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

Abstract

The embodiment of the invention relates to the technical field of spaceflight control, in particular to a magnetic suspension CMG group micro-vibration cancellation method based on rotor imbalance adjustment. The method comprises the following steps: establishing models of unbalanced force and unbalanced moment of each magnetic suspension rotor; establishing a dynamic synthesis model of the CMG group; establishing a star attitude kinetic equation according to the kinetic synthesis model and an Euler equation; establishing a CMG group control model; constructing a target function by using a CMG group control model and a star attitude kinetic equation; establishing a current control model between power and current when the rotor translates along the radial direction and rotates around the radial direction; establishing a power rotation equation that the high-speed rotor translates along the radial direction and rotates around the radial direction; and according to the power rotation equation, the control model determines an output current so as to adjust the unbalance amount and the phase of the rotor, and offset the same-frequency harmonic vibration of the magnetic suspension CMG rotor.

Description

Technical Field

[0001] The embodiments of the present invention relate to the field of aerospace control technology, and in particular to a method for canceling micro-vibration of a magnetically suspended CMG group based on rotor imbalance adjustment. Background Art

[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, and higher and higher requirements are placed on 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 the related technology, the satellite body mainly uses inertial actuators such as control torque gyroscope (CMG) to control the satellite attitude stability. The high-speed rotor in the magnetically suspended CMG is suspended and supported by active magnetic bearings (AMB). The measurement, controller and actuator in the AMB form a closed loop, which can actively control the micro-vibration transmitted from the rotor. When the rotor is dynamically balanced, the imbalance of the rotor is often controlled to the extreme. However, when the rotor is running, there is still industrial frequency vibration. This is due to the combined effect of system errors such as vibration measurement errors during dynamic balancing and weighing errors of the dynamic balancing compensation mass, resulting in incomplete dynamic balancing. It can be seen that it is more difficult to further reduce the imbalance in this case. Summary of the invention

[0004] The embodiment of the present invention provides a method for canceling micro-vibration of a magnetically suspended CMG group based on rotor imbalance adjustment, which can reduce the micro-vibration of a magnetically suspended CMG group.

[0005] The embodiment of the present invention provides a method for canceling micro-vibration of a magnetically suspended CMG group based on rotor imbalance adjustment, comprising:

[0006] Establishing a second model of unbalanced force and unbalanced torque of each magnetically suspended rotor;

[0007] According to the transfer matrix, the installation position of the rotor mass center in the body orbit 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 mass center;

[0008] According to the third model, a dynamic synthesis model of the CMG group is established; wherein the dynamic synthesis model includes a resultant force and a resultant moment;

[0009] Establishing the stellar attitude dynamics equation according to the dynamics synthesis model and Euler equation;

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

[0011] The objective function is constructed by using the CMG group control model and the satellite attitude dynamics equation to establish the functional relationship between the resultant force and resultant moment of the CMG group and the unbalanced force and unbalanced moment;

[0012] A current control model between the power and current of the rotor's radial translation and radial rotation is established to control the resultant force and torque of the CMG group through the magnetic suspension CMG current;

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

[0014] The output current is determined according to the power rotation equation and the control model to adjust the unbalance and phase of the rotor and cancel the same-frequency harmonic vibration of the magnetically suspended CMG rotor.

[0015] In a possible design, establishing the unbalanced force and unbalanced torque models of each magnetic suspension rotor includes:

[0016] Establishing a first model expressing the relationship between the rotor unbalance amount and the offset amount and the deflection amount; wherein the rotor unbalance amount includes a static unbalance amount and a dynamic unbalance amount;

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

[0018] A second model for expressing unbalanced force and unbalanced moment is established according to the transformation matrix and the first model.

