CN110045744B - Rotating load stability control method based on magnetic suspension bearing active stiffness regulation - Google Patents
Rotating load stability control method based on magnetic suspension bearing active stiffness regulation Download PDFInfo
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Abstract
A rotating load stability control method based on active stiffness regulation and control of a magnetic suspension bearing belongs to the field of spacecraft bearing joint stiffness modeling and control. The invention solves the problems that the existing method can not realize the precise modeling of the rigidity of the magnetic suspension bearing floating in the stator space and the active regulation and control of the low rigidity of the magnetic suspension bearing. According to the working mode and the structural characteristics of the rotating load satellite system, the invention designs an algorithm which can solve the magnetic gap change of each magnetic pole according to the displacement change of the bearing center and the space relative attitude information of the satellite platform and the rotating load, further establishes an electromagnetic action model equivalent to the center of the magnetic suspension bearing according to an electromagnetic theory, solves to obtain a rigidity model of the magnetic suspension bearing, designs a controller parameter according to the rigidity model to perform low-rigidity active regulation and control, and realizes the stable control of the rotating load. The method can be applied to the field of spacecraft bearing joint rigidity modeling and control.
Description
Technical Field
The invention belongs to the field of spacecraft bearing joint rigidity modeling and control, and particularly relates to a remote sensing satellite on-satellite rotating load attitude high-stability stable control method based on a magnetic suspension bearing active rigidity regulation and control technology.
Background
With the continuous increase of the space task demand, the requirement on the attitude stability of the load on the remote sensing satellite is higher and higher. In order to improve the spinning precision of the rotating load on the satellite of the remote sensing satellite and inhibit the high-frequency vibration transfer in the satellite, the magnetic suspension bearing with lower rigidity (compared with a mechanical bearing) is applied to a remote sensing satellite system as a load connection joint at the present stage so as to realize flexible connection, and the method has wide application prospect.
The magnetic suspension bearing is a non-contact bearing for realizing rotor floating by utilizing electromagnetic force, has the characteristics of high rotating speed, low power consumption, no abrasion, no need of lubrication, active adjustable rigidity damping and the like, and the rigidity of the bearing has great influence on a satellite system. On the premise that the damping of the magnetic suspension bearing is constant, the angular velocity of the satellite platform and the angular velocity vibration of the spinning load relative to the satellite platform are obvious due to high bearing rigidity, the angular velocity vibration of the load relative to an inertial system is large after the accumulated transmission of all error links, the stability of the three-axis attitude is poor, and the working capacity of the spinning load is influenced; and the lower bearing rigidity enables the attitude angular speed control result of the load relative to the inertia system to be smooth and stable, the attitude stability of the load is improved, and the stable control of the rotating load can be realized.
Although the magnetic suspension bearing has advantages in many aspects, the prior art still cannot realize the precise modeling of the rigidity of the magnetic suspension bearing floating in the stator space and the active regulation and control of the low rigidity of the magnetic suspension bearing, so that the application of the magnetic suspension bearing is limited to a certain extent. Therefore, in order to meet the working requirement of the rotary load, the magnetic suspension bearing rigidity model and the active rigidity regulation and control technology are researched, the stable control of the load is favorably realized, an ultrastable and hyperstatic working environment can be provided for the rotary load, and the method has high academic value and engineering significance.
Disclosure of Invention
The invention aims to solve the problems that the existing method can not realize the precise modeling of the rigidity of the magnetic suspension bearing floating in the stator space and the active regulation and control of the low rigidity of the magnetic suspension bearing.
