A magnetic suspension CMG group micro-vibration cancellation method based on rotor imbalance adjustment

Abstract

This invention relates to the field of aerospace control technology, and particularly to a method for canceling micro-vibrations of a magnetically levitated CMG group based on rotor imbalance adjustment. The method includes: establishing models of the unbalanced forces and torques of each magnetically levitated rotor; establishing a dynamic synthesis model of the CMG group; establishing the celestial attitude dynamics equations based on the dynamic synthesis model and Euler equations; establishing a CMG group control model; constructing an objective function using the CMG group control model and the celestial attitude dynamics equations; establishing a current control model between the power and current of the rotor's radial translation and radial rotation; establishing the dynamic rotation equations of the high-speed rotor's radial translation and radial rotation; and determining the output current based on the dynamic rotation equations and the control model to adjust the rotor's imbalance and phase, thereby canceling the harmonic vibrations of the magnetically levitated CMG rotor.

Description

Technical Field

[0001] This invention relates to the field of aerospace control technology, and in particular to a method for canceling micro-vibrations of magnetically levitated CMG groups based on rotor imbalance adjustment. Background Technology

[0002] With the rapid development of aerospace technology, the payloads of high-precision spacecraft such as high-resolution remote sensing satellites, laser communication satellites and space telescopes are extremely sensitive to micro-vibrations, which puts forward increasingly higher requirements for the attitude accuracy, stability and quietness of the payloads. Therefore, suppressing on-board micro-vibrations is a necessary condition for achieving ultra-quiet satellite platforms and ensuring the performance of payloads and sensors.

[0003] In related technologies, satellites primarily employ inertial actuators such as control moment gyroscopes (CMGs) to control their attitude stability. In magnetically levitated CMGs, the high-speed rotor is suspended and supported by active magnetic bearings (AMBs). The measurement, control, and actuator components within the AMB form a closed loop, actively controlling the micro-vibrations transmitted from the rotor. During dynamic balancing of the rotor, the imbalance is often controlled to its limit. However, during rotor operation, power frequency vibrations still exist. This is due to the combined effect of systematic errors, such as vibration measurement errors during dynamic balancing and weighing errors in the dynamic balancing compensation mass, leading to incomplete dynamic balancing. Therefore, further reducing the imbalance under these conditions is quite difficult. Summary of the Invention

[0004] This invention provides a method for canceling micro-vibrations of magnetically levitated CMG groups based on rotor imbalance adjustment, which can reduce the micro-vibrations of magnetically levitated CMG groups.

[0005] This invention provides a method for canceling micro-vibrations of magnetically levitated CMG groups based on rotor imbalance adjustment, comprising:

[0006] A second model is established for the unbalanced forces and unbalanced torques of each magnetic levitation rotor;

[0007] Based on the transfer matrix, the installation position of the rotor's center of mass in the orbital coordinate system, and the second model, a third model is established to express the transmission of the unbalanced force and unbalanced torque generated by the rotor to the star's center of mass.

[0008] Based on the third model, a dynamic composition model of the CMG group is established; wherein, the dynamic composition model includes resultant force and resultant moment;

[0009] Based on the aforementioned dynamic synthesis model and Euler equations, establish the celestial attitude dynamic equations.

[0010] Based on the PID control law, a CMG group control model is established; wherein, the CMG group control model includes group control force and group control torque;

[0011] Using the CMG group control model and the aforementioned celestial attitude dynamics equations, an objective function is constructed to obtain the functional relationship between the resultant force and resultant torque of the CMG group and the unbalanced force and unbalanced torque.

[0012] A current control model is established between the power and current of the rotor's radial translation and rotation, so as to control the resultant force and resultant torque of the CMG group through the current of the magnetically levitated CMG.

[0013] Establish the dynamic rotation equations for the radial translation and radial rotation of the high-speed rotor;

[0014] The output current is determined based on the dynamic rotation equation and control model to adjust the rotor's imbalance and phase, thereby canceling the harmonic vibration of the magnetically levitated CMG rotor.

[0015] In one possible design, establishing the unbalanced force and unbalanced torque models for each magnetically levitated rotor includes:

[0016] A first model is established to express the relationship between rotor imbalance and offset and skew; wherein rotor imbalance includes static imbalance and dynamic imbalance.

[0017] Establish the transformation matrix from the rotor body coordinate system to the star orbit coordinate system;

[0018] Based on the transformation matrix and the first model, a second model is established to express the unbalanced force and unbalanced torque.

[0019] In one possible design, the first model is:

[0020]

[0021] Where, m stk and m dyk These are the static and dynamic imbalances of the rotating body, respectively, each generating a centrifugal force f. gk And an uneven couple moment g gk The zero-time phases of the centrifugal force and the unbalanced torque are α and α, respectively. k and β k ω k Let ω be the rotor angular frequency, and ε be the rotor shaft offset. k The skewness of the rotor shaft is ξ. k The rotor mass is m, and J is the rotor's moment of inertia.