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

[0020]

[0021] Among them, m stk and m dyk They are the static unbalance and dynamic unbalance of the rotating body, which generate a centrifugal force f gk and an uneven moment g gk The zero-time phases of the centrifugal force and the unbalanced torque are α k and β k ,ω k is the rotor angular frequency, and the offset of the rotor shaft is ε k , the deflection of the rotor shaft is ξ k , the rotor mass is m, and J is the rotor's moment of inertia.

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

[0023] Unbalanced force:

[0024]

[0025] Unbalanced torque:

[0026]

[0027] in, R sg is the transformation matrix.

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

[0029]

[0030] T sgfk is the coordinate system from the kth magnetic suspension rotor to the planet orbit The vibration force transfer matrix of the origin; T sggk is the coordinate system from the kth magnetic suspension rotor to the planet orbit The vibration torque transfer matrix of the origin; l wk is the mass center of the kth magnetic suspension rotor in the planetary orbit coordinate system The installation position in, I is the inertia;

[0031] The kinetic synthesis model is:

[0032]

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

[0034] In a possible design, the star attitude dynamics equation is:

[0035]

[0036] Among them, m s is the mass of the satellite platform; I s is the inertia matrix of the satellite platform; X s is the linear vibration vector of the satellite platform; θ s is the attitude vector of the satellite platform.

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

[0038]

[0039] Among them, k Pz and k Pθ is the proportional control coefficient, which provides a certain support stiffness for the magnetic bearing; k Iz and k Iθk is the integral control coefficient, which accumulates the deflection error of the magnetic bearing and improves the control accuracy; Dz and k Dθ is the differential control coefficient.

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

[0041]

[0042] Among them, the eccentricity weighting coefficient matrix P = P T >0; skew angle weighting coefficient matrix Q = Q T >0.

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

[0044]

[0045] Among them, f c (t) is the equivalent control force applied by the radial magnetic bearing to the rotor mass center; g c (t) is the equivalent control torque of the radial magnetic bearing to the rotor mass center; k f is the radial magnetic bearing force coefficient, i cf is the radial magnetic bearing driving current; k g is the torque coefficient of the radial magnetic axis, i cg is the driving current of the motor.

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

[0047]

[0048] Among them, K τ is the rotor radial displacement stiffness; K θ is the rotor radial angular stiffness; F o is the radial unbalanced force of the rotor; g o is the unbalanced torque of the rotor in radial direction; F c g is the radial control force of the magnetic bearing on the rotor; c is the radial control torque of the magnetic bearing on the rotor.

[0049] The advantages of the present invention compared with the prior art are:

[0050] (1) Traditional satellites generally carry out 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, it is necessary to perform passive vibration isolation, active and passive integrated vibration isolation and active vibration isolation on the payload again. Although two-level vibration isolation is also achieved, the weight and other costs paid are relatively large and the system is relatively complex. This patent is aimed at the distributed magnetic levitation CMG on the ultra-quiet satellite. For the first time, it uses the characteristics of the CMG rotor speed being fixed and the rotor shaft eccentricity and deflection being actively controllable. It proposes a method for actively adjusting the imbalance of each rotor in the distributed CMG, including its amplitude and phase, to achieve vibration cancellation. Without adding any additional hardware, the static and dynamic imbalance of each rotor is allocated only according to the satellite's attitude information, so as to achieve micro-vibration cancellation of different CMG rotors and improve the attitude stability of the entire satellite.

[0051] (2) This patent accurately establishes the dynamic model of the magnetically suspended CMG rotor and the dynamic model of the satellite, and carries out joint simulation of the control system and the dynamic system, which 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 the control law, so this patent has direct engineering application value. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0053] Figure 1 This is a schematic diagram of the layout of the magnetically suspended CMG group on the super-quiet satellite of the present invention;

[0054] Figure 2 A schematic diagram of the angular momentum of a single control moment gyroscope of 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 It is a block diagram of the magnetic suspension CMG group rotor control law control system of the present invention;

[0057] Figure 5 It is a regular pentagonal pyramid configuration of the magnetically suspended CMG group of the present invention. DETAILED DESCRIPTION

