CN114859948A - Radial pose decoupling control method and system for magnetic suspension rotary scanning load - Google Patents
Radial pose decoupling control method and system for magnetic suspension rotary scanning load Download PDFInfo
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Abstract
A decoupling control method for radial pose of magnetic suspension rotary scanning load belongs to the technical field of aerospace control. Aiming at a non-ideal rotary scanning rotor (a load cabin) and a satellite platform cabin, the invention carries out satellite two-body dynamic modeling, in order to realize high-precision directional control of the load cabin by means of the force from a magnetic suspension rotary joint to the platform cabin and ensure that the relative linear displacement of a stator and a rotor of a laser communication point is zero, a pose decoupling control law is designed for the magnetic suspension rotary joint, the validity of a model is verified through the combined simulation of a power system and a pose control system, and model reference is provided for the control law design and ground simulation verification of the subsequent high-precision pose control of the satellite.
Description
Technical Field
The invention relates to a decoupling control method and a decoupling control system for radial pose of magnetic suspension rotary scanning load, and belongs to the technical field of control.
Background
The magnetic suspension bearing is a high-performance bearing for suspending a rotor by using magnetic field force. The magnetic suspension bearing has the advantages of no friction, no abrasion, no need of lubrication, low cost, low loss, long service life and the like, so that the magnetic suspension bearing can be applied to the occasions of high-speed motion and the low-speed clean occasions and the like and can be widely applied to the fields.
The rotary scanning satellite realizes the intersection of a scanning track and a flying track through swinging, circular scanning (also called conical scanning) and the like of a load (such as a camera and the like) rotating at a stable speed, so that the scanning range of the load is remarkably expanded. Under the modes of fast scanning imaging or splicing imaging of loads such as a camera and the like, ultra-wide imaging of kilokilometers can be realized. The magnetic suspension rotary scanning satellite can be used for fast large-range high-resolution imaging of high-resolution loads and the like. The method can be used for ground detailed search and fast search and large-range tracking of moving targets on the sea surface, the land and the air.
The magnetic suspension bearing is applied to a rotary scanning satellite to form a magnetic suspension rotary scanning imaging remote sensing satellite, and the magnetic suspension rotary scanning imaging remote sensing satellite can realize the ultra-wide high-resolution imaging of remote sensing load. The satellite mainly comprises a platform cabin for providing system services such as energy, attitude and orbit control, thermal control and the like, and a load cabin mainly composed of a rotary scanning camera, a star sensor and the like; the moving cabin and the static cabin are flexibly connected through a magnetic suspension rotary joint, the magnetic suspension rotary joint can isolate broadband disturbance vibration of the platform cabin and can perform secondary fine adjustment on the pose of the load cabin, so that the pointing direction of loads such as a camera and the like has ultra-precise, ultra-stable, ultra-static and ultra-wide 'ultra' potential, and a good working environment is created for load imaging; meanwhile, the relative position between the stator and the rotor can be adjusted, and the rapid and effective data transmission of wireless communication is guaranteed.
(1) Measurement index requirement for camera optical axis orientation
In order to meet the requirements of the camera on the rotating imaging quality, the pointing direction of the camera needs to be accurately controlled; or processing such as correcting an image taken by the camera using data such as the attitude of the camera.
(2) Laser communication to rotary joint index requirements
The laser transmission receiving and transmitting antenna in the satellite is arranged on the rotary joint, and the requirement of the pointing alignment precision of the laser transmission receiving and transmitting antenna during the camera imaging period is met: the smaller the displacement deviation, the larger the allowable deviation angle error. Therefore, the displacement deviation is controlled to be as small as possible, and the directional control of the load is more favorably realized.
Therefore, the magnetic suspension rotary joint provides precise support and rotation control for the load cabin, the pointing control precision of the rotating shaft of the load cabin is ensured through the angle (rotary transformer) and displacement (eddy current displacement sensor) measuring component, the platform cabin attitude measuring component and the load cabin attitude measuring component of the magnetic suspension rotary joint, and high-precision pointing measurement data is provided for the optical axis of a camera and the like. Therefore, measurement feedback is carried out through the sensor, signal processing and control signal generation are carried out through the controller, and attitude maneuvering and maintaining of the load cabin are achieved through the actuation of the magnetic bearings.
In order to convert the 'super' potential into 'super' capacity and ensure the ultra-wide high-resolution imaging of the magnetic suspension rotating scanning satellite, methods such as directional control of load and the like need to be optimally designed, and sufficient system performance test verification is carried out. The rotary scanning satellite is a multi-body structure formed by a load cabin, a platform cabin and the like, and dynamics between the load cabin and the platform cabin are coupled through a magnetic suspension bearing in the middle; the load cabin rotates in the orbit plane, the dynamic model is a multi-degree-of-freedom nonlinear time-varying coupling differential equation set, and the parameters are time-varying functions related to the attitude.
Disclosure of Invention
The technical problem solved by the invention is as follows: the method overcomes the defects of the prior art, designs the attitude control method of a two-body system aiming at the two-body system of a rotating body mainly comprising a load cabin and a non-rotating body mainly comprising a platform cabin, designs a radial attitude decoupling control law for the magnetic suspension rotating joint, realizes the force borrowing of the magnetic suspension rotating joint to the platform cabin, develops the combined simulation of a dynamic system and an attitude control system, realizes the high-precision attitude control of the load cabin, and provides reference for the control law design of the high-precision attitude control of the subsequent satellite and the ground simulation verification.