[0022] In one possible design, the second model is:

[0023] Unbalanced forces:

[0024]

[0025] Unbalanced torque:

[0026]

[0027] in, R sg Let be the transformation matrix.

[0028] In one possible design, the third model is:

[0029]

[0030] T sgfk Let the coordinate system be from the k-th magnetic levitation rotor to the celestial orbit coordinate system. Vibrational force transmission matrix at the origin; T sggk Let the coordinate system be from the k-th magnetic levitation rotor to the celestial orbit coordinate system. Vibration torque transfer matrix at the origin; l wk Let the center of mass of the k-th magnetically levitated rotor be in the coordinate system of the celestial orbit. The installation location is shown in the figure, where I is the moment of inertia.

[0031] The kinetic synthesis model is as follows:

[0032]

[0033] Among them, F s and M s These are the external forces and torques acting on the satellite platform.

[0034] In one possible design, the celestial attitude dynamics equations are:

[0035]

[0036] Where, m s For the quality of the satellite platform; I s X is the inertia matrix of the satellite platform; s θ is the linear vibration vector of the satellite platform. s This is the attitude vector of the satellite platform.

[0037] In one possible design, the CMG group control model is:

[0038]

[0039] Where, k Pz and k Pθ k is the proportional control coefficient, providing a certain supporting stiffness for the magnetic bearing. Iz and k IθThe integral control coefficient is used to accumulate the deflection error of the magnetic bearing, thereby improving the control accuracy; k Dz and k Dθ This is the differential control coefficient.

[0040] In one possible design, the objective function is:

[0041]

[0042] Wherein, the eccentricity weighted coefficient matrix P = P T >0; Skew angle weighted coefficient matrix Q = Q T >0.

[0043] In one possible design, the current control model is:

[0044]

[0045] Among them, f c (t) represents the equivalent control force applied to the rotor's center of mass by the radial magnetic bearing; g c (t) represents the equivalent control torque of the radial magnetic bearing at the rotor's center of mass; k f i is the radial magnetic bearing force coefficient. cf For radial magnetic bearing drive current; k g i is the torque coefficient of the radial magnetic axis. cg This represents the drive current of the motor.

[0046] In one possible design, the dynamic rotation equation is:

[0047]

[0048] Among them, K τ K represents the rotor radial displacement stiffness. θ F is the rotor radial angular stiffness. o The unbalanced force in the radial direction of the rotor; g o F is the unbalanced torque in the radial direction of the rotor. c The magnetic bearing exerts a radial control force on the rotor; g c This refers to the control torque exerted by the magnetic bearing on the rotor's radial direction.

[0049] The advantages of this invention compared to the prior art are:

[0050] (1) Traditional satellites generally use active vibration reduction and isolation for actuators such as flywheels and CMGs. If the requirements for the attitude accuracy, stability and quietness of the payload are higher, passive vibration isolation, active-passive integrated vibration isolation and active vibration isolation are required for the payload. Although two-stage vibration isolation is achieved, the resulting cost, such as weight, is relatively high and the system is more complex. This patent is for the first time to utilize the characteristics of fixed rotor speed and active controllability of rotor shaft eccentricity and skewness in the distributed magnetic levitation CMG on ultra-quiet satellites. It proposes a method to actively adjust the unbalance of each rotor in the distributed CMG, including its amplitude and phase, so as to achieve vibration cancellation. Without adding any additional hardware, the static and dynamic unbalance of each rotor is allocated based solely on the attitude information of the satellite, realizing the cancellation of micro-vibrations of different CMG rotors and improving the attitude stability of the entire satellite.

[0051] (2) This patent accurately establishes the dynamic model of the magnetically levitated CMG rotor and the dynamic model of the satellite, and conducts joint simulation of the control system and the dynamic system. It can be directly applied to model development, especially for the design of high-precision satellite attitude control laws. This model can simulate the attitude of the system with high precision and verify the implementation of control laws, etc. Therefore, this patent has direct engineering application value. Attached Figure Description

[0052] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0053] Figure 1 This is a schematic diagram of the ultra-quiet on-board magnetic levitation CMG group layout of the present invention;

[0054] Figure 2 A schematic diagram of the angular momentum of a single control torque gyroscope according to the present invention;

[0055] Figure 3 This is a block diagram of the ultra-quiet satellite 6DOF micro-vibration cancellation control system of the present invention;

[0056] Figure 4 This is a block diagram of the magnetic levitation CMG group rotor control system of the present invention;

[0057] Figure 5 This is the regular pentagonal pyramidal configuration of the magnetic levitation CMG group of the present invention. Detailed Implementation

[0058] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are some embodiments of the present invention, but not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0059] Please refer to Figure 1 This invention provides a method for canceling micro-vibrations of magnetically levitated CMG groups based on rotor imbalance adjustment, comprising:

[0060] A second model is established for the unbalanced forces and unbalanced torques of each magnetic levitation rotor;

[0061] Based on the transfer matrix, the installation position of the rotor's center of mass in the orbital coordinate system, and the second model, a third model is established to express the transmission of the unbalanced force and unbalanced torque generated by the rotor to the star's center of mass.