The technical scheme adopted by the invention for solving the technical problems is as follows: a rotating load stable control method based on magnetic suspension bearing active stiffness regulation comprises the following steps:
step one, determining the composition and the working mode of a rotating load satellite system, and defining an earth center equatorial coordinate system oxyz and an orbit coordinate system ooxoyozoCenter of mass coordinate system o of rotating load satellite systemsxsyszsSatellite platform body coordinate system obxbybzbAnd a rotational load body coordinate system opxpypzp；
Solving the magnetic gap change of the magnetic poles of the left radial bearing and the right radial bearing according to the space relative attitude information of the satellite platform and the rotating load and the central displacement information of the magnetic suspension bearing;
solving the magnetic gap change of the magnetic pole of the axial bearing according to the space relative attitude information of the satellite platform and the rotating load and the central displacement information of the magnetic suspension bearing;
step four, setting the magnetic bearing magnetic gap control principle as PD control, and calculating the electromagnetic force of each magnetic pole pair of the left radial bearing and the right radial bearing and the electromagnetic force of the magnetic pole pair of the axial bearing according to the magnetic gap change of the magnetic poles of the left radial bearing and the right radial bearing solved in the step two and the magnetic gap change of the magnetic poles of the axial bearing solved in the step three by combining a Maxwell electromagnetic force equation;
according to the electromagnetic force of each magnetic pole pair of the left radial bearing and the right radial bearing and the electromagnetic force of the magnetic pole pair of the axial bearing, the electromagnetic resultant force vector F of the electromagnetic acting force of each magnetic pole pair equivalent to the center of the magnetic suspension bearing is obtainedmProjecting F under the system of satellite platformmbAnd the electromagnetic acting force of each magnetic pole pair is equivalent to the electromagnetic resultant torque vector T on the center of the magnetic suspension bearingmProjecting T under satellite platform systemmb；
Step fiveAnd the resultant electromagnetic force vector F obtained according to the step fourmProjecting F under the system of satellite platformmbAnd electromagnetic resultant torque vector TmProjecting T under satellite platform systemmbSolving and sorting to obtain a displacement stiffness model and an angular stiffness model of the magnetic suspension bearing;
and step six, simplifying the displacement stiffness model and the angular stiffness model of the magnetic suspension bearing obtained in the step five, designing the proportional control parameters of the radial bearing and the proportional control parameters of the axial bearing by using the simplified models, and actively regulating and controlling the stiffness of the magnetic suspension bearing through the designed proportional control parameters of the radial bearing and the axial bearing to realize the stable control of the rotating load.
The invention has the beneficial effects that: according to the method for stably controlling the rotating load based on the active rigidity regulation of the magnetic suspension bearing, an algorithm capable of solving the magnetic gap change of each magnetic pole according to the bearing center displacement change and the space relative attitude information of the satellite platform and the rotating load is designed according to the working mode and the structural characteristics of a rotating load satellite system, an electromagnetic action model equivalent to the center of the magnetic suspension bearing is further built according to an electromagnetic theory, a magnetic suspension bearing rigidity model is obtained through solving, and then the controller parameters are designed according to the rigidity model to perform low rigidity active regulation and control, so that the stable control of the rotating load is realized.
Drawings
FIG. 1 is a flow chart of a rotating load smooth control method based on active stiffness regulation of a magnetic suspension bearing according to the invention;
FIG. 2 is a schematic diagram of the structural makeup and mode of operation of the rotary payload satellite system of the present invention;
FIG. 3 is a schematic illustration of the coordinate system definition of the present invention;
FIG. 4 is a schematic structural diagram of a magnetic suspension bearing of the present invention;
in the figure, AC and BD are the pole pair of the left radial bearing, EG and FH are the pole pair of the right radial bearing, and MN is the pole pair of the axial bearing;
FIG. 5 is a schematic illustration of a left and right radial bearing magnetic gap solution;
FIG. 6 is a schematic illustration of axial bearing magnetic gap resolution.