The technical solution of the invention is as follows: a radial pose decoupling control method for a magnetic suspension rotary scanning load comprises the following steps:
(1) modeling the control force and moment of the magnetic bearing;
the modeling of control forces and moments for a magnetic bearing includes:
in the system in the load cabin, the relationship between the current of the magnetic bearing and the generated acting force and moment is analyzed as follows:
the forces and moments generated by the magnetic bearing in the y-direction are as follows:
upper radial magnetic suspension bearing M 1 And a lower radial magnetic suspension bearing M 2 The generated y-direction acting force is equivalent to the acting force at the mass center
Sum moment
The following were used:
wherein the content of the first and second substances,
a mounting matrix for the y-direction bearing;
is a constitutive model of the y-direction magnetic bearing;
indicating magnetic bearing M 1 Drive current in the y-direction;
indicating magnetic bearing M 2 Drive current in the y-direction;
the forces and moments generated by the magnetic bearing in the z-direction are as follows:
upper radial magnetic suspension bearing M 1 And a lower radial magnetic suspension bearing M 2 The generated z-direction force is equivalent to the force at the centroid
Sum moment
The following were used:
wherein the content of the first and second substances,
is a mounting matrix of the bearing in the z direction;
a drive matrix for the z-direction magnetic bearing;
indicating magnetic bearing M 1 A drive current in the z-direction;
indicating magnetic bearing M 2 A drive current in the z-direction;
the radial magnetic bearing operates according to the following law:
in a load cabin body coordinate system, an upper radial magnetic suspension bearing M is obtained according to the equivalent control force and moment at the required mass center 1 And a lower radial magnetic suspension bearing M 2 Control current of (2):
(2) carrying out attitude dynamics modeling on the load cabin;
the attitude dynamics modeling of the load compartment comprises the following steps:
in the body coordinate system F of the rotating body ub The attitude kinetic equation of the rotating body is as follows:
wherein the content of the first and second substances,
in a body coordinate system F of the rotating body ub The relative derivative of angular momentum with respect to time; omega ub In a rotor body coordinate system F for the rotor ub An inner angular velocity vector;
representing a matrix of angular velocity parameters; h ub In a rotor body coordinate system F for the rotor ub An inner angular momentum vector; m ub In the body coordinate system F of the rotating body to which the rotating body is subjected ub An internal external moment;
virtual applied moment
C uib As a body coordinate system F of the rotating body ub To an inertial frame F i A coordinate transformation matrix between (1); c ubi Is a matrix C uib The inverse matrix of (d);
(3) performing translation dynamics modeling on a two-body system;
the modeling of the translation dynamics of the two-body system comprises the following steps:
the translational dynamic model of the load compartment is as follows:
wherein, F uoy Control force of y, F, generated for magnetic bearings uoz A z-direction control force generated for the magnetic bearing; m is u Representing the mass of the rotating body; y is uo Representing the centroid of the revolution with respect to the orbital coordinate system F o Displacement in the y-axis direction; z is a radical of uo Representing the centroid of the revolution with respect to the orbital coordinate system F o Displacement in the z-axis direction;
the mass center position relationship of the rotating body and the non-rotating body connected in the magnetic suspension mode is as follows:
wherein the content of the first and second substances,
representing the displacement of the mass center of the load compartment in the y-axis direction of the system in the load compartment;
representing the displacement of the mass center of the load compartment in the z-axis direction of the system in the load compartment; m is d Representing the mass of the platform deck;
representing the representation of the displacement of the platform cabin mass center in the y direction under the system of the load cabin;
representing the representation of the displacement of the platform cabin mass center in the z direction under the system of the load cabin;
(5) carrying out relative displacement observation of the stator and the rotor at the laser communication position;
the observation of the relative displacement of the stator and the rotor at the laser communication position comprises the following steps:
the relative displacement of the stator and the rotor at the laser communication position in the y-axis direction is as follows:
wherein the content of the first and second substances,
a coordinate system F of the stator and rotor axes at the laser communication position in the rotating body ub Relative distance in the y-direction; l represents the distance between the two centroids of the rotating body and the non-rotating body;
representing the radial attitude angle of the mass center of the load cabin in the z direction;
representing a radial attitude angle of the platform cabin in a mass center z direction; h is dj Indicating the distance from the laser communication to the non-rotating body centroid.