[0058] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments in the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0059] Please refer to Figure 1 The embodiment of the present invention provides a method for canceling micro-vibration of a magnetically suspended CMG group based on rotor imbalance adjustment, comprising:

[0060] Establishing a second model of unbalanced force and unbalanced torque of each magnetically suspended rotor;

[0061] According to the transfer matrix, the installation position of the rotor mass center in the body orbit 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 mass center of the star body;

[0062] According to the third model, a dynamic synthesis model of the CMG group is established; wherein the dynamic synthesis model includes resultant force and resultant moment;

[0063] The stellar attitude dynamics equations are established based on the dynamics synthesis model and Euler equations;

[0064] According to 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;

[0065] The objective function is constructed by using the CMG group control model and the satellite attitude dynamics equation, and the functional relationship between the CMG group resultant force and resultant moment and the unbalanced force and unbalanced moment is established;

[0066] A current control model between the power and current of the rotor's radial translation and radial rotation is established to control the resultant force and torque of the CMG group through the magnetic suspension CMG current;

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

[0068] The output current is determined according to the dynamic rotation equation and control model to adjust the rotor imbalance and phase, and to cancel the same-frequency harmonic vibration of the magnetically suspended CMG rotor.

[0069] In order to overcome the problems of insufficient accuracy and stability of onboard payload attitude caused by the traditional attitude control mode based on satellite service platforms, as well as the difficulty in controlling the micro-vibration of traditional inertial attitude actuators, this patent provides a method for canceling micro-vibration of a magnetically suspended CMG group based on rotor imbalance adjustment. For the distributed magnetically suspended CMG on ultra-quiet satellites, the CMG rotor speed is fixed and the eccentricity and deflection of the rotor shaft are actively controllable. The static and dynamic imbalance amplitudes and phases are allocated to each rotor according to the satellite's attitude and acceleration information, and then the imbalance of each rotor in the distributed CMG is actively adjusted through the magnetic bearings of each rotor, including its amplitude and phase, to achieve micro-vibration cancellation of multiple magnetically suspended CMG rotors on the satellite, improve the attitude stability of the entire satellite, and thus achieve ultra-stable and ultra-quiet performance of the payload attitude.

[0070] In some embodiments of the present invention, the unbalanced force and unbalanced torque model of each magnetic suspension rotor is established, including:

[0071] Establishing a first model expressing the relationship between the rotor unbalance amount and the offset amount and the deflection amount; wherein the rotor unbalance amount includes a static unbalance amount and a dynamic unbalance amount;

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

[0073] According to the transformation matrix and the first model, a second model expressing the unbalanced force and the unbalanced moment is established.

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

[0075]

[0076] Among them, m stk and m dyk They are the static unbalance and dynamic unbalance of the rotating body, which generate a centrifugal force f gk and an uneven moment g gk The zero-time phases of the centrifugal force and the unbalanced torque are α k and β k ,ω k is the rotor angular frequency, and the offset of the rotor shaft is ε k , the deflection 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 deflection and displacement of the rotor shaft will generate unbalanced vibration, which is the main source of micro-vibration of the actuator and also the active micro-vibration control force and torque of the present invention. For this reason, a vibration model of the rotor is established.

[0078] For the magnetic suspension rotor system, if the rotor and rotating body of the magnetic suspension bearing are regarded as rigid bodies, they constitute a rotating body and are supported on the frame through electromagnetic coupling; and the magnetic suspension stator and frame are regarded as a rigid assembly, and then installed on the satellite cabin through the frame base. And establish the following coordinate system:

[0079] Planet orbit coordinate system o o x o y o z o Its origin is o o Located at the center of mass of the satellite platform, the satellite is flying in the direction of x o Axis, the normal direction of the satellite orbital plane is y o Axis, z o The axes are 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 center of mass o of the rotor g , with the high-speed rotor axis 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 mass center o w ; Take the axis of rotation as y w Axis, with the rotor radial main inertia axis as z w Axis, x w The axis is determined by the right-hand rule and rotates synchronously with the rotor.

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

[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 three inertia products are zero, that is, 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 an imbalance:

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

[0087] ε k =m stk m -1 (1)

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

[0089] Assume that the dynamic unbalance mass is m dyk , and is located in the yoz plane, and the unbalanced mass block is located at (0, b, r). And the deflection angle of the inertia axis relative to the rotor axis is ξ k , from which the moment of inertia can be calculated as:

[0090]

[0091] The product of inertia is:

[0092]

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

[0094]

[0095] Because J k For a real symmetric matrix, there must be three real eigenvalues, and its eigenvectors are the three principal axes of inertia. The principal axes of inertia are obtained by taking the extreme value of the moment of inertia of the rigid body about any axis. Assume that the angle between the axis normal vector n and the coordinate axes x, y, and z after the offset caused by the dynamic unbalance is ξ k , γ k Indicates that the vector n can be expressed as (cosζ k cos k cosγ k ) T The moment of inertia of a rigid body with respect to vector n is:

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

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

[0098] Since the unbalanced mass is located in the yoz plane, cosζ k = 0, and ξ k +γ k =π / 2, formula (5) can be simplified to:

[0099] J k =J y cos 2 ξ k +J z sin 2 ξ k -2J yz cos 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 The function of , and its derivative:

[0102]

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

[0104]

[0105] In view of the small dynamic unbalance, J yz →0,ξ k →0, then From this, the deflection angle of the principal axis of inertia can be solved as:

[0106]

[0107] Therefore, dynamic unbalance u dyk Approximately:

[0108]

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

[0110]

[0111] Among them, ω k is the rotor angular frequency. As can be seen from the above formula, by actively controlling the offset ε of the high-speed rotor shaft k and the skewness ξ k The static and dynamic imbalance of the rotor can be controlled, and then the centrifugal force and couple generated by the rotor imbalance can be controlled; and by actively adjusting the deflection and offset direction of the high-speed rotor shaft, the phase of the centrifugal force and couple of the rotor can be controlled, thereby generating an active control action.

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

[0113] Unbalanced force:

[0114]

[0115] Unbalanced torque:

[0116]

[0117] in, R sg is the transformation matrix.

[0118] In this embodiment, it is assumed that the high-speed rotor of any control moment gyro k is in the planetary orbit coordinate system Installation location in (x k ,y k ,z k ), the initial coordinate system of CMG-k coincides with the star coordinate system, its initial high-speed rotation axis points to the y direction, and the initial frame rotation axis points to the z direction, and passes through After rotation, it becomes Figure 2 The situation shown. Take the mass center of the high-speed rotor as the origin o, and g k Indicates that the frame rotation axis of the kth CMG is The unit direction vector under k Indicates that the rotation axis of the magnetically suspended rotor of the kth CMG in the CMGs is The unit direction vector under t k =g k× h k , when the CMG frame moves along g k The axis has an angular velocity ω k When rotating, because the angular momentum of the rotor is in the direction h k Change, external disturbance torque causes gyroscopic effect, located at t k The gyroscopic torque generated externally is the torque output axis of the CMG, which is located at -t k Axial. Its azimuth is Its frame axis g k The angle between the z-axis and k Angular momentum h k Around the frame axis g k Turn over k The initial frame angle δ k = 0, that is, the position is located in the xoy plane. Its high-speed rotation axis is in the star orbit coordinate system Installation position in Euler rotation matrix:

[0119]

[0120] From the stellar orbital coordinate system To CMG frame coordinate system Then to the rotor body coordinate system The transformation matrix inside is: From the rotor local system to the star orbit coordinate system The transformation matrix inside is:

[0121]