Detailed Description
The first embodiment is as follows: this embodiment will be described with reference to fig. 1. The method for controlling the rotating load to be stable based on the active stiffness regulation of the magnetic suspension bearing comprises the following steps:
step one, determining the composition and the working mode of a rotating load satellite system, and defining an earth center equatorial coordinate system oxyz and an orbit coordinate system ooxoyozoCenter of mass coordinate system o of rotating load satellite systemsxsyszsSatellite platform body coordinate system obxbybzbAnd a rotational load body coordinate system opxpypzp；
Solving the magnetic gap change of the magnetic poles of the left radial bearing and the right radial bearing according to the space relative attitude information of the satellite platform and the rotating load and the displacement information of the center of the magnetic suspension bearing (namely the central position of the thrust disc or the middle position of the left radial bearing and the right radial bearing);
solving the magnetic gap change of the magnetic pole of the axial bearing according to the space relative attitude information of the satellite platform and the rotating load and the central displacement information of the magnetic suspension bearing;
step four, setting the magnetic bearing magnetic gap control principle as PD control, and calculating the electromagnetic force of each magnetic pole pair of the left radial bearing and the right radial bearing and the electromagnetic force of the magnetic pole pair of the axial bearing according to the magnetic gap change of the magnetic poles of the left radial bearing and the right radial bearing solved in the step two and the magnetic gap change of the magnetic poles of the axial bearing solved in the step three by combining a Maxwell electromagnetic force equation;
according to the electromagnetic force of each magnetic pole pair of the left radial bearing and the right radial bearing and the electromagnetic force of the magnetic pole pair of the axial bearing, the electromagnetic acting force equivalent to the electromagnetic resultant force vector F on the center of the magnetic suspension bearing of each magnetic pole pair of the magnetic suspension bearing (comprising each magnetic pole pair of the left radial bearing and the right radial bearing and the magnetic pole pair of the axial bearing) is obtainedmProjecting F under the system of satellite platformmbAnd the electromagnetism of each magnetic pole pair of the magnetic suspension bearingElectromagnetic resultant torque vector T with acting force equivalent to center of magnetic suspension bearingmProjecting T under satellite platform systemmbObtaining the electromagnetic effect expression of the magnetic suspension bearing;
step five, obtaining an electromagnetic resultant force vector F according to the step fourmProjecting F under the system of satellite platformmbAnd electromagnetic resultant torque vector TmProjecting T under satellite platform systemmbSolving and sorting to obtain a displacement stiffness model and an angular stiffness model of the magnetic suspension bearing; the influence of the structural parameters, the electromagnetic parameters and the parameters of the bearing controller on the rigidity of the magnetic suspension bearing is embodied in a model;
and step six, simplifying the displacement stiffness model and the angular stiffness model of the magnetic suspension bearing obtained in the step five, designing the proportional control parameters of the radial bearing and the proportional control parameters of the axial bearing by using the simplified models, and actively regulating and controlling the stiffness of the magnetic suspension bearing through the designed proportional control parameters of the radial bearing and the axial bearing to realize the stable control of the rotating load.
The method combines the working mode and the structural characteristics of a rotary load satellite system, and starts from the motion characteristic of a stator, on the basis of considering the magnetic gap coupling between the radial displacement and the axial displacement of a rotating shaft and the moment coupling between the radial bearing and the axial bearing in the magnetic suspension bearing, a magnetic gap resolving model and a bearing electromagnetic action model are established, and then a magnetic suspension bearing rigidity model is established, so that the influence of the structural parameters, the electromagnetic parameters and the bearing controller parameters of the bearing on the rigidity of the bearing can be embodied in the model, a theoretical basis is provided for the active rigidity regulation and control design, and the low rigidity regulation and control of the bearing and the stable control of the load are realized.