The relative displacement of the stator and the rotor at the laser communication position in the z-axis direction is as follows:
wherein the content of the first and second substances,
displacement sensor w representing electric eddy current 2 The stator and rotor axes in the measuring section are in the rotor body coordinate system F ub Relative distance in the z direction;
the radial attitude angle represents the y direction of the mass center of the load cabin;
representing the radial attitude angle of the platform cabin in the y direction of the mass center;
(6) establishing a load cabin directional decoupling control law in the track system;
the directional decoupling control law of the load cabin in the formulated track system comprises the following steps:
the forces and moments that control the radial displacement at the laser communication and control the pointing of the load compartment are as follows:
wherein the content of the first and second substances,
and
is a control law;
pitching and yawing postures of load cabin
The method comprises the steps of measuring in real time through a high-dynamic star sensor and a gyroscope of a load cabin; radial relative attitude
The electric eddy current sensor is used for resolving;
alternatively, the first and second electrodes may be,
the attitude measured by the very high star sensor and the gyroscope of the platform cabin in real time is converted into the system of the body of the rotating body and then combined with the attitude measured by the load cabin
Subtracting to obtain the relative attitude;
when the satellite needs to perform attitude or orbit maneuvering, the load cabin adopts relative pointing control, and S is equal to 1;
when the load stably rotates, the load cabin adopts absolute pointing control, S is 0 at the moment, the platform cabin adopts follow-up control, the radial attitude of the platform cabin tracks the attitude of a radial corresponding shaft of the load cabin, and the relation between the driving current of the magnetic suspension joint and the radial attitude of the center of mass of the rotating body is as follows:
wherein the content of the first and second substances,
and
are all diagonal control matrixes; wherein, g uy (s) is a y-direction translation control law; g uz (s) is a z-direction translation control law; g uθy (s) is a control law for rotation around the y axis; g uθz (s) is a control law for rotation about the z-axis, s being a complex variable.
By passing
And
SISO is obtained between the driving current and the pose signal, decoupling control of the magnetic suspension joint is realized, and the decoupling control law is as follows:
the system of the radial pose decoupling control method according to the magnetic suspension rotary scanning load comprises the following steps:
a first module for performing control force and moment modeling of a magnetic bearing;
the second module is used for carrying out attitude dynamics modeling on the load cabin;
the third module is used for carrying out translation dynamics modeling on the two-body system;
the fourth module is used for observing the relative displacement of the stator and the rotor at the laser communication position;
and the fifth module is used for establishing a load cabin directional decoupling control law in the track system.
A computer readable storage medium, having stored thereon a computer program which, when being executed by a processor, carries out the steps of the above-mentioned method for radial pose decoupling control of magnetically levitated rotary scan loads.
The radial pose decoupling control device for the magnetic levitation rotary scanning load cabin comprises a memory, a processor and a computer program which is stored in the memory and can run on the processor, wherein the processor executes the computer program to realize the steps of the radial pose decoupling control method for the magnetic levitation rotary scanning load.
Compared with the prior art, the invention has the advantages that:
(1) most of the existing satellites are load and platform integrated structures or separated satellites and other structures with no relative rotation motion in cabins, and the existing satellites cannot generate large interference torque due to rapid rotation. The rotary scanning load supported by the machine generally has smaller moment of inertia and basically performs balance and dynamic balance, so that the generated interference torque is smaller, and in the past, the radar-type load rotary scanning is mainly performed, the requirements on attitude precision and stability are lower, so that the smaller interference torque can be compensated to a certain extent through an on-satellite attitude executing mechanism, and the reduction of precision stability of the load attitude caused by residual interference is ignored; the two-cabin rotary scanning satellite with the magnetically suspended rotary joint in flexible connection is mainly used for rotary scanning high-resolution imaging of a high-resolution optical remote sensing satellite, and any disturbance of the attitude can cause great influence on the optical imaging, so that the problem that the load cabin is accurately and stably controlled by large disturbance torque generated by rapid rotation needs to be overcome.
(2) The attitude control of the load is directly carried out by an attitude control system of a platform cabin aiming at the satellite with the load rigidly connected with the platform, and the two-cabin rotary scanning satellite with the magnetically suspended rotary joint in soft connection is the first time. In the invention, the inertia of the rotating bodies with different rotational inertia of each shaft changes along with time in the continuous rotating process, and the interferences of variable inertia, moment of reaction, gyro moment and the like are generated. The invention aims at the dynamic model of the magnetic suspension rotary scanning load, realizes the attitude control of the load cabin by the aid of the magnetic suspension rotary joint to the platform cabin, combines the decoupling control of the two-body translational dynamic characteristics, and has higher innovation compared with the traditional translational decoupling control aiming at the single rigid body mass center. The invention provides a model basis for the design of a high-precision attitude control law, provides a model basis for the simulation of a ground system, and lays theoretical and engineering foundation for model development.
(3) The two-body attitude simulation of the magnetic suspension asymmetric rotating scanning satellite accurately establishes a dynamic model of the magnetic suspension asymmetric rotating scanning satellite, develops the combined simulation of a control system and a dynamic system, can be directly applied to model development, and particularly can be applied to the design of a high-precision satellite attitude control law. And because the thrust of the magnetic bearing in the magnetic suspension rotary scanning satellite is small, and the magnetic bearing is difficult to suspend under the action of ground gravity, the ground test cannot be carried out, and the model can simulate the attitude of a system with high precision and verify the implementation conditions of a control law and the like. The controller can be directly integrated into the controller without additional hardware equipment, and almost no cost is needed; therefore, the invention has direct engineering application value. The method provides a basis for realizing the directional ultra-precise ultra-stable and ultra-static control of the load cabin, and also provides a model basis for ground simulation and ground test.
Drawings
FIG. 1 is a simplified model of a magnetically levitated rotary scanning satellite system in accordance with the present invention;
FIG. 2 is a radial pose decoupling control technology route diagram of a magnetic levitation rotary scanning load in the present invention;
FIG. 3 is a simplified model of a two-body satellite according to the present invention, together with coordinate systems and parameters;
FIG. 4 is a block diagram of a radial pose decoupling control system for magnetic levitation rotary scanning loads in the present invention;
fig. 5 is an attitude control simulation example of a maglev rotating scanning satellite in the present invention.