[0122] in, Other angles are similar, install the matrix Only related to the configuration of CMG; R3(δ k ) is related to the frame angular position; R2(ω k t+χ k ) is related to the position of the unbalanced amount in the rotor body coordinate system. ψ kis a parameter related only to the installation condition of CMG-k. Then the unbalanced force and moment in this state can be expressed in the stellar coordinate system as:

[0123]

[0124] If the phase angle of the unbalanced force is assumed to be α k , the unbalanced force in formula (14) can be further expanded as:

[0125]

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

[0127] If the phase angle of the unbalanced force is assumed to be β k , the unbalanced moment in formula (14) can be further expanded as:

[0129]

[0130] It can be seen that by actively controlling the imbalance, the opposite force and torque can be generated to cancel the micro-vibration.

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

[0132]

[0133] T sgfk is the coordinate system from the kth magnetic suspension rotor to the planet orbit The vibration force transfer matrix of the origin; T sggk is the coordinate system from the kth magnetic suspension rotor to the planet orbit The vibration torque transfer matrix of the origin; l wk is the mass center of the kth magnetic suspension rotor in the planetary orbit coordinate system The installation position in, I is the inertia;

[0134] The kinetic synthesis model is:

[0135]

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

[0137] In this embodiment, the vibration of the magnetic levitation CMG and the force and torque of the active control will be transmitted through the star structure, affecting the position and posture of the star, so the influence of vibration transmission must be considered in the process of vibration control. However, in order to simplify the description of the vibration control method, the present invention will simplify the micro-vibration transmission characteristics of the structure, and the accurate vibration transmission model will be obtained by actual measurement in subsequent projects. For this reason, this article will study the transmission of vibration control force and torque based on the simplified transmission model, and equate the force and torque to the center of mass of the star.

[0138] In view of the small deformation of the elastic boundary under the active control of the magnetic levitation rotor, it is assumed that the direction of the control force and torque remains unchanged. Considering that the control force of the rotor will generate a torque rotating around the center of mass, it can be obtained that the unbalanced control force and torque rigidity generated by the magnetic levitation rotor is equivalent to the center of mass of the star:

[0139]

[0140] Among them, T sgfk is the coordinate system from the kth magnetic suspension rotor to the planet orbit The vibration force transfer matrix of the origin; T sggk is the coordinate system from the kth magnetic suspension rotor to the planet orbit The vibration torque transfer matrix of the origin; l wk is the mass center of the kth magnetic suspension rotor in the planetary orbit coordinate system The installation position in the middle; then the unbalanced control force and torque generated by the magnetic suspension rotor transmitted to the center of mass of the star is:

[0141]

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

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

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

[0145]

[0146] Among them, F s and M s The external forces and moments on the satellite platform. The amount of effect that can be achieved Different. Given the action P s The dimension of the space is generally less than the control degree of freedom 4n of n-SGCMG. From equation (14), it can be seen that a point in the control space of n-SGCMG is in the action space P s can only correspond to one point, and the action space P s A point in corresponds to at least one mapping point in the control space of n-SGCMG.

[0147] Since the magnetic suspension CMGs used on a satellite are of the same type, the speed of the high-speed rotors of each CMG is the same, and the unbalanced vibration frequency ω k The same, all ω.

[0148]

[0149] It can be seen from formula (20) that when the unbalanced amplitude and phase of each rotor in the magnetically suspended CMG group are appropriately adjusted, the harmonic vibrations introduced by the rotors in the magnetically suspended CMG group can cancel each other, achieving zero vibration of the CMG group output to the entire satellite, thereby reducing the micro-vibration response of the satellite.

[0150] In some embodiments of the present invention, the star attitude dynamics equation is:

[0151]

[0152] Among them, m s is the mass of the satellite platform; I s is the inertia matrix of the satellite platform; X s is the linear vibration vector of the satellite platform; θ s is the attitude vector of the satellite platform.

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

[0154] If the structural damping of the three-axis stabilized satellite is not considered, the translational dynamic equation of the satellite is established, and according to the Euler equation The attitude dynamics equation of the celestial body can be established as follows:

[0155]

[0156] Among them, m s is the mass of the satellite platform; I s is the inertia matrix of the satellite platform;

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

[0158] It can be seen that the micro-vibration on the star will affect the dynamic response of the star, affecting its linear vibration and angular vibration.

[0159] Any micro-vibration of a fixed frequency on the satellite can be expressed as the synthesis of the circular vibration caused by the rotating mechanism and the linear vibration of the linear reciprocating mechanism, in which the linear vibration needs to be controlled by a linear actuator; the circular vibration can be generated by a linear actuator, or directly controlled by a circular vibration actuator. This can be used to suppress the linear vibration of the satellite by the axial active vibration control of the magnetically suspended rotor; the circular vibration of the satellite can be suppressed by unbalanced vibration control, thereby achieving the ultra-quiet performance of the satellite with full degrees of freedom.

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

[0161]

[0162] Among them, k Pz and k Pθ is the proportional control coefficient, which provides a certain support stiffness for the magnetic bearing; k Iz and k Iθ k is the integral control coefficient, which accumulates the deflection error of the magnetic bearing and improves the control accuracy; Dz and k Dθ is the differential control coefficient.

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

[0164]

[0165] Among them, k Pz and k Pθ is the proportional control coefficient, which provides a certain support stiffness for the magnetic bearing; k Iz and k Iθ k is the integral control coefficient, which accumulates the deflection error of the magnetic bearing and improves the control accuracy; Dz and k Dθ is the differential control coefficient, which provides 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] Among them, the eccentricity weighting coefficient matrix P = P T >0; skew angle weighting coefficient matrix Q = Q T >0.

[0170] In this embodiment, in order to realize three-axis attitude control, there should be no less than 4 CMGs on the satellite, and the frame axes of at least 2 CMGs are not collinear. In this case, the rank of matrix A is 3 and the rank of matrix M is 6. At this time, after the desired torque is given, equation (19) has infinite solutions. It is necessary to realize the 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 amount will be performed below.

[0171] The objective function is constructed using the CMG unbalanced force / torque vector:

[0172]

[0173] Among them, the eccentricity weighting coefficient matrix P = P T >0; skew angle weighting coefficient matrix Q = Q T >0. At this time, the torque distribution strategy is: solve the minimum value of the index function J2 under the constraint of equation (19), and through active unbalance control, make the vibration of the magnetic suspension CMG group zero under the condition of making the rotor offset and deflection as small as possible, so as to obtain the optimal unbalanced force and torque of each rotor. Then, the equivalent force and torque acting on the center of mass of the star can be obtained, realizing the optimal cancellation of the power frequency vibration. The distribution block diagram of the system is shown in Figure 4 shown.

[0174] In this configuration, five CMGs are evenly distributed on the five faces of the pentagonal pyramid. The cone angle of the pentagonal pyramid is designed according to the angular momentum requirement: the frame axes of the five CMGs are installed along the edges of the pentagonal pyramid, the bottom surface is a regular pentagon, the angle β=63.4°, the frame axes are perpendicular to the five faces of the pentagonal pyramid, and the angular momentum is parallel to the bottom surface when the frame angle is zero; 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:

[0177]

[0178] Among them, f c (t) is the equivalent control force applied by the radial magnetic bearing to the rotor mass center; g c (t) is the equivalent control torque of the radial magnetic bearing to the rotor mass center; k f is the radial magnetic bearing force coefficient, icf is the radial magnetic bearing driving current; k g is the torque coefficient of the radial magnetic axis, i cg is the driving current of the motor.

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

[0180]

[0181] Among them, f c (t) is the equivalent control force applied by the radial magnetic bearing to the rotor mass center; g c (t) is the equivalent control torque of the radial magnetic bearing to the rotor mass center. k f is the radial magnetic bearing force coefficient, i cf is the radial magnetic bearing driving current; k g is the torque coefficient of the radial magnetic axis, i cg is 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 the high-speed rotor, the relative deformation of each component is very small. It is assumed that the deformation of all components is within the linear elastic range of the material, that is, the stiffness parameter in the above formula is a constant; and it is assumed that the damping parameters are also constants. That is, the high-speed rotor system is a linear system.

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

[0184]

[0185] Among them, K τ is the rotor radial displacement stiffness; K θ is the rotor radial angular stiffness; F o is the radial unbalanced force of the rotor; g o is the unbalanced torque of the rotor in radial direction; F c g is the radial control force of the magnetic bearing on the rotor; c is the radial control torque of the magnetic bearing on the rotor.

[0186] In this embodiment, the zero initial time of the high-speed rotor operation is and The three axes are parallel and rotated by 2-1-3: θ oy ,θ ox ,θ oz , where θ ox and θ ozThey are all very small angles, so the corresponding trigonometric functions can be approximately linearized. The dynamic equations of 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 is the rotor radial displacement stiffness; K θ is the rotor radial angular stiffness. o is the radial unbalanced force of the rotor; g o is the unbalanced torque in the rotor radial direction. c g is the radial control force of the magnetic bearing on the rotor; c is the radial control torque of the magnetic bearing on the rotor.

[0189] Simulink is used to perform joint simulation on the dynamics and control system of ultra-quiet satellites to verify the effectiveness of the micro-vibration cancellation method based on distributed magnetic suspension CMG rotor imbalance control.

[0190] It can be seen that the high-speed rotor of the magnetic suspension CMG is both an exciter on the satellite and a vibration damper on the satellite. The former is mainly because there is no force and torque sensor installed for a single magnetic suspension CMG, and the inertia axis of its high-speed rotor cannot be estimated, making it difficult to avoid unbalanced vibration; however, the eddy current sensor of each magnetic suspension rotor can accurately measure the relative displacement of the rotor relative to the frame. More precisely, the increment of the unbalanced mass amplitude and phase of the rotor can be relatively adjusted, and finally the cancellation of the harmonic vibration of the magnetic suspension CMG rotor at the same frequency is completed through the large closed loop of the satellite system. When the unbalanced amount is adjusted in a certain harmonic form, it is possible to modulate the vibration of other frequency components on the basis of the power frequency vibration, and it can also cancel the vibration generated by other actuators on the satellite to a certain extent, thereby further improving the ultra-quiet performance of the satellite.

[0191] In short, by actively adjusting the dynamic and static imbalance amplitude and phase of each high-speed rotor in the magnetically suspended CMG group, a canceling effect on micro-vibration is produced, thereby achieving ultra-static and stable control of the linear / angular vibration of the star.

[0192] It can be seen that this patented method can be used for precise and ultra-quiet attitude control of high-performance satellites such as on-board optical satellites and laser communication satellites; it has strong versatility and a broad field of application.

[0193] It should be noted that, in this article, relational terms such as first and second are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions, the elements defined by the statement "comprise a ..." do not exclude the presence of other identical factors in the process, method, article or device including the elements.

[0194] A person of ordinary skill in the art can understand that all or part of the steps of implementing the above method embodiments can be completed by hardware related to program instructions, and the aforementioned program can be stored in a computer-readable storage medium. When the program is executed, it executes the steps of the above method embodiments; and the aforementioned storage medium includes: ROM, RAM, magnetic disk or optical disk, etc., various media that can store program codes.

[0195] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for canceling micro-vibration of a magnetically suspended CMG group based on rotor imbalance adjustment, characterized in that: include: Establishing a second model of unbalanced force and unbalanced torque of each magnetically suspended rotor; According to the transfer matrix, the installation position of the rotor mass center in the body orbit 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 mass center; According to the third model, a dynamic synthesis model of the CMG group is established; wherein the dynamic synthesis model includes a resultant force and a resultant moment; Establishing the stellar attitude dynamics equation according to the dynamics synthesis model and Euler equation; According to the PID control law, a CMG group control model is established; wherein the CMG group control model includes a group control force and a group control torque; The objective function is constructed by using the CMG group control model and the satellite attitude dynamics equation to establish the functional relationship between the resultant force and resultant moment of the CMG group and the unbalanced force and unbalanced moment; A current control model between the power and current of the rotor's radial translation and radial rotation is established to control the resultant force and torque of the CMG group through the magnetic suspension CMG current; Establish the dynamic rotation equations of the high-speed rotor in radial translation and radial rotation; The output current is determined according to the power rotation equation and the control model to adjust the unbalance and phase of the rotor and cancel the same-frequency harmonic vibration of the magnetically suspended CMG rotor.

2. The method according to claim 1, characterized in that The method of establishing the unbalanced force and unbalanced torque model of each magnetic suspension rotor includes: Establishing a first model expressing the relationship between the rotor unbalance amount and the offset amount and the deflection amount; wherein the rotor unbalance amount includes a static unbalance amount and a dynamic unbalance amount; Establish the transformation matrix from the rotor body coordinate system to the planet orbit coordinate system; A second model for expressing unbalanced force and unbalanced moment is established according to the transformation matrix and the first model.

3. The method according to claim 2, characterized in that The first model is: Among them, m stk and m dyk They are the static unbalance and dynamic unbalance of the rotating body, which generate a centrifugal force f gk and an uneven moment g gk The zero-time phases of the centrifugal force and the unbalanced torque are α k and β k ,ω k is the rotor angular frequency, and the offset of the rotor shaft is ε k , the deflection of the rotor shaft is ξ k , the rotor mass is m, and J is the rotor's moment of inertia.

4. The method according to claim 2, characterized in that: The second model is: Unbalanced force: Unbalanced torque: in, R sg is the transformation matrix.

5. The method according to claim 1, characterized in that The third model is: T sgfk is the coordinate system from the kth magnetic suspension rotor to the planet orbit The vibration force transfer matrix of the origin; T sggk is the coordinate system from the kth magnetic suspension rotor to the planet orbit The vibration torque transfer matrix of the origin; l wk is the mass center of the kth magnetic suspension rotor in the planetary orbit coordinate system The installation position in, I is the inertia; The kinetic synthesis model is: Among them, F s and M s are the external forces and moments acting on the satellite platform.

6. The method according to claim 1, characterized in that The stellar attitude dynamics equation is: Among them, m s is the mass of the satellite platform; I s is the inertia matrix of the satellite platform; X s is the linear vibration vector of the satellite platform; θ s is the attitude vector of the satellite platform.

7. The method according to claim 1, characterized in that The CMG group control model is: Among them, k Pz and k Pθ is the proportional control coefficient, which provides a certain support stiffness for the magnetic bearing; k Iz and k Iθ k is the integral control coefficient, which accumulates the deflection error of the magnetic bearing and improves the control accuracy; Dz and k Dθ is the differential control coefficient.

8. The method according to claim 1, characterized in that The objective function is: Among them, the eccentricity weighting 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: Among them, f c (t) is the equivalent control force applied by the radial magnetic bearing to the rotor mass center; g c (t) is the equivalent control torque of the radial magnetic bearing to the rotor mass center; k f is the radial magnetic bearing force coefficient, i cf is the radial magnetic bearing driving current; k g is the torque coefficient of the radial magnetic axis, i cg is the driving current of the motor.

10. The method according to claim 1, characterized in that The dynamic rotation equation is: Among them, K τ is the rotor radial displacement stiffness; K θ is the rotor radial angular stiffness; F o is the radial unbalanced force of the rotor; g o is the unbalanced torque in the rotor radial direction; F c is the radial control force of the magnetic bearing on the rotor; g c is the radial control torque of the magnetic bearing on the rotor.

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