[0062] Based on the third model, a dynamic composition model of the CMG group is established; the dynamic composition model includes resultant force and resultant moment.

[0063] Based on the dynamic synthesis model and Euler's equations, the dynamic equations of the celestial attitude are established.

[0064] Based on the PID control law, a CMG group control model is established; the CMG group control model includes group control force and group control torque.

[0065] By using the CMG group control model and the star attitude dynamics equations, an objective function is constructed, and the functional relationship between the resultant force and resultant moment of the CMG group and the unbalanced force and unbalanced moment is established.

[0066] A current control model is established between the power and current of the rotor's radial translation and rotation, so as to control the resultant force and resultant torque of the CMG group through the current of the magnetically levitated CMG.

[0067] Establish the dynamic rotation equations for the radial translation and radial rotation of the high-speed rotor;

[0068] The output current is determined based on the dynamic rotation equation and control model to adjust the unbalance and phase of the rotor, thereby canceling the harmonic vibration of the magnetically levitated CMG rotor.

[0069] To overcome the problems of insufficient attitude accuracy and stability of onboard payloads caused by traditional attitude control modes based on satellite service platforms, and the difficulty in controlling micro-vibrations of traditional inertial attitude actuators, this patent provides a method for canceling micro-vibrations of a magnetically levitated CMG group based on rotor imbalance adjustment. For distributed magnetically levitated CMGs on ultra-quiet satellites, this method utilizes the fixed rotor speed and actively controllable rotor shaft eccentricity and skewness. Based on the satellite's attitude and acceleration information, the static and dynamic imbalance amplitudes and phases are allocated to each rotor. Then, the imbalance of each rotor in the distributed CMG, including its amplitude and phase, is actively adjusted through the magnetic bearings of each rotor. This achieves micro-vibration cancellation of multiple magnetically levitated CMG rotors on the satellite, improving the overall attitude stability of the satellite and thus achieving ultra-stable and ultra-quiet payload attitude performance.

[0070] In some embodiments of the present invention, models of unbalanced forces and unbalanced torques for each magnetically levitated rotor are established, including:

[0071] A first model is established to express the relationship between rotor imbalance and offset and skew; wherein rotor imbalance includes static imbalance and dynamic imbalance.

[0072] Establish the transformation matrix from the rotor body coordinate system to the star orbit coordinate system;

[0073] Based on the transformation matrix and the first model, a second model is established to express the unbalanced force and unbalanced torque.

[0074] In some embodiments of the present invention, the first model is:

[0075]

[0076] Where, m stk and m dyk These are the static and dynamic imbalances of the rotating body, respectively, each generating a centrifugal force f. gk And an uneven couple moment g gk The zero-time phases of the centrifugal force and the unbalanced torque are α and α, respectively. k and β k ω k Let ω be the rotor angular frequency, and ε be the rotor shaft offset. k The skewness of the rotor shaft is ξ. k The rotor mass is m, and J is the rotor's moment of inertia.

[0077] In this embodiment, the skewness and offset of the rotor shaft will generate unbalanced vibration, which is the main source of micro-vibration of the actuator. It is also the active micro-vibration control force and torque of the present invention. Therefore, a vibration model of the rotor is established.

[0078] For a magnetic levitation rotor system, if the rotor and rotating body of the magnetic levitation bearing are considered as rigid bodies, forming a rotating body supported by a frame via electromagnetic coupling; and the magnetic levitation stator and frame are considered as a rigid assembly, mounted on the spacecraft's cabin plate via a frame base, and the following coordinate system is established:

[0079] Star orbit coordinate system o o x o y o z o Its origin o o Located at the center of mass of the satellite platform, the satellite's flight direction is x. o The axis is y, and the direction of the normal to the satellite's orbital plane is y. o axis, z o The axis is determined by the right-hand rule.

[0080] CMG Frame Coordinate System o g x g y g z g Its origin o is located at the rotor's center of mass o. g With the high-speed rotor shaft as y g With the frame axis as z g axis, x g The axis is determined by the right-hand rule and rotates synchronously with the frame.

[0081] Rotor body coordinate system o w x w y w z w Fixed to the rotor's center of mass. w With the axis of rotation as y w The axis is z, with the radial principal inertia axis of the rotor as z. w axis, x w The shaft is determined by the right-hand rule and rotates synchronously with the rotor.

