An Output Constraint Singularity Avoidance Manipulation Law for Hybrid Actuators

Abstract

The present invention belongs to the technical field of spacecraft attitude actuators, and relates to a singular avoidance control law for output constraints of a hybrid actuator. The establishment method is as follows: according to the configuration of the hybrid actuator, find the singular angular momentum closest to the current system angular momentum, add the distance between the system angular momentum and the singular angular momentum to the optimization function, and add the system angular momentum to the influence term related to the frame angular velocity. By updating the optimization function, a singular avoidance control law without output constraints is designed. Under the condition of considering the output constraints of the hybrid actuator, a torque distribution strategy under different output constraint conditions is designed to obtain a singular avoidance control law for output constraints. The present invention can achieve singular avoidance of the control moment gyro system under the output constraints of the actuator, make full use of the output capabilities of each actuator, and can output high-precision error-free command torques.

Description

Technical Field

[0001] The present invention belongs to the technical field of spacecraft attitude actuator applications, and relates to an output constraint singularity avoidance control law for a hybrid actuator. Background Technique

[0002] With the continuous development of the space 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. For tasks such as space debris cleaning, failed satellite repair, and fuel refueling for non-cooperative space targets, spacecraft are required to have fast attitude maneuvering and tracking capabilities. An attitude actuator that can output high-precision large torques is the basis for an agile satellite to achieve fast maneuvers. Generally, control moment gyros (CMGs) are used, which do not consume fuel, are suitable for long-term on-orbit operation, can output continuous torques, and have higher control precision. However, it has a singularity problem. Under certain gimbal angle combinations, the output torques of the CMG system are in the same plane. At the same time, when the output torque capacity is limited, the CMG system often generates output torque errors during the process of escaping from the singularity. Therefore, it is of great significance to design a control law considering output constraints to complete singularity avoidance and make the system output an error-free command torque.

[0003] Due to the complexity of space missions, most spacecraft attitude controls use hybrid actuators, which can utilize the advantages of each actuator. As a commonly used attitude control actuator for existing satellites, the flywheel can utilize its high output precision characteristics and be used as a hybrid actuator with a control moment gyro. The flywheel is used to assist the control moment gyro to avoid the singular state and at the same time provide high-precision large torques for the 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 constraint singularity avoidance control law for a hybrid actuator, which can achieve singularity avoidance of the 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 solutions are adopted for implementation.

[0006] A method for establishing an output constraint singularity avoidance control law for a hybrid actuator includes the following steps:

[0007] S1. According to the configuration of the hybrid actuator, through the command torque u and the gimbal angle δ of the SGCMG system, find the singular angular momentum closest to the current angular momentum of the SGCMG system the closest singular angular momentum ;

[0008] S2. The current angular momentum of the SGCMG system The distance between the obtained singular angular momentum is added to the optimization function, and the angular momentum of the current SGCMG system is used to calculate the angular momentum of the SGCMG system with influence terms added and influence terms related to the frame angular velocity are added. The optimization function is updated, and the Lagrangian function is constructed based on the updated optimization function. By solving the partial derivatives of the Lagrangian function, a singularity avoidance control law without output constraints is established;

[0009] S3. Considering the output constraint conditions of the hybrid actuator, the output constraint conditions are designed as , and , and torque distribution strategies under the output constraint conditions are formulated respectively , and ;

[0010] 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 by updating the torque distribution strategy under this output constraint condition, an output constraint singularity avoidance control law is obtained.

[0011] As a preferred solution of the present invention, the search process of the singular angular momentum includes the following steps:

[0012] S11. According to the configuration of the hybrid actuator, a spacecraft reference frame is established to obtain the system matrix of the hybrid actuator;

[0013] S12. The frame angles of each SGCMG are combined into the frame angle set of the SGCMG system, and the singular angular momentum closest to the th SGCMG frame angle is obtained through the commanded torque u and the SGCMG system frame angle δ:

[0014] S13. The singular rotor angular momenta closest to all SGCMG frame angles are added together, which is the singular angular momentum corresponding to the SGCMG system:

[0015] ;

[0016] ;

[0017] In the formula, is the frame angle of the th SGCMG; are respectively the two singular frame angles corresponding to the commanded torque is the control torque; is the th SGCMG rotor angular momentum direction corresponding to the singular frame angle; is the th SGCMG frame angle corresponding to the nearest rotor singular angular momentum direction; is the nearest singular angular momentum of the SGCMG system.

