lagrange multiplier; If the frame angular velocity obtained from the above formula is greater than the maximum frame angular velocity, the output frame angular velocity of SGCMG is updated as: ； In the formula, The torque acting on the SGCMG system is calculated for the updated singularity avoidance maneuvering law. Respectively The maximum output frame angular velocity of the SGCMG and the output frame angular velocity obtained by the updated singular avoidance control law.
6. The output constraint singularity avoidance control law for hybrid actuators according to claim 4, characterized in that: When the SGCMG calculated by the singularity avoidance maneuvering law in step S23 Output constraints are not met: hour, The updating process of the torque distribution strategy under output constraints: When the SGCMG calculated by the singularity avoidance maneuvering law in step S23 Output constraints exceeded: , then update the system parameters as: ； In the formula, The torque acting on the SGCMG system is calculated by the singularity avoidance maneuvering law in step S23, Respectively The maximum output frame angular velocity of the SGCMG and the output frame angular velocity obtained by the singular avoidance maneuvering law in step S23; The remaining command torque can be used to obtain the rotor rotation angular acceleration of RW for: ； If the obtained rotational angular acceleration is greater than the maximum value of the rotational angular acceleration, a torque error will occur. Updated to: ； In the formula, To update the rotor rotation angular acceleration and calculate the torque acting on the RW system, Respectively The maximum output angular acceleration of each RW and the output angular acceleration obtained after updating the rotor rotation angular acceleration.
7. The output constraint singularity avoidance control law for hybrid actuators according to claim 4, characterized in that: When the RW calculated by the singular avoidance maneuvering law in step S23 and SGCMG The respective output constraints are not satisfied: hour, The updating process of the torque distribution strategy under output constraints: If the RW calculated by the singular avoidance maneuvering law in step S23 and SGCMG Exceeded their respective output constraints: , then update the system parameters as: ； In the formula, The torque acting on the SGCMG system is calculated by the singularity avoidance maneuvering law in step S23, The torque acting on the RW system is calculated by the singular avoidance maneuvering law in step S23, Respectively The maximum output frame angular velocity of the SGCMG and the output frame angular velocity obtained by the singular avoidance maneuvering law in step S23, Respectively The maximum output angular acceleration of each RW and the output angular acceleration obtained by the singular avoidance control law in step S23.
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