[0082] Assuming that the structural parameters of each control moment gyroscope are approximately the same, the following analysis examines the high-speed rotor of any control moment gyroscope k in the rotor body coordinate system. The skewness and offset of the rotating shaft.

[0083] In an ideal situation:

[0084] In the high-speed rotor coordinate system, the three coordinate axes are approximately the three principal inertia axes of the rotating body, and the product of the three inertia is zero, i.e., J yz0 =0; J zx0 =0; J xy0 =0, then the inertia matrix is: J0 = diag(J x0 J y0 Jz0 ).

[0085] In the presence of imbalance:

[0086] Assume the rotor mass is m and the static unbalanced mass is m. stk The equivalent eccentricity ε of the rotor system k for:

[0087] ε k =m stk m -1 (1)

[0088] Assuming the unbalanced mass is distributed along the rotor radius r, the polar moment of inertia generated by the rotor's static unbalance is: m stk r 2 This is much smaller than the moment of inertia of each axis; and m stk It will not cause the rotation axis coordinate system to be skewed, and will not generate an inertia product, so the effect of static unbalance on the rotational inertia of the rotating body can be ignored.

[0089] And assume the dynamic unbalanced mass is m dyk The unbalanced mass block is located in the yoz plane, at position (0, b, r). The skew angle of the moment axis relative to the rotor axis is ξ. k Therefore, the moment of inertia can be calculated as follows:

[0090]

[0091] The product of inertia is:

[0092]

[0093] The rotor inertia matrix considering static and dynamic imbalance is J. k for:

[0094]

[0095] Because J k For a real symmetric matrix, there must exist three real eigenvalues, whose eigenvectors are the three principal axes of inertia. The principal axes of inertia are obtained by taking the extrema of the moments of inertia of the rigid body about any axis. Assume that the angle between the normal vector n of the principal axes of inertia caused by the dynamic imbalance and the coordinate axes x, y, z is... ξ k γ k The vector n can be represented as (cosζ) k cosξ k cosγ k ) T The moment of inertia of a rigid body about vector n:

[0096] J k =Jx cos 2 ζ k +J y cos 2 ξ k +J z cos 2 γ k +

[0097] -2J yz cosξ k cosγ k -2J zx cosγ k cosζ k -2J xy cosζ k cosξ k (5)

[0098] Since the unbalanced mass lies in the yoz plane, cosζ k =0, and ξ k +γ k =π / 2, equation (5) simplifies to:

[0099] J k =J y cos 2 ξ k +J z sin 2 ξ k -2J yz cosξ k sinξ k

[0100] =J y +(J z -J y sin 2 ξ k -J yz sin2ξ k (6)

[0101] It can be seen that the above formula is ξ k Take the derivative of the function:

[0102]

[0103] Then its extreme value condition is: Right now:

[0104]

[0105] Given that the dynamic imbalance is relatively small, J yz →0, ξ k →0, then Therefore, the deflection angle of the principal axis of inertia can be solved as follows:

[0106]

[0107] Therefore, the dynamic imbalance quantity u dyk Approximately:

[0108]

[0109] In the CMG frame coordinate system The static imbalance m of the rotating body stk and dynamic imbalance m dyk Each will generate a centrifugal force f gk And an uneven couple moment g gk Assume their phases at time zero are α and α, respectively. k and β k Then the centrifugal force and the couple are respectively:

[0110]

[0111] Where, ω k Let ε be the rotor angular frequency. As can be seen from the above equation, by actively controlling the offset ε of the high-speed rotor shaft... k and skewness ξ k This allows control over the static and dynamic imbalance of the rotor, thereby controlling the magnitude of the centrifugal force and torque generated by the rotor imbalance; and by actively adjusting the skew and offset of the high-speed rotor shaft, the phase of the centrifugal force and torque of the rotor can be controlled, thus generating an active control effect.

[0112] In some embodiments of the present invention, the second model is:

[0113] Unbalanced forces:

[0114]

[0115] Unbalanced torque:

[0116]

[0117] in, R sg Let be the transformation matrix.

[0118] In this embodiment, it is assumed that the high-speed rotor of the arbitrary control torque gyroscope k is in the celestial orbit coordinate system. Installation location (x) k ,y k ,z k The initial coordinate system of CMG-k coincides with the coordinate system of the celestial body. Its initial high-speed rotation axis points in the y-direction, and its initial frame rotation axis points in the z-direction. After rotation, it becomes like Figure 2 The situation is shown below. Taking the center of mass of the high-speed rotor as the origin o, and g as... k This indicates that the frame rotation axis of the k-th CMG is at... The unit direction vector below; with h k This indicates that the magnetic levitation rotor axis of the k-th CMG in CMGs is in The unit direction vector under; define t k =g k× h k When the CMG frame is along g k The axis has an angular velocity ω k During rotation, because the direction of the rotor's angular momentum is h k Changes in external disturbance torque cause gyroscopic effects, located at t k The axial direction, while the external gyroscopic torque, which is the torque output axis of the CMG, is located at -t. k Axial direction. Its azimuth angle is Its frame axis g k The angle between the z-axis and the z-axis is ψ k ; angular momentum h k Around the frame axis g k Turn through δ k Initial frame angle δ k =0, meaning the position is located within the xoy plane. Its high-speed rotation axis is in the celestial orbit coordinate system. Installation orientation Euler rotation matrix:

[0119]

[0120] From the celestial orbit coordinate system To the CMG frame coordinate system Then to the rotor body coordinate system The transformation matrix within is: Then from the rotor's intrinsic coordinate system to the celestial orbit coordinate system The transformation matrix within is:

[0121]

[0122] in, Similar to other angles, install the matrix. It only depends on the configuration of CMG; R3(δ k R2(ω) is related to the position of the frame angle; k t+χ k This is related to the position through which the unbalance has rotated within the rotor's coordinate system. ψ kThese parameters are relevant only to the installation condition of CMG-k. The unbalanced forces and moments in this state can then be expressed in stellar coordinates as follows:

[0123]

[0124] If we assume the phase angle of the unbalanced force is α k The unbalanced force in equation (14) can be further expanded as follows:

[0125]

[0126] in, They are only related to the frame orientation.

[0127] If we assume the phase angle of the unbalanced force is β k The unbalanced torque in equation (14) can be further expanded as follows:

[0128]

[0129]

[0130] It is evident that by actively controlling the imbalance, an antiphase force and torque can be generated to counteract micro-vibrations.

[0131] In some embodiments of the present invention, the third model is:

[0132]

[0133] T sgfk Let the coordinate system be from the k-th magnetic levitation rotor to the celestial orbit coordinate system. Vibrational force transmission matrix at the origin; T sggk Let the coordinate system be from the k-th magnetic levitation rotor to the celestial orbit coordinate system. Vibration torque transfer matrix at the origin; l wk Let the center of mass of the k-th magnetically levitated rotor be in the coordinate system of the celestial orbit. The installation location is shown in the figure, where I is the moment of inertia.

[0134] The kinetic synthesis model is as follows:

[0135]

[0136] Among them, F s and M s These are the external forces and torques acting on the satellite platform.

[0137] In this embodiment, the vibration of the magnetically levitated CMG and the forces and torques of active control are all transmitted through the celestial structure, affecting the celestial attitude. Therefore, the influence of vibration transmission must be considered during vibration control. However, to simplify the explanation of the vibration control method, this invention simplifies the micro-vibration transmission characteristics of the structure. The accurate vibration transmission model will be obtained through experimental measurements in subsequent engineering. Therefore, this paper will study the transmission of vibration control forces and torques based on the simplified transmission model, and equate the forces and torques to the celestial center of mass.

[0138] Given that the deformation of the elastic boundary is minimal under the active control of the magnetically levitated rotor, it is assumed that the directions of the control force and torque remain unchanged. Considering that the control force of the rotor will generate a torque rotating about the center of mass, the equivalent stiffness of the unbalanced control force and torque generated by the magnetically levitated rotor to the center of mass of the celestial body can be obtained as follows:

[0139]

[0140] Among them, T sgfk Let the coordinate system be from the k-th magnetic levitation rotor to the celestial orbit coordinate system. Vibrational force transmission matrix at the origin; T sggk Let the coordinate system be from the k-th magnetic levitation rotor to the celestial orbit coordinate system. Vibration torque transfer matrix at the origin; l wk Let the center of mass of the k-th magnetically levitated rotor be in the coordinate system of the celestial orbit. The installation position in the middle; then the unbalanced control force and torque generated by the magnetic levitation rotor are transmitted to the center of mass of the star as follows:

[0141]

[0142] It is evident that the active vibration control force and torque required by the celestial body can be generated by controlling the rotor imbalance.

[0143] For three-axis attitude control of satellites, multiple CMGs are generally used to form a CMG group. Through the coordinated work of each individual unit, the attitude control torque required by the satellite in any direction is generated. The dynamics of the CMG group is the configuration result of each individual unit and is the basis of attitude control.

[0144] For an n-SGCMG group containing n (n≥4) CMG elements, the resultant force and resultant moment generated by active unbalance control are:

[0145]

[0146] Among them, F s and M s These represent the external forces and moments acting on the satellite platform. Different frame angle combinations in the n-SGCMG system... The amount of effect that can be achieved Different. Given the action P s The dimension of the control space is generally less than the 4n degrees of freedom of the n-SGCMG. As can be seen from equation (14), a point in the control space of the n-SGCMG is in the action space P. s It can only correspond to one point, while the action space P s One point in the n-SGCMG corresponds to at least one mapping point in the control space.