[0018] As a preferred embodiment of the present invention, the specific process of obtaining the singular angular momentum closest to the th SGCMG frame angle includes the following steps:

[0019] S121. In the coordinate system definition of the SGCMG, is the unit vector of the th SGCMG frame installation direction, is the unit vector of the rotor angular velocity direction, is the unit vector in the opposite direction of the gyro output torque;

[0020] S122. Considering the th SGCMG, if the control torque is , assuming the commanded torque , then is considered as the output torque direction, and the output torque of the SGCMG system satisfies ;

[0021] S123. Since the frame axis is fixed, is constrained in the vertical plane. If the SGCMG is in a singular state, is also located in the vertical plane. At this time, coincides with the intersection line of these two planes, and has two choices, which are respectively , The corresponding control torque gyro frame angle is the singular frame angle ;

[0022] S124. Define as the th SGCMG rotor angular momentum direction corresponding to the singular frame angle , divide the vertical plane into two parts and compare The included angle with the singular rotor angular momentum Among them, the one with the smaller included angle is the direction of the singular angular momentum corresponding to the closest distance.

[0023] As a preferred solution of the present invention, the specific process of constructing a singular avoidance control law without output constraints:

[0024] S21. Add the distance between the current SGCMG system angular momentum and the singular angular momentum to the optimization function; where: the optimization function is:

[0025] ;

[0026] 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 SGCMG system angular momentum; is the system matrix; where: the coefficients in the weight matrix are:

[0027] ;

[0028] 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;

[0029] 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 gimbal angular velocity to update the optimization function; where: the calculation formula of the SGCMG system angular momentum is:

[0030] ;

[0031] 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;

[0032] The updated optimization function is as follows:

[0033] ;

[0034] Denote ;

[0035] 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 as follows:

[0036] ;

[0037] In the formula, is the Lagrange multiplier;

[0038] By solving the partial derivatives of the Lagrangian function , obtain:

[0039] ;

[0040] In the formula, is the coefficient matrix, is the constant matrix, and its form is as follows:

[0041] ;

[0042] ;

[0043] The relationship between the coefficients in the matrix and the system matrix is as follows:

[0044] ;

[0045] ;

[0046] In the formula, the system matrix ; is the element in the row and column of the system matrix ;

[0047] Solve for the Lagrange multiplier:

[0048] ;

[0049] ;

[0050] In the formula, , ; is a matrix the row and column element of is a matrix the row and column element of respectively are the component magnitudes along each axis in the body coordinate system;

[0051] The obtained singularity avoidance control law without output constraints is:

[0052] ;

[0053] In the formula, is the coefficient matrix, is the constant matrix, is the obtained Lagrange multiplier.

[0054] 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: at this time, the update process of the torque distribution strategy under the output constraint condition:

[0055] When the of RW calculated by the singularity avoidance control law in step S23 exceeds the output constraint condition: then update the system parameters to:

[0056] ;

[0057] In the formula, is the torque acting on the RW system calculated by the singularity avoidance control law in step S23, respectively 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;

[0058] Solve the output gimbal angular velocity of SGCMG with the remaining commanded torque, and the optimization function becomes:

[0059] ;

[0060] In the formula, is the weight matrix of SGCMG;

[0061] Take the partial derivative of the Lagrangian function to get:

[0062] ;

[0063] In the formula, the system matrix and the constant matrix are updated to:

[0064] ;

[0065] ;

[0066] Let , , substitute into step S23 to get , then the updated singularity avoidance manipulation law is:

[0067] ;

[0068] In the formula, is the updated coefficient matrix, is the updated constant matrix, is the updated Lagrange multiplier;

[0069] 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:

[0070] ;

[0071] In the formula, is the torque acting on the SGCMG system calculated by the updated singularity avoidance manipulation law, are respectively the th maximum output frame angular velocity of the SGCMG and the output frame angular velocity obtained from the updated singularity avoidance manipulation law.