Detailed Description
In order to better understand the technical solutions, the technical solutions of the present application are described in detail below with reference to the accompanying drawings and specific embodiments, and it should be understood that the specific features in the embodiments and examples of the present application are detailed descriptions of the technical solutions of the present application, and are not limitations of the technical solutions of the present application, and the technical features in the embodiments and examples of the present application may be combined with each other without conflict.
The following further describes a radial pose decoupling control method for a magnetic levitation rotary scanning load provided by the embodiment of the application with reference to the attached drawings of the specification. The invention aims at designing a radial pose decoupling control law for a magnetic suspension rotary joint aiming at the absolute orientation of a magnetic suspension rotary scanning load. And based on the measured postures of the load cabin and the platform cabin and the relative position of the rotor measured by the sensor, carrying out posture control on the magnetic suspension rotary joint and the load cabin, and carrying out two-body posture simulation according to the structural parameters of the satellite. A structurally simplified model of a rotating scanning satellite is shown in figure 1. The flow chart of the two-body posture simulation method provided by the invention is shown in fig. 2, and the two-body posture simulation method of the magnetic suspension rotary scanning load cabin comprises the following steps:
(1) coordinate system establishment for two-body system
When the rotor, the load compartment, and the like of the magnetic levitation rotary joint are regarded as rigid bodies, a rotary body (or collectively referred to as a load compartment) is formed; the stator of the magnetic suspension rotary joint and the platform cabin form a non-rotating body (or are collectively called as the platform cabin).
The coordinate system and related parameters of the magnetically levitated rotating scanning satellite are shown in FIG. 3.
(2) Modeling control forces and moments for magnetic bearings
In FIG. 3, the upper radial magnetic suspension bearing is M 1 The lower radial magnetic suspension bearing is M 2 。H c Showing two magnetic bearings M 1 And M 2 Axial span therebetween. H u1 Showing radial magnetic bearing M 1 The distance of the active cross section of (a) to the center of mass of the rotating body; h u2 Showing radial magnetic bearing M 2 Is arranged at a distance H from the active cross-section to the center of mass of the rotating body u2 ＝H u1 +H c 。
In the body coordinate system F of the rotating body ub The relationship between the internal analysis magnetic bearing current and the generated acting force and moment is as follows:
forces and moments generated by the magnetic bearing in the y-direction:
magnetic bearing M 1 And M 2 The relationship between the generated y-direction force and its control current is:
wherein the content of the first and second substances,
indicating magnetic bearing M 1 The output y-direction acting force;
Magnetic bearing M 1 And M 2 The resulting y-direction force is equivalent to the force and moment at the center of mass:
wherein, the mounting matrix of the magnetic bearing in the y direction is as follows:
constitutive model matrix of the magnetic bearing in the y direction:
forces and moments generated by the magnetic bearing in the z-direction:
similarly, the magnetic bearing M 1 And M 2 The relationship between the generated z-direction force and its control current is:
wherein the content of the first and second substances,
indicating magnetic bearing M 1 The output z-direction force;
Magnetic bearing M 1 And M 2 The resulting z-direction force is equivalent to the force and moment at the center of mass:
wherein, the magnetic bearing is installed in the matrix of z direction:
constitutive model matrix of the magnetic bearing in the z direction:
operation of radial magnetic bearingLongitudinal law:
the model between the magnetic bearing control current and the resulting equivalent to control force and moment at the centroid is then:
therefore, in the load cabin body coordinate system, the magnetic bearing M can be obtained according to the equivalent control force and moment at the required mass center 1 And M 2 The control current of (2).
(3) Performing attitude dynamics modeling of a load cell
Newton mechanics is built within the inertial system, so there is a relationship within the inertial system according to the theorem of moment of momentum:
wherein the content of the first and second substances,
the moment vector of the external force applied to the rotating body; m ui As vectors of external moments
In an inertial frame F i The vector of the inner;
ω ui for the body of revolution in an inertial frame F i The inner angular velocity vector.
The inertial coordinate system F i Conversion of internal dynamic model to body coordinate system F of rotating body ub Internal:
wherein H ub In a rotor body coordinate system F for the rotor ub An inner angular momentum vector;
ω ub in a rotor body coordinate system F for the rotor ub An inner angular velocity vector;
C uib As a body coordinate system F of the rotating body ub To an inertial frame F i A coordinate transformation matrix between (a) and (b).
Therefore, the attitude dynamics in the non-inertial system is directly related to the coordinate transformation relationship from the inertial system to the body system, and the dynamic adaptability condition caused by the coordinate transformation relationship is analyzed below.
The star body is in a small-angle rotation mode:
if the star body rotates at a small angle, the coordinate transformation matrix C uib The off-diagonal element of (A) is a small quantity, i.e. C uib Is approximated as a unit matrix, in this case
In this case, equation (7) can be simplified:
namely the attitude dynamics equation under the body coordinate system in view of the coordinate transformation matrix C uib Reversible, therefore:
therefore, when the star rotates at a small angle, the attitude dynamics can be calculated under the body coordinate system. The star body is in a large-angle rotation mode:
when the star rotates at a large angle, the coordinate transformation matrix C uib No longer approximated to a unit array, and thus this time
In this case, the kinetic model of formula (7) is deformed:
it can be seen that the star dynamics (9) in the low angle rotation mode is only a special case of the star dynamics (10) in the high angle rotation mode, and therefore (10) has more general applicability.