[0147] Given that the magnetic levitation CMGs used on a satellite are all of the same type, and the high-speed rotors of each CMG rotate at the same speed, the resulting unbalanced vibration frequency ω k They are the same, both being ω.

[0148]

[0149] As can be seen from equation (20), when the unbalance amplitude and phase of each rotor in the magnetically levitated CMG group are appropriately adjusted, the harmonic vibrations introduced by the rotors in the magnetically levitated CMG group can cancel each other out, so that the vibration of the CMG group to the whole satellite output is zero, thereby reducing the micro-vibration response of the satellite.

[0150] In some embodiments of the present invention, the celestial attitude dynamics equations are as follows:

[0151]

[0152] Where, m s For the quality of the satellite platform; I s X is the inertia matrix of the satellite platform; s θ is the linear vibration vector of the satellite platform. s This is the attitude vector of the satellite platform.

[0153] In this embodiment, the satellite's vibrations include linear vibrations and angular vibrations. Therefore, dynamic modeling must be performed from the perspectives of translational dynamics and attitude dynamics to analyze the influence of micro-vibration forces and moments on the satellite's translation and attitude.

[0154] If we disregard the structural damping of a three-axis stable satellite, we establish the translational dynamics equations of the celestial body and apply Euler's equations. The attitude dynamics equations of the celestial body can be established as follows:

[0155]

[0156] Where, m s For the quality of the satellite platform; I s The inertia matrix of the satellite platform;

[0157] X s θ is the linear vibration vector of the satellite platform. s This is the attitude vector of the satellite platform.

[0158] It is evident that micro-vibrations on a star will affect its dynamic response, influencing its linear and angular vibrations.

[0159] For any micro-vibration at a fixed frequency on the satellite, it can be represented as a synthesis of circular vibration caused by the rotating mechanism and linear vibration caused by the linear reciprocating mechanism. The linear vibration needs to be controlled by a linear actuator, while the circular vibration can be generated by a linear actuator or directly controlled by a circular vibration actuator. This allows us to use the axial active vibration control of the magnetically levitated rotor to suppress the satellite's linear vibration; and to suppress the satellite's circular vibration through unbalanced vibration control, thereby achieving the satellite's ultra-quiet performance with full degrees of freedom.

[0160] In some embodiments of the present invention, the CMG group control model is as follows:

[0161]

[0162] Where, k Pz and k Pθ k is the proportional control coefficient, providing a certain supporting stiffness for the magnetic bearing. Iz and k Iθ The integral control coefficient is used to accumulate the deflection error of the magnetic bearing, thereby improving the control accuracy; k Dz and k Dθ This is the differential control coefficient.

[0163] In this embodiment, magnetic levitation CMG is used to stabilize the ultra-quiet satellite platform. To simplify verification, PID control with linear acceleration and angular velocity feedback is temporarily adopted. The system block diagram is as follows. Figure 3 As shown. Assume a PID control law:

[0164]

[0165] Where, k Pz and k Pθ k is the proportional control coefficient, providing a certain supporting stiffness for the magnetic bearing. Iz and k Iθ The integral control coefficient is used to accumulate the deflection error of the magnetic bearing, thereby improving the control accuracy; k Dz and k Dθ Let be the differential control coefficient, providing a certain damping for the magnetic bearing. Then the control force and torque should be:

[0166]

[0167] In some embodiments of the present invention, the objective function is:

[0168]

[0169] Wherein, the eccentricity weighted coefficient matrix P = P T >0; Skew angle weighted coefficient matrix Q = Q T >0.

[0170] In this embodiment, in order to achieve three-axis attitude control, there should be no fewer than four onboard CMGs, and at least two of them should have non-collinear frame axes. In this case, the rank of matrix A is 3 and the rank of matrix M is 6. Given the desired torque, equation (19) has infinitely many solutions. It is necessary to achieve a one-to-one mapping between the desired force / torque and the CMG group force / torque according to certain indicators or constraints. Therefore, the optimal allocation of the control quantity will be performed below.

[0171] Construct the objective function using the CMG unbalanced force / torque vector:

[0172]

[0173] Wherein, the eccentricity weighted coefficient matrix P = P T >0; Skew angle weighted coefficient matrix Q = Q T >0. At this time, the torque distribution strategy is: solve for the minimum value of the index function J2 under the constraint of equation (19), and through active unbalance control, make the vibration of the magnetically levitated CMG group zero under the condition that the rotor offset and skew are minimized, so as to obtain the optimal unbalance force and torque of each rotor. Then the equivalent force and torque acting on the center of mass of the star can be obtained, so as to achieve the optimal cancellation of the power frequency vibration. The distribution block diagram of the system is as follows. Figure 4 As shown.