[0072] As a preferred solution 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: the update process of the torque distribution strategy under the output constraint condition:

[0073] When the of the SGCMG calculated by the singularity avoidance manipulation law in step S23 exceeds the output constraint condition:

[0074] ;

[0075] In the formula, is the torque acting on the SGCMG system calculated by the singularity avoidance manipulation law in step S23, are respectively the The maximum output frame angular velocity of each SGCMG and the output frame angular velocity obtained by the singularity avoidance control law in step S23;

[0076] The rotor angular acceleration of the RW can be obtained using the remaining commanded torque. It is:

[0077] ;

[0078] If the obtained angular acceleration is greater than the maximum value of the angular acceleration, there will be a torque error at this time, and the rotor angular acceleration of the RW is updated to:

[0079] ;

[0080] In the formula, is the torque acting on the RW system calculated after updating the rotor angular acceleration, are respectively the maximum output angular acceleration of the

[0081] As a preferred embodiment of the present invention, when the of the RW and the of the SGCMG calculated by the singularity avoidance control law in step S23 do not satisfy their respective output constraint conditions: At this time, Update process of the torque distribution strategy under the output constraint conditions:

[0082] If the of the RW and the of the SGCMG calculated by the singularity avoidance control law in step S23 exceed their respective output constraint conditions: Then update the system parameters to:

[0083] ;

[0084] In the formula, is the torque acting on the SGCMG system calculated by the singularity avoidance control law in step S23, is the torque acting on the RW system calculated by the singularity avoidance control law in step S23, are respectively the maximum output frame angular velocity of the are respectively the maximum output angular acceleration of the

[0085] 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. A weighting coefficient is introduced to consider the output capabilities of each actuator and make full use of its torque output ability; 3. Considering the output ability constraints of the actuators, the singular avoidance control law is updated to satisfy the actual limitations while outputting the commanded torque without error, which has important practical significance; 4. Singular avoidance of the SGCMG system is achieved, and high-precision commanded torque can be output. Considering the actual output constraints, the angular momentum trajectory of the system is optimized in real time, which has certain reference significance for the application of hybrid actuators. BRIEF DESCRIPTION OF THE DRAWINGS

[0086] Figure 1 is the overall workflow diagram of the present invention;

[0087] Figure 2 is the workflow diagram of the output constraint singular avoidance control law of the present invention;

[0088] Figure 3 is the schematic diagram of the hybrid actuator configuration of the present invention;

[0089] Figure 4 is the schematic diagram of the singular angular momentum of the present invention;

[0090] Figure 5 is the schematic diagram of the singular angular momentum closest to the system angular momentum of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0091] The present invention will be further described with reference to the embodiments and the drawings.

[0092] As an embodiment of the present invention, as Figure 1 shown, a method for establishing an output constraint singular avoidance control law for a hybrid actuator includes the following steps:

[0093] S1. According to the configuration of the hybrid actuator, find the singular angular momentum closest to the current SGCMG system angular momentum through the commanded torque u and the SGCMG system gimbal angle δ; where: the singular angular momentum is:

[0094] ;

[0095] ;

[0096] In the formula, is the gimbal angle of the th SGCMG; They are the command torque respectively The two corresponding singular frame angles is the control torque; is the th SGCMG rotor angular momentum direction corresponding to the singular frame angle; is the th rotor singular angular momentum direction closest to the frame angle of the SGCMG; is the current SGCMG system angular momentum the closest singular angular momentum;

[0097] 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:

[0098] S21. Add the distance between the current SGCMG system angular momentum in step S1 and the obtained singular angular momentum to the optimization function; where: the optimization function is:

[0099] ;

[0100] 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:

[0101] ;

[0102] In the formula, is the magnitude of the rotor angular momentum of each SGCMG, are the maximum frame angular velocity of the SGCMG and the maximum rotational angular acceleration of the RW respectively;

[0103] 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 of the SGCMG system angular momentum is:

[0104] ;

[0105] In the formula, is the system angular momentum with the influence term added; is the frame angular velocity of the th SGCMG; is the output torque direction of the th SGCMG;

[0106] The updated optimization function is:

[0107] ;

[0108] Denote ;

[0109] 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:

[0110] ;

[0111] In the formula, is the Lagrange multiplier;

[0112] The singularity avoidance control law without output constraints is:

[0113] ;

[0114] In the formula, is the coefficient matrix, is the constant matrix, is the obtained Lagrange multiplier;

[0115] S3. Considering the output constraint conditions of the hybrid actuator, design the output constraint conditions as , and , and formulate the torque distribution strategies under the , and output constraint conditions respectively;