The second embodiment is as follows: the first difference between the present embodiment and the specific embodiment is: the specific process of the step one is as follows:
as shown in fig. 2, the structure of the satellite system for determining the rotating load comprises a satellite platform subsystem, a load subsystem and a rotating joint; the satellite platform subsystem in turn comprises: the system comprises a satellite platform, a platform three-axis orthogonal flywheel and platform bilateral solar sailboards; the load subsystem in turn comprises: a rotating load and a load inner flywheel; the rotary joint is a magnetic suspension bearing (and is provided with a mechanical bearing and a driving motor), the magnetic suspension bearing consists of a left radial bearing, a right radial bearing, an axial bearing and a rotating shaft, a stator part of the magnetic suspension bearing is fixedly connected with the satellite platform subsystem, and a rotor part (the rotating shaft) of the magnetic suspension bearing is fixedly connected with the load subsystem;
operating mode of the rotating load satellite system: the satellite platform keeps the earth orientation through a three-axis orthogonal flywheel of the platform, and the solar sailboard single-axis drive at the two sides of the platform keeps the sun orientation so as to provide energy required by the satellite; the rotary joint is provided with a magnetic suspension bearing for connection, and a mechanical bearing is reserved as an emergency protection scheme; the rotating load is controlled by a flywheel in the load to keep rotating at a constant speed, and when the angular momentum of the flywheel in the load is saturated, a magnetic torquer and a driving motor are required to provide an unloading scheme;
the coordinate system is defined as follows: as shown in fig. 3;
establishing an earth center equatorial coordinate system (inertial coordinate system) oxyz by taking the earth center as a coordinate origin o, wherein the x axis of the earth center equatorial coordinate system points to a vernalization point at the moment J2000 from the earth center in a J2000 earth plane equatorial plane, the z axis is a normal line of the J2000 earth plane equatorial plane and points to the north pole direction, and the y axis, the x axis and the z axis form a right-hand system;
using the center of mass of the rotating load satellite system as the origin of coordinates ooEstablishing a track coordinate system ooxoyozoX of said orbital coordinate systemoThe axis being in the orbital plane and pointing in the direction of advance, z, of the satellite system carrying the rotary loadsoThe axis points from the center of mass of the satellite system to the center of the earth, yoAxis is same as xoAxis and zoThe shaft constitutes a right-hand system;
using the center of mass of the rotating load satellite system as the origin of coordinates osEstablishing a centroid coordinate system o of the rotating load satellite systemsxsyszs(attached to the body) z of the rotating payload satellite system centroid coordinate systemsThe axis points to the satellite platform axial direction, xsAxis and ysThe axis being located within the axial section, x, of the satellite platformsAxis, ysAxis and zsThe shaft constitutes a right-hand system; in no postureUnder the control error, the three axes of the mass center coordinate system of the rotating load satellite system point to the co-orbital coordinate system ooxoyozoThe three axes of (A) are parallel;
using the center of mass of the satellite platform as the origin of coordinates obEstablishing a body coordinate system o of the satellite platformbxbybzb(connected with the body) and the three-axis direction co-rotating load satellite system mass center coordinate system o of the satellite platform body coordinate systemsxsyszs；
Using the center of mass of the rotating load as the origin of coordinates opEstablishing a body coordinate system o of the rotary loadpxpypzp(connected with the body), z of the body coordinate system of the rotating loadpWith axis directed in the direction of the rotary load axial, xpAxis and ypThe axis lying in the axial section of the rotary load, xpAxis, ypAxis and zpThe shaft constitutes a right-hand system; when the connection error of the rotary joint is zero and the self-rotation angle of the rotary load is zero, the coordinate system o of the rotary load bodypxpypzpThree-axis pointing same-rotation load satellite system centroid coordinate system osxsyszs。
The third concrete implementation mode: this embodiment will be described with reference to fig. 4. The second embodiment is different from the first embodiment in that: the specific process of the second step is as follows:
definition vector r5A vector r representing the position of the desired center of the magnetic bearing pointing to the current center of the magnetic bearing6A position vector representing the point at which the current center of the magnetic suspension bearing points to the action point of the left radial bearing, a vector r7A position vector representing the desired center of the magnetic bearing pointing to the action point of the left radial bearing, vector r8A position vector representing the point at which the current center of the magnetic bearing points to the right radial bearing, vector r9Representing a position vector of the expected center of the magnetic suspension bearing pointing to the action point of the right radial bearing;