[0174] In this configuration, five CMGs are evenly distributed on the five faces of a pentagonal pyramid. The pyramid's angles are designed according to angular momentum requirements. The frame axes of the five CMGs are installed along the edges of the pyramid, the base is a regular pentagon with an included angle β = 63.4°, and the frame axes are perpendicular to the five faces of the pyramid. When the frame angle is zero, the angular momentum is parallel to the base. The specific configuration is as follows: Figure 5 As shown. Then the angular momentum of each CMG in this configuration is:

[0175] α=0°,72°,144°,216°,288°andβ=63.4° (25)

[0176] In some embodiments of the present invention, the current control model is as follows:

[0177]

[0178] Among them, f c (t) represents the equivalent control force applied to the rotor's center of mass by the radial magnetic bearing; g c (t) represents the equivalent control torque of the radial magnetic bearing at the rotor's center of mass; k f i is the radial magnetic bearing force coefficient.cf For radial magnetic bearing drive current; k g i is the torque coefficient of the radial magnetic axis. cg This represents the drive current of the motor.

[0179] In this embodiment, the dynamic equations for the rotor's radial translation and radial rotation are:

[0180]

[0181] Among them, f c (t) represents the equivalent control force applied to the rotor's center of mass by the radial magnetic bearing; g c (t) represents the equivalent control torque of the radial magnetic bearing at the rotor's center of mass. k f i is the radial magnetic bearing force coefficient. cf For radial magnetic bearing drive current; k g i is the torque coefficient of the radial magnetic axis. cg Let be the driving current of the motor. Then the vibration force and torque of the radial magnetic bearing on the frame are the reaction force and torque of the above formula.

[0182] During the operation of a high-speed rotor, the relative deformation of each component is very small. We can assume that the deformation of all components is within the linear elastic range of the material, meaning that the stiffness parameter in the above formula is constant; and we can also assume that the damping parameter is constant. That is, the high-speed rotor system is a linear system.

[0183] In some embodiments of the present invention, the dynamic rotation equation is:

[0184]

[0185] Among them, K τ K represents the rotor radial displacement stiffness. θ F is the rotor radial angular stiffness. o The unbalanced force in the radial direction of the rotor; g o F is the unbalanced torque in the radial direction of the rotor. c The magnetic bearing exerts a radial control force on the rotor; g c This refers to the control torque exerted by the magnetic bearing on the rotor's radial direction.

[0186] In this embodiment, the zero initial moment of high-speed rotor operation, and The three axes are parallel, and it is rotated 2-1-3: θ oy ,θ ox ,θ oz , where θ ox and θ ozThese are all very small angles, therefore their corresponding trigonometric functions can be approximated as linear. The dynamic equations for the high-speed rotor's radial translation and radial rotation are:

[0187]

[0188] The physical meaning of each stiffness coefficient in the formula is: K τ K represents the rotor radial displacement stiffness. θ f is the rotor radial angular stiffness. o The unbalanced force in the radial direction of the rotor; g o This represents the unbalanced torque in the rotor's radial direction. f c The magnetic bearing exerts a radial control force on the rotor; g c This refers to the control torque exerted by the magnetic bearing on the rotor's radial direction.

[0189] For the dynamics and control system of ultraquiet satellites, Simulink was used for co-simulation to verify the effectiveness of the micro-vibration cancellation method based on the unbalance control of distributed magnetic levitation CMG rotor.

[0190] Therefore, the high-speed rotor of the magnetically levitated CMG serves as both an exciter and a vibration damper for the satellite. The former is primarily because individual magnetically levitated CMGs lack force and torque sensors, making it impossible to estimate their high-speed rotor's axis of inertia, thus making unbalanced vibrations unavoidable. However, the eddy current sensors on each magnetically levitated rotor can accurately measure the relative displacement of the rotor relative to the frame. More precisely, they can relatively adjust the amplitude and phase increment of the rotor's unbalanced mass, ultimately canceling the harmonic vibrations of the magnetically levitated CMG rotor through the large closed loop of the satellite system. By adjusting the unbalance according to a specific harmonic pattern, vibrations of other frequencies can be modulated onto the power frequency vibration, and vibrations generated by other actuators on the satellite can be canceled to a certain extent, thereby further improving the satellite's ultra-quiet performance.

[0191] In summary, by actively adjusting the dynamic and static imbalance amplitude and phase of each high-speed rotor in the magnetically levitated CMG group, a counteracting effect on micro-vibrations is generated, thereby achieving ultrastatic stability control of the linear / angular vibration of the celestial body.

[0192] Therefore, this patented method can be used for the precise and stable attitude control of high-performance satellites such as onboard optical satellites and laser communication satellites; it has strong versatility and a wide range of applications.

[0193] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0194] Those skilled in the art will understand that all or part of the steps of the above method embodiments can be implemented by hardware related to program instructions. The aforementioned program can be stored in a computer-readable storage medium. When the program is executed, it performs the steps of the above method embodiments. The aforementioned storage medium includes various media that can store program code, such as ROM, RAM, magnetic disk, or optical disk.