[0116] If the of RW and the of SGCMG calculated by the singularity avoidance control law in step S2 satisfy the output constraint conditions: , or , the moment distribution strategy under the output constraint condition is adopted to obtain the output constraint singularity avoidance control law;

[0117] If the of RW and the of SGCMG calculated by the singularity avoidance control law in step S2 , or do not meet the output constraint conditions: Figure 2 , as shown in

[0118] When the of RW calculated by the singularity avoidance control law in step S23 does not meet the output constraint conditions: , Update process of the moment distribution strategy under the output constraint condition:

[0119] When the of RW calculated by the singularity avoidance control law in step S23 exceeds the output constraint conditions: , the system parameters are updated to:

[0120] ;

[0121] In the formula, is the moment 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;

[0122] Solve the output gimbal angular velocity of SGCMG with the remaining commanded moment, and the optimization function becomes:

[0123] ;

[0124] In the formula, is the weight matrix of SGCMG;

[0125] Take the partial derivative of the Lagrangian function to get:

[0126] ;

[0127] In the formula, the system matrix and the constant matrix are updated to:

[0128] ;

[0129] ;

[0130] Let , , substitute into step S23 to get , then the updated singularity avoidance manipulation law is:[[]]

[0131] ;

[0132] In the formula, is the updated coefficient matrix, is the updated constant matrix, is the updated Lagrange multiplier;

[0133] 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:[[]]

[0134] ;

[0135] In the formula, is the torque acting on the SGCMG system calculated by the updated singularity avoidance manipulation law, are respectively the th maximum output frame angular velocity of the SGCMG and the output frame angular velocity obtained by the updated singularity avoidance manipulation law.[[]]

[0136] As a preferred solution of the present invention, when the of the SGCMG calculated by the singularity avoidance manipulation law in step S23 does not meet the output constraint condition:[[]] When Update process of the torque distribution strategy under the output constraint condition:[[]]

[0137] When the of the SGCMG calculated by the singularity avoidance manipulation law in step S23 exceeds the output constraint condition:[[]] , then update the system parameters to:[[]]

[0138] ;

[0139] In the formula, is the torque acting on the SGCMG system calculated by the singularity avoidance manipulation law in step S23, are respectively the th maximum output frame angular velocity of the SGCMG and the output frame angular velocity obtained by the singularity avoidance manipulation law in step S23;

[0140] The rotor rotational angular acceleration of the RW can be obtained with the remaining command torque is:[[]]

[0141] ;

[0142] If the calculated rotational angular acceleration is greater than the maximum value of the rotational angular acceleration, a torque error will occur at this time, and the rotational angular acceleration of the rotor of RW is updated to:

[0143] ;

[0144] In the formula, is the torque acting on the RW system calculated after updating the rotational angular acceleration of the rotor, are respectively the th maximum output angular acceleration of RW and the output angular acceleration obtained after updating the rotational angular acceleration of the rotor.

[0145] As a preferred solution of the present invention, when the of RW and the of SGCMG calculated by the singular avoidance manipulation law in step S23 do not satisfy their respective output constraint conditions: At this time, Update process of the torque distribution strategy under the output constraint conditions:

[0146] If the of RW and the of SGCMG calculated by the singular avoidance manipulation law in step S23 exceed their respective output constraint conditions: , then the system parameters are updated to:

[0147] ;

[0148] In the formula, is the torque acting on the SGCMG system calculated by the singular avoidance manipulation law in step S23, is the torque acting on the RW system calculated by the singular avoidance manipulation law in step S23, are respectively the th maximum output frame angular velocity of SGCMG and the output frame angular velocity obtained by the singular avoidance manipulation law in step S23, are respectively the th maximum output angular acceleration of RW and the output angular acceleration obtained by the singular avoidance manipulation law in step S23.

[0149] 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 a singular avoidance control law without output constraints; if the output command obtained by solving exceeds the output constraint, the commanded torque is redistributed to obtain an updated singular avoidance control law; finally, the gimbal angular velocity and the flywheel rotational angular acceleration commands 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.