Further, the rotation-induced accessory term in the kinetic equation is taken as the virtual effective moment:
at this time (10), the right end acting torque becomes
It can be used for a rotator body coordinate system F ub And (4) the following steps.
In the body coordinate system F of the rotating body ub Attitude power of internal rotatorThe chemical equation is as follows:
therefore, when the system rotates within a large angle range, a proper correction term needs to be added, and the dynamic model with the correction term added can be used as an object model for attitude control of the magnetic suspension rotating scanning satellite under the system.
(4) Modeling of two-body system translation dynamics
Modeling translation dynamics of the load compartment:
according to the stress analysis of the magnetic bearing, the orbit coordinate system F of the rotator can be known uo In the y and z direction control forces [ F ] generated by the magnetic bearing uoy F uoz ] T The (acting on the load compartment) is:
wherein the content of the first and second substances,
to be measured from a rotating body coordinate system F ub To an inertial frame F o Within which a coordinate rotation matrix exists. Omega ux Is the angular velocity of rotation of the load compartment, t is the time;
for a load and joint rotor system, if structural damping is not considered, a radial translation kinetic equation of the system is as follows:
the relative translation relationship of the mass centers of the two bodies is as follows:
since the angular rotational speeds of the two bodies and their relative linear velocities are small, the coriolis force is temporarily ignored in the present invention. And assumes that the connection between the load compartment and the platform compartment is only the lorentz force of the magnetic bearings and no damping force. Universal gravitation G of the earth to the star e Providing full-star normal accelerationa n I.e. changing the direction of the satellite's velocity, i.e. (m) u +m d )a n ＝G e . And m is u Representing the mass of the rotating body; m is d Representing the mass of the non-rotating body. In addition, the external force of the star body in the y direction and the z direction of the orbit coordinate system is zero, so that a dynamic model of the mass center of two cabins of the magnetic suspension rotating scanning satellite in the radial direction is established according to the momentum theorem of a particle system as follows:
wherein, y uo Representing the mass centre of the revolution with respect to the orbital coordinate system F o Displacement in the y-axis direction;
z uo representing the centroid of the revolution with respect to the orbital coordinate system F o Displacement in the z-axis direction;
y do representing the centroid of the non-rotating body relative to an orbital coordinate system F o Displacement in the y-axis direction.
z do Representing the centroid of the non-rotating body relative to an orbital coordinate system F o Displacement in the z-axis direction;
y co representing the whole star centroid relative to the orbital coordinate system F o An offset in the y-axis direction;
z co representing the whole star centroid relative to the orbital coordinate system F o Offset in the z-axis direction.
This can solve the following: y is co (t)＝0；z co (t) ═ 0, indicating that the two combined centroids are stationary and present:
the relation of the mass center positions of the rotating body and the non-rotating body connected in a magnetic suspension manner can be solved by the formula (16):
the above formula reflects the relative motion relationship of the two mass centers of the load cabin and the platform cabin which are not subjected to the external force. Further, both sides simultaneously make a left-hand multiplication from the inertial coordinate system F o To the body coordinate system of the rotating body F ub Intrinsic existence coordinate rotation matrix
Then the following results are obtained:
wherein the content of the first and second substances,
representing the displacement of the mass center of the load compartment in the y-axis direction of the system in the load compartment;
representing the displacement of the mass center of the load compartment in the z-axis direction of the system in the load compartment;
representing the representation of the displacement of the platform cabin mass center in the y direction under the system of the load cabin;
representing a representation of the z-direction displacement of the platform pod centroid under the system in the load pod.
Therefore, the motion relation of the two mass centers of the load cabin and the platform cabin which are not subjected to the external force in the load cabin body coordinate system is basically consistent with that in the track coordinate system.
(5) Relative displacement observation of stator and rotor at laser communication position
In FIG. 3, the upper radial eddy current sensor is W 1 The lower radial eddy current sensor is W 2 。h w Indicating two radial eddy current sensors W 1 And W 2 Axial span therebetween.