in conjunction with the geometric relationship shown in FIG. 5, the following equation holds:
wherein: r is5bIs a vector r5The lower component of the system in the satellite platform is denoted as r5b＝[δx δy δz]T，δxIs r5System x in satellite platformbComponent under the shaft, δyIs r5Y of system in satellite platformbComponent under the shaft, δzIs rzZ of system in satellite platformbA down-axis component; the upper corner mark T is the transposition operation of the matrix; r is7bIs a vector r7The lower component of the system in the satellite platform is denoted as r7b＝[Δxl Δyl -L]TL is half the span from the left radial bearing to the right radial bearing, Δ xlAnd Δ ylRespectively representing the change of x and y magnetic gaps at the left radial bearing; r is6pIs a vector r6The lower component of the system in the rotational load, denoted as r6p＝[0 0 z6]T，z6Representing an intermediate variable;
representing an attitude transformation matrix of the rotating load body system relative to the satellite platform body system;
describing attitude information of a rotating load relative to a satellite platform by using an xyz sequence, and rotated relative attitude angle
Is recorded as:
satellite platform body coordinate system obxbybzbAround xbAngle of rotation of the shaft
To the intermediate system 1, the intermediate system 1 is turned through an angle theta around its own (intermediate system 1) y-axis to the intermediate system 2, the intermediate system 2 is turned around the rotating load bodyZ of a coordinate systempAxis passing angle psi to rotational load body coordinate system opxpypzp；
Both theta and psi are angular errors;
solving equation (1) to obtain the x and y two-way magnetic gap variation at the left radial bearing:
r8pis a vector r8The lower component of the system in the rotational load, denoted as r8p＝[0 0 z8]T，z8Representing an intermediate variable;
similarly, the following equation holds true in conjunction with the geometric relationship shown in FIG. 5:
r9bis a vector r9The lower component of the system in the satellite platform is denoted as r9b＝[Δxr Δyr L]T(ii) a Wherein: Δ xrAnd Δ yrRespectively representing the change of x and y two-way magnetic gaps at the right radial bearing;
solving equation (3) to obtain the x and y two-way magnetic gap variation at the right radial bearing:
arranging the formulas (2) and (4) into the following matrix form:
wherein:
and
are all intermediate variables.
Therefore, the magnetic gap change at the left radial bearing and the right radial bearing can be obtained according to the space relative attitude information of the satellite platform and the rotating load and the central displacement information of the magnetic suspension bearing.
The fourth concrete implementation mode: the third difference between the present embodiment and the specific embodiment is that: the specific process of the third step is as follows:
as shown in fig. 6, the following vector is defined:
definition vector r10A vector r representing the position of the center of expectation of the magnetic bearing pointing to a certain balance point of the axial bearing11A vector r representing the position of the current center of the magnetic suspension bearing pointing to a certain balance point of the axial bearing12A position vector representing the point at which a balance point of the axial bearing points to the current point of action of the axial bearing, vector r13Representing the position vector of the current action point of the magnetic suspension bearing pointing to the axial bearing at the current center;
the following equation holds in connection with the geometry shown in fig. 6:
wherein: r is10bIs a vector r10In the system lower component of the satellite platform, since the axial bearing is a ring magnetic pole, it is necessary to indicate the magnetic gap change at a certain radius r and a certain angle phi, r10b＝[rcosφ rsinφ 0]TR represents a certain radius corresponding to the axial bearing, and phi represents a certain angle corresponding to the axial bearing; the value range of r is: inner ring [ R ]1,R2]Outer ring [ R ]4,R5](ii) a Phi is in the range of [0,2 pi ]]；r12bIs a vector r12The system lower component, r, in the satellite platform12b＝[0 0 Δzrφ]T，ΔzrφIndicating the magnetic gap variation of the axial bearing at radius r and angle phiMelting; r is13pIs a vector r13The lower component of the system in the rotational load, r13p＝[x13 y13 0]TWherein: x is the number of13And y13Are all intermediate variables; solving equation (6) yields:
wherein: beta is [ 001 ]]TAnd I is a three-dimensional identity matrix,
is an intermediate variable; r is13bIs a vector r13In the satellite platform, the system has
If true;
therefore, the magnetic gap change at a certain angle and a certain radius of the axial bearing can be obtained according to the platform load relative attitude information and the magnetic suspension bearing center displacement change information.