[0150] 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:

[0151] 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;

[0152] S12. Combine the gimbal angles of each SGCMG into a 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; where: the specific process of obtaining the singular angular momentum is as Figure 4 and Figure 5 shown, and includes the following steps:

[0153] S121. In the coordinate system definition of the control moment gyro, is the unit vector of the th SGCMG gimbal installation direction, is the unit vector of the rotor angular velocity direction, is the unit vector in the opposite direction of the gyro output torque;

[0154] S122. Considering the th SGCMG, if the control torque is , assuming the commanded torque , then is considered as the output torque direction, and the output torque of the SGCMG system satisfies ;

[0155] S123. Since the gimbal axis is fixed, is constrained in the vertical plane. If the SGCMG is in a singular state, Simultaneously located in the vertical plane, at this time coincides with the intersection line of these two planes, at this time there are two choices, which are respectively , the corresponding control moment gyro frame angle is the singular frame angle , as Figure 4 shown;

[0156] S124. Define as the singular frame angle corresponding to the th SGCMG rotor angular momentum direction. Divide the vertical plane of into two parts, and compare with the singular rotor angular momentum . The part with the smaller included angle is corresponding to the closest singular angular momentum direction, as Figure 5 shown;

[0157] S13. Add up the closest singular rotor angular momenta corresponding to all SGCMG frame angles to obtain the singular angular momentum corresponding to the SGCMG system:

[0158] ;

[0159] ;

[0160] In the formula, is the frame angle of the th SGCMG; are respectively the two singular frame angles corresponding to the command torque , is the control torque; is the th SGCMG rotor angular momentum direction corresponding to the singular frame angle; is the closest rotor singular angular momentum direction corresponding to the frame angle of the th SGCMG; is the closest singular angular momentum of the SGCMG system.

[0161] As an embodiment of the present invention, the specific construction process of the singular avoidance control law without output constraints:

[0162] According to the updated optimization function obtained in step S22, establish the Lagrangian function , and its expression is:

[0163] ;

[0164] In the formula, is the Lagrange multiplier;

[0165] Taking the partial derivatives of the Lagrangian function, we get:

[0166] ;

[0167] In the formula, is the coefficient matrix, is the constant matrix, and its form is as follows:

[0168] ;

[0169] ;

[0170] The relationship between the coefficients in the matrix and the system matrix is:

[0171] ;

[0172] ;

[0173] In the formula, the system matrix ; is the element in the th row and th column of the system matrix ;

[0174] Solving for the Lagrange multiplier:

[0175] ;

[0176] ;

[0177] 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;

[0178] The obtained singularity avoidance control law without output constraints is:

[0179] .

[0180] In the formula, is the coefficient matrix, is the constant matrix, is the obtained Lagrange multiplier.

[0181] 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 replacements, 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 H of the current SGCMG system through the command torque u and the SGCMG system frame angle δ CMG The nearest singular angular momentum H s , including the following steps: S11. According to the configuration of the hybrid actuator, a spacecraft reference system is established to obtain a system matrix A of the hybrid actuator; S12, combine the frame angles of each SGCMG into the frame angle set of the SGCMG system δ = [δ1, δ2, ..., δ i ] T , and obtain the i-th SGCMG frame angle δ through the command torque u and the SGCMG system frame angle δ i The nearest singular angular momentum: S13, all SGCMG frame angles δ i 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, δ i is the frame angle of the i-th SGCMG; The command torque u=-T c The corresponding two singular frame angles, T c is the control torque; is the direction of the angular momentum of the i-th SGCMG rotor corresponding to the singular frame angle; is the direction of the closest rotor singular angular momentum corresponding to the frame angle of the i-th SGCMG; H s is the nearest singular angular momentum of the SGCMG system; S2. The current SGCMG system angular momentum H CMG The obtained singular angular momentum H s The distance between them is added into the optimization function, and the angular momentum H of the current SGCMG system is CMG 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: Get the angle δ with the i-th SGCMG frame i The specific process of the nearest singular angular momentum includes the following steps: S121. In the SGCMG coordinate system definition, g i is the unit vector of the installation direction of the i-th SGCMG frame, s i is the unit vector in the direction of the rotor angular velocity, t i is the unit vector in the opposite direction of the gyro output torque; S122, consider the i-th SGCMG, if the control torque is T c , let the command torque u=-T c , then we think that t i is the output torque direction, and the output torque of the SGCMG system satisfies S123, because the frame axis is fixed, t i Constrained to g i If the SGCMG is in a singular state, t i At the same time, it is located in the vertical plane of u, at this time t i coincides with the intersection of these two planes, t i 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 angular momentum direction of the i-th SGCMG rotor, G i The vertical plane is divided into two parts, comparing s i and singular rotor angular momentum The angle of For i The corresponding distance is the direction of the singular angular momentum that is closest.