[0195] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for canceling micro-vibrations of magnetically levitated CMG groups based on rotor imbalance adjustment, characterized in that, include: A second model is established for the unbalanced forces and unbalanced torques of each magnetic levitation rotor; Based on the transfer matrix, the installation position of the rotor's center of mass in the orbital coordinate system, and the second model, a third model is established to express the transmission of the unbalanced force and unbalanced torque generated by the rotor to the star's center of mass. Based on the third model, a dynamic composition model of the CMG group is established; wherein, the dynamic composition model includes resultant force and resultant moment; Based on the aforementioned dynamic synthesis model and Euler equations, establish the celestial attitude dynamic equations. Based on the PID control law, a CMG group control model is established; wherein, the CMG group control model includes group control force and group control torque; Using the CMG group control model and the aforementioned celestial attitude dynamics equations, an objective function is constructed to obtain the functional relationship between the resultant force and resultant torque of the CMG group and the unbalanced force and unbalanced torque. A current control model is established between the power and current of the rotor's radial translation and rotation, so as to control the resultant force and resultant torque of the CMG group through the current of the magnetically levitated CMG. Establish the dynamic rotation equations for the radial translation and radial rotation of the high-speed rotor; The output current is determined based on the dynamic rotation equation and control model to adjust the rotor's imbalance and phase, thereby canceling the harmonic vibration of the magnetically levitated CMG rotor.

2. The method according to claim 1, characterized in that, The establishment of unbalanced force and unbalanced torque models for each magnetically levitated rotor includes: A first model is established to express the relationship between rotor imbalance and offset and skew; wherein rotor imbalance includes static imbalance and dynamic imbalance. Establish the transformation matrix from the rotor body coordinate system to the star orbit coordinate system; Based on the transformation matrix and the first model, a second model is established to express the unbalanced force and unbalanced torque.

3. The method according to claim 2, characterized in that, The first model is: in, m stk and m dyk These are the static and dynamic imbalances of the rotating body, respectively, each of which generates a centrifugal force. f gk and an uneven couple moment g gk The zero-time phases of the centrifugal force and the unbalanced torque are respectively α k and β k , ω k Where is the rotor angular frequency, and the rotor shaft offset is . ε k The rotor shaft skewness is ξ k The rotor mass is m , J This is the moment of inertia of the rotor.

4. The method according to claim 2, characterized in that, The second model is: Unbalanced forces: Unbalanced torque: in, , Let be the transformation matrix.

5. The method according to claim 1, characterized in that, The third model is: For from the first k A magnetically levitated rotor to the coordinate system of a celestial orbit Vibration force transmission matrix at the origin; For from the first k A magnetically levitated rotor to the coordinate system of a celestial orbit Vibration torque transfer matrix at the origin; For the first k The center of mass of the magnetically levitated rotor is in the coordinate system of the celestial orbit. The installation location is shown in the figure, where I is the moment of inertia. The kinetic synthesis model is as follows: in, F s and M s These are the external forces and torques acting on the satellite platform.

6. The method according to claim 1, characterized in that, The celestial attitude dynamics equation is: in, m s For the quality of the satellite platform; I s The inertia matrix of the satellite platform; X s This represents the linear vibration vector of the satellite platform. θ s This is the attitude vector of the satellite platform.

7. The method according to claim 1, characterized in that, The CMG group control model is as follows: in, k Pz and k Pθ This is a proportional control coefficient, providing a certain level of support stiffness for the magnetic bearing; k Iz and k Iθ The integral control coefficient is used to accumulate the deflection error of the magnetic bearing, thereby improving the control accuracy. k Dz and k Dθ This is the differential control coefficient.

8. The method according to claim 1, characterized in that, The objective function is: Among them, the eccentricity weighted coefficient matrix P = P T >0; Skew angle weighting coefficient matrix Q = Q T >0.

9. The method according to claim 1, characterized in that, The current control model is as follows: in, f c ( t The equivalent control force applied to the rotor's center of mass by the radial magnetic bearing; g c ( t The equivalent control torque of the radial magnetic bearing at the rotor's center of mass is denoted as . k f This is the radial magnetic bearing force coefficient. i cf This is the driving current for the radial magnetic bearing; k g The torque coefficient of the radial magnetic axis. i cg This represents the drive current of the motor.

10. The method according to claim 1, characterized in that, The equation for the dynamic rotation is: in, K τ This refers to the rotor radial displacement stiffness. K θ This refers to the rotor radial angular stiffness; f o This is the unbalanced force in the radial direction of the rotor; g o This represents the unbalanced torque in the radial direction of the rotor. f c This refers to the radial control force exerted by the magnetic bearing on the rotor. g c This refers to the control torque exerted by the magnetic bearing on the rotor's radial direction.

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