The fifth concrete implementation mode: the fourth difference between this embodiment and the specific embodiment is that: the specific process of the step four is as follows:
setting the magnetic gap control principle of the magnetic suspension bearing as PD control, wherein the control mode of the magnetic pole adopts differential control; assuming that the number of coil turns, the cross-sectional area of a magnetic circuit and the reference point of each magnetic pole pair of the left radial bearing and the right radial bearing are the same (namely the initial magnetic gap and the initial current of the left radial bearing and the right radial bearing are the same), on the basis of the assumed condition, the current stiffness and the displacement stiffness of each channel of the left radial bearing and the right radial bearing are the same, and k is usedirAnd klrThe current stiffness and the displacement stiffness of the radial bearings (including the left and right radial bearings) are shown as follows:
wherein: mu.s0Is air permeability, NrIs the number of turns of the radial bearing coil, ir0Is the radial bearing coil initial current, ArIs the cross-sectional area of the magnetic path of the radial bearing, x0The initial magnetic gap of each magnetic pole pair of the radial bearing is obtained;
then, by combining the maxwell electromagnetic force equation, the electromagnetic forces of the magnetic pole pairs of the left radial bearing and the right radial bearing are respectively obtained as follows:
wherein: fACIs the electromagnetic resultant force of the left radial bearing AC magnetic pole pair (i.e. x direction)BDIs the electromagnetic resultant force, F, of the pole pair (i.e. y direction) of the left radial bearing BDEGIs the electromagnetic resultant force F of EG magnetic pole pair (namely x direction) of the right radial bearingFHIs the electromagnetic resultant force of the right radial bearing FH pole pair (i.e., y direction); Δ ilx、Δily、ΔirxAnd Δ iryPole pair AC, BD, EG and FH current changes, respectively;
assuming that the magnetic gap change of the inner ring magnetic pole of the axial bearing does not change along with the change of the radius length, R is taken1And R2Average value R of3Calculating the magnetic gap change; assuming that the change of the magnetic gap of the outer ring magnetic pole of the axial bearing does not change along with the change of the radius length, R is taken4And R5Average value R of6Calculating the magnetic gap change;
assuming equal pole areas of the inner and outer rings of the axial bearing, R3la＝R6lbIs established, R3Represents R1And R2Average value of (1), R6Represents R4And R5Average value of (d); on the basis of the assumption that the conditions are satisfied, magnetic pole attraction force of the axial bearing at a certain radius and a certain angle is calculated according to a Maxwell electromagnetic force equation, length integration is carried out on the radius, and the electromagnetic resultant force F of the magnetic pole pair of the axial bearing MN at the angle phi to the thrust disc is obtained by combining a differential control modezφComprises the following steps:
wherein: laIs the radial thickness of the inner ring magnetic pole, /)bIs the radial thickness of the outer ring magnetic pole, NzIs the number of turns of the axial bearing coil, iz0Is the axial bearing coil initial current, z0Is the initial magnetic gap of the axial bearing magnetic pole, Δ zaφIs the radius R3Magnetic gap variation at angle phi, Δ zbφIs the radius R6The magnetic gap at the angle phi changes;
carrying out angle integral to obtain the electromagnetic force F of the axial bearing magnetic pole pair MNMNAnd electromagnetic torque TzbComprises the following steps:
wherein k isizAnd kzz' Current stiffness and Displacement stiffness, respectively, of an axial bearing, [ Delta ] izIs the change of the magnetic pole to MN current; a. theaIs the axial bearing pole area;
represents a pair of r13bTaking coordinate square matrix operation, r13bIs a vector r13Projecting under the system of the satellite platform,
β＝[001]Ti is a three-dimensional identity matrix;
due to r10bInfluenced by radius