3. The output constraint singularity avoidance control law for hybrid actuator according to claim 1, 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 H CMG and the singular angular momentum H s The distance between them is added into the optimization function; where the optimization function is: In the formula, is the frame angle and flywheel angular velocity derivative; J CMG is the Jacobian matrix of the SGCMG system; J RW =diag(J RW1 ,J RW2 ,J RW3 ) is the moment of inertia of the flywheel; P = diag (S1, S2, ... S7), Q = diag (S8, S8, S8) is the weight matrix; H CMG is the current angular momentum of the SGCMG system; A is the system matrix; where: the coefficients in the weight matrix are: Where h0 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 H in step S21 CMG Calculate the angular momentum of the SGC MG 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; is the frame angular velocity of the i-th SGCMG; t i is the output torque direction of the i-th SGCMG; Δt is a very small positive constant; The updated optimization function is: Remember H s -H CMG =[H x ,H y ,H z ] T ; 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: Where λ = [λ1,λ2,λ3] T is the Lagrange multiplier; By solving the Lagrangian function The partial derivative of , we get: In the formula, a is the coefficient matrix and C is the constant matrix, which is in the following form: C=[C1 C2 C3 C4 000] T ; The relationship between the coefficients in the matrix and the system matrix A is: C i =2S8H x ΔtA 1i +2S8H x ΔtA 2i +2S8H x ΔtA 3i ; In the formula, the system matrix A=[J CMG ,J RW ]; A ij (i=1,2,3,j=1,2,…7) is the element in the i-th row and j-th column of the system matrix A; Solve for the Lagrange multipliers: Where b = -Aa -1 A T ,u * =u+Aa -1 C; b i (i=1,2,3) is the element of the i-th row and i-th column of matrix b, b ij (i=1,2,3;j=1,2,3;i≠j) is the element of the i-th row and j-th column of matrix b, u * 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, a is the coefficient matrix, C is the constant matrix, To obtain the Lagrange multiplier.

4. The output constraint singularity avoidance control law for a hybrid actuator according to claim 3, 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 follows: In the formula, u RW The torque acting on the RW system is calculated by the singular avoidance maneuvering law in step S23, are respectively the maximum output angular acceleration of the i-th RW and the output angular acceleration obtained by the singular avoidance maneuvering law in step S23; Use the remaining command torque to solve the output frame angular velocity of the SGCMG The optimization function becomes: Where P CMG =diag(S1,S2,S3,S4) is the weight matrix of SGCMG; For the Lagrangian function Taking partial derivatives we get: In the formula, the system matrix a and the constant matrix C are updated as follows: C=[C1 C2 C3 C4] T ; make u * =uu RW +J CMG a -1 C, substitute into step S23 to get λ * , then the updated singular avoidance control law is: In the formula, a is the updated coefficient matrix, C is the updated constant matrix, is the updated Lagrange multiplier; If the frame angular velocity obtained by the above formula is greater than the maximum frame angular velocity, the output frame angular velocity of SGCMG is updated as: In the formula, u CMG The torque acting on the SGCMG system is calculated for the updated singularity avoidance maneuvering law. are the maximum output frame angular velocity of the i-th SGCMG and the output frame angular velocity obtained by the updated singular avoidance maneuver law, respectively.

5. The output constraint singularity avoidance control law for hybrid actuator according to claim 3, 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 follows: In the formula, u CMG The torque acting on the SGCMG system is calculated by the singularity avoidance maneuvering law in step S23, are respectively the maximum output frame angular velocity of the i-th 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, u RW To update the rotor rotation angular acceleration and calculate the torque acting on the RW system, are the maximum output angular acceleration of the i-th RW and the output angular acceleration obtained after updating the rotor rotation angular acceleration, respectively.

6. The output constraint singularity avoidance control law for hybrid actuator according to claim 3, 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 follows: In the formula, u CMG The torque acting on the SGCMG system is calculated by the singularity avoidance maneuvering law in step S23, u RW The torque acting on the RW system is calculated by the singular avoidance maneuvering law in step S23, are the maximum output frame angular velocity of the i-th SGCMG and the output frame angular velocity obtained by the singular avoidance maneuvering law in step S23, They are respectively the maximum output angular acceleration of the j-th RW and the output angular acceleration obtained by the singular avoidance control law in step S23.

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