h u1 Indicating upper radial eddy current sensor W 1 Measuring cross section to rotationDistance at the center of mass of the body; h is u2 Indicating lower radial eddy current sensor W 2 Is measured to the distance h from the center of mass of the rotating body u2 ＝h u1 +h w ；h uj The distance from the laser communication position to the center of mass of the rotating body is represented;
h d2 indicating lower radial eddy current sensor W 2 The distance of the measured cross section to the centroid of the non-rotating body; h is d1 Indicating upper radial eddy current sensor W 1 Is measured to the distance h from the centroid of the non-rotating body d1 ＝h d2 +h w ；h dj Representing the distance from the laser communication position to the mass center of the non-rotating body;
when L represents the distance between the two centroids of the rotating body and the non-rotating body, the relationship exists:
translational and radial attitude angle of load compartment centroid
And translation and radial attitude angle of platform cabin mass center
The resulting y-displacement at the two sets of radial eddy current sensors is:
wherein the content of the first and second substances,
represents the offset of the measurement center of the eddy current sensor W1 in the y direction caused by the deflection of the load compartment;
The translational and radial attitude angles of the center of mass of the load compartment
And translation and radial attitude angle of platform cabin mass center
The resulting z-displacement at the two sets of eddy current sensors is:
wherein the content of the first and second substances,
the offset of the measurement center of the eddy current sensor W1 in the z direction caused by the deflection of the load compartment is represented;
Suppose that
Displacement sensor w representing electric eddy current 1 The stator and rotor axes in the measuring section are in the rotor body coordinate system F ub Relative distance in the y-direction;
displacement sensor w representing electric eddy current 2 In the rotor body coordinate system F of the stator and rotor axes in the measuring section ub Relative distance in the y-direction;
a coordinate system F of the stator and rotor axes at the laser communication position in the rotating body ub Relative distance in the y-direction. Displacement transducer w of eddy current caused by centroid movement and deflection 1 、w 2 The relative displacement of the axis of the internal stator at the position of the measuring section and the laser communication
And
can be calculated by equation (19):
suppose that
Displacement sensor w representing electric eddy current 1 The stator and rotor axes in the measuring section are in the rotor body coordinate system F ub Relative distance in the z direction;
displacement sensor w representing electric eddy current 2 The stator and rotor axes in the measuring section are in the rotor body coordinate system F ub Relative distance in the z direction;
displacement sensor w representing electric eddy current 2 The stator and rotor axes in the measuring section are in the rotor body coordinate system F ub Relative distance in the z-direction. Displacement transducer w of eddy current caused by centroid movement and deflection 1 、w 2 Measuring section and laser communication position of the inner stator axis relative displacement
And
can be calculated by equation (20):
this is obtained by the following equation (21):
therefore, the relative displacement in the y-axis direction at the laser communication position is as follows:
wherein h is d1j Indicating upper radial eddy current sensor W 1 Measuring the distance from the cross section to the laser communication position; h is dj2 Radial eddy current sensor W for indicating laser communication position to lower part 2 The distance of the measurement cross section of (1); then the relationship exists: h is d1j ＝h d1 -h dj ；h dj2 ＝h dj -h d2 . Laser communication in which the model estimatesThe theoretical value of the relative displacement is a feedback signal when the following controller is designed, and the relative displacement of the laser communication position estimated by the sensor is a feedback signal when the laser communication position works actually. This is solved by the formula (22):
therefore, the relative displacement in the z-axis direction at the laser communication position is as follows:
the above formula reflects the relative displacement of the axis of the fixed rotor in the laser communication section caused by the radial movement of the two bodies.
(6) Method for establishing directional decoupling control law of load cabin in track system
In view of the constraint of laser communication and the like on the relative motion of the joint stator and the joint rotor, the radial displacement of the laser communication position is controlled, and the pointing direction (including absolute pointing direction and relative pointing direction) of the load cabin is controlled, and the acting force and the moment of the load cabin are controlled:
wherein the content of the first and second substances,
and
is a control law. Pitching and yawing postures of load cabin
The method can be measured in real time through a high-dynamic star sensor and a gyroscope; while being in radial phaseTo the gesture
Can be obtained by resolving through an eddy current sensor; the attitude measured by the very high star sensor and the gyroscope of the platform cabin in real time can be converted into the system of the rotating body, and then the relative attitude is obtained by subtracting the attitude measured by the load cabin.
obviously, the latter is the norm of satellite operation. Under the normal working condition, the radial translation and the rotation dynamics of the rotating body are decoupled, the radial translation and the rotation feedback signals are also decoupled, the actuator control law of the magnetic suspension bearing is also decoupled, and therefore the attitude decoupling control of the system can be realized by designing a decoupling control law.
Under the master-slave cooperative control action of a load cabin (directional control) and a platform cabin (attitude follow-up control), S is 0, and
i.e. in case the platform capsule tracks the radial attitude of the load capsule well, then equations (27) and (28) can be simplified as follows:
the relationship between the driving current of the magnetic suspension joint and the radial pose at the centroid of the rotating body is as follows:
wherein the content of the first and second substances,
and
are all programmable diagonal control matrices, where g uy (s) is a y-direction translation control law; g uz (s) is a z-direction translation control law; g uθy (s) is a control law for rotation around the y axis; g uθz (s) is a control law for rotation about the z-axis, s being a complex variable.
Therefore, the decoupling control law of the magnetic suspension rotary joint is as follows:
due to the fact that
And
the magnetic suspension joint decoupling control method is characterized in that the magnetic suspension joint decoupling control method is a diagonal matrix, SISO (single input single output) between driving current and pose signals can be obtained through formulas (31) and (32), and decoupling control over the magnetic suspension joint is achieved.
The radial pose decoupling control law obtained by the method of the invention is subjected to simulation verification of the attitude of the vertical orbiting scanning satellite:
FIG. 4 is a block diagram of a radial pose decoupling control system for magnetic levitation rotary scanning loads in the present invention;
load chamber rotational scanning imaging mainly comprises vertical rail scanning, circular scanning (or called conical scanning), orbital scanning (spin satellite scanning mode) and the like. The invention takes the first vertical rail scanning as an example to carry out simulation analysis. The load compartment rotates about the flight direction x-axis. Considering that the attitude control is carried out in the orbital system, the control target is attitude stabilization relative to the orbital system, more precisely attitude stabilization control relative to the orbital system nominal rotation coordinate system, for the load in any rotation scanning period (with the zero phase in one period as the timing starting point), the attitude change in the inertial system caused by orbital rotation is small (the rotation scanning period is less than 1% of the orbital period), and at any attitude control time, C is uib ＝C uio C uob ≈C uob . According to the star layout, the following parameters can be temporarily taken:
h 1u ＝1.291；h 2u ＝1.577；h 1d ＝0.742；h 2d ＝0.456；h uj ＝1.191；h dj ＝0.842；
the models of the radial magnetic suspension bearing are initially assumed to be the same according to the design parameters of the magnetic bearing, and are as follows:
under the interference action of various interference moments, dynamic unbalance and the like on the load cabin, adopting a cooperative control strategy taking the load cabin as a main strategy, if the load cabin is subjected to the interference action of various interference moments, dynamic unbalance and the like, adopting a cooperative control strategy taking the load cabin as a main strategy, and adopting a cooperative control strategy
And
PID control mode is adopted, and each transmission is as follows:
the initial values of the PID control parameters can be taken as: k is a radical of P ＝1000；k I ＝100；k D 1. Meanwhile, the attitude controller of the platform cabin is also controlled by PID, dynamics and control system simulation of the two-cabin system are carried out by Simulink, and the simulation result is shown in FIG. 5.
Through the cooperative control of the magnetic suspension rotary joint and the attitude of the platform cabin, the high-precision attitude control of the two cabins is realized, and the relative pose relation of the stator and the rotor required by wireless communication is ensured. The dynamic model established by the invention is a reference for the satellite to comprise the load cabin pointing control and the platform cabin attitude control based on the magnetic suspension rotary joint, is also a basis for ground system dynamics simulation, and provides a basis for the ultra-precise ultra-stable and ultra-static attitude control of the load cabin.
The control system of the radial pose decoupling control method according to the magnetic suspension rotary scanning load comprises the following steps:
a first module for performing control force and moment modeling of a magnetic bearing;
the second module is used for carrying out attitude dynamics modeling on the load cabin;
the third module is used for carrying out translation dynamics modeling on the two-body system;
the fourth module is used for observing the relative displacement of the stator and the rotor at the laser communication position;
and the fifth module is used for establishing a load cabin directional decoupling control law in the track system.
A computer readable storage medium storing a computer program which, when executed by a processor, implements the steps (1) to (6) of the method for estimating a radial pose of a magnetically levitated rotary scan load cell.
A radial pose decoupling control device of a magnetic suspension rotary scanning load cabin comprises a memory, a processor and a computer program which is stored in the memory and can run on the processor, wherein the processor realizes the steps (1) to (6) of the radial pose estimation method of the magnetic suspension rotary scanning load cabin when executing the computer program.
As will be appreciated by one skilled in the art, embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, optical storage, and the like) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
It will be apparent to those skilled in the art that various changes and modifications may be made in the present application without departing from the spirit and scope of the application. Thus, if such modifications and variations of the present application fall within the scope of the claims of the present application and their equivalents, the present application is intended to include such modifications and variations as well.
Those skilled in the art will appreciate that those matters not described in detail in the present specification are well known in the art.
Claims (10)
1. A radial pose decoupling control method for a magnetic suspension rotary scanning load is characterized by comprising the following steps:
modeling the control force and moment of the magnetic bearing;
carrying out attitude dynamics modeling on the load cabin;
performing translation dynamics modeling on a two-body system;
carrying out relative displacement observation of the stator and the rotor at the laser communication position;
and establishing a load cabin directional decoupling control law in the track system.
2. The method for radial pose decoupling control of magnetic levitation rotary scan loads as claimed in claim 1, wherein said performing magnetic bearing control force and torque modeling comprises:
in the system in the load cabin, the relationship between the current of the magnetic bearing and the generated acting force and moment is analyzed as follows:
the forces and moments generated by the magnetic bearing in the y-direction are as follows:
upper radial magnetic suspension bearing M 1 And a lower radial magnetic suspension bearing M 2 The generated y-direction acting force is equivalent to the acting force at the mass center
Sum moment
The following were used:
wherein the content of the first and second substances,
a mounting matrix for the y-direction bearing;
is a constitutive model of the y-direction magnetic bearing;
indicating magnetic bearing M 1 Drive current in the y-direction;
indicating magnetic bearing M 2 Drive current in the y-direction;
the forces and moments generated by the magnetic bearing in the z-direction are as follows:
upper radial magnetic suspension bearing M 1 And a lower radial magnetic suspension bearing M 2 The generated z-direction force is equivalent to the force at the centroid
Sum moment
The following were used:
wherein the content of the first and second substances,
is a mounting matrix of the bearing in the z direction;
a drive matrix for the z-direction magnetic bearing;
indicating magnetic bearing M 1 A drive current in the z-direction;
indicating magnetic bearing M 2 A drive current in the z-direction;
the radial magnetic bearing operates according to the following law:
in a load cabin body coordinate system, an upper radial magnetic suspension bearing M is obtained according to the equivalent control force and moment at the required mass center 1 And a lower radial magnetic suspension bearing M 2 Control current of (2):
3. the method for controlling the radial pose decoupling of the magnetic levitation rotary scanning load according to claim 1, wherein the modeling of the attitude dynamics of the load capsule comprises:
in the body coordinate system F of the rotating body ub The attitude kinetic equation of the rotating body is as follows:
wherein the content of the first and second substances,
in a body coordinate system F of the rotating body ub The relative derivative of angular momentum with respect to time; omega ub In a rotor body coordinate system F for the rotor ub An inner angular velocity vector;
representing a matrix of angular velocity parameters; h ub In a rotor body coordinate system F for the rotor ub An inner angular momentum vector; m ub In the body coordinate system F of the rotating body to which the rotating body is subjected ub An internal external moment;
virtual applied moment
C uib As a body coordinate system F of the rotating body ub To an inertial frame F i A coordinate transformation matrix between (1); c ubi Is a matrix C uib The inverse matrix of (c).
4. The method for controlling the radial pose decoupling of the magnetic levitation rotary scanning load according to claim 1, wherein the modeling of the two-body system translational dynamics comprises:
the translational dynamic model of the load compartment is as follows:
wherein m is u Representing the mass of the rotating body; f uoy Control force of y, F, generated for magnetic bearings uoz A z-direction control force generated for the magnetic bearing; y is uo Representing the centroid of the revolution with respect to the orbital coordinate system F o Displacement in the y-axis direction; z is a radical of uo Representing the centroid of the revolution with respect to the orbital coordinate system F o Displacement in the z-axis direction;
the mass center position relationship of the rotating body and the non-rotating body connected in the magnetic suspension mode is as follows:
wherein m is d Representing the mass of the platform deck;
representing the displacement of the mass center of the load compartment in the y-axis direction of the system in the load compartment;
representing the displacement of the mass center of the load compartment in the z-axis direction of the system in the load compartment;
representing the representation of the displacement of the platform cabin mass center in the y direction under the system of the load cabin;
representing a representation of the z-direction displacement of the platform pod centroid under the system in the load pod.
5. The method for controlling the radial pose decoupling of the magnetic levitation rotary scanning load according to claim 4, wherein the observing the relative displacement of the stator and the rotor at the position of laser communication comprises:
the relative displacement of the stator and the rotor at the laser communication position in the y-axis direction is as follows:
wherein the content of the first and second substances,
a coordinate system F of the stator and rotor axes at the laser communication position in the rotating body ub Relative distance in the y-direction; l represents the distance between the two centroids of the rotating body and the non-rotating body;
representing the radial attitude angle of the mass center of the load cabin in the z direction;
representing a radial attitude angle of the platform cabin in a mass center z direction; h is dj Representing the distance from the laser communication position to the mass center of the non-rotating body;
the relative displacement of the stator and the rotor at the laser communication position in the z-axis direction is as follows:
wherein the content of the first and second substances,
displacement sensor w representing electric eddy current 2 The stator and rotor axes in the measuring section are in the rotor body coordinate system F ub Relative distance in the z direction;
the radial attitude angle represents the y direction of the mass center of the load cabin;
and the radial attitude angle of the platform cabin mass center y direction is represented.
6. The radial pose decoupling control method of the magnetic levitation rotary scanning load according to claim 5, wherein the formulating a load cabin pointing decoupling control law in a track system comprises:
the forces and moments that control the radial displacement at the laser communication and control the pointing of the load compartment are as follows:
wherein the content of the first and second substances,
and
is a control law;
when the satellite needs to perform attitude or orbit maneuvering, the load cabin adopts relative pointing control, and S is equal to 1;
when the load stably rotates, the load cabin adopts absolute pointing control, S is 0 at the moment, the platform cabin adopts follow-up control, the radial attitude of the platform cabin tracks the attitude of a radial corresponding shaft of the load cabin, and the relation between the driving current of the magnetic suspension joint and the radial attitude of the center of mass of the rotating body is as follows:
wherein the content of the first and second substances,
and
are all diagonal control matrixes; wherein, g uy (s) is a y-direction translation control law; g uz (s) is a z-direction translation control law; g uθy (s) is a control law for rotation around the y axis; g uθz (s) is a control law for rotation about the z axis; s is a complex number;
by passing
And
SISO is obtained between the driving current and the pose signal, and decoupling control on the magnetic suspension joint is realizedThe decoupling control law is as follows:
7. the radial pose decoupling control method of the magnetic levitation rotary scanning load according to claim 6, wherein the formulating a load compartment pointing decoupling control law in the track system further comprises:
pitching and yawing postures of load cabin
The method comprises the steps of measuring in real time through a high-dynamic star sensor and a gyroscope of a load cabin; radial relative attitude
The electric eddy current sensor is used for resolving;
alternatively, the first and second electrodes may be,
the attitude measured by the very high star sensor and the gyroscope of the platform cabin in real time is converted into the system of the body of the rotating body and then combined with the attitude measured by the load cabin
And
the relative attitude is obtained by subtraction.
8. The system for controlling the radial pose decoupling of the magnetic levitation rotary scanning load according to any one of claims 1 to 7, comprising:
a first module for performing control force and moment modeling of a magnetic bearing;
the second module is used for carrying out attitude dynamics modeling on the load cabin;
the third module is used for carrying out translation dynamics modeling on the two-body system;
the fourth module is used for observing the relative displacement of the stator and the rotor at the laser communication position;
and the fifth module is used for establishing a load cabin directional decoupling control law in the track system.
9. A computer-readable storage medium, in which a computer program is stored which, when being executed by a processor, carries out the steps of the method according to any one of claims 1 to 7.
10. A radial pose decoupling control apparatus of a magnetically levitated rotary scan load cell comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: the processor, when executing the computer program, performs the steps of the method according to any one of claims 1 to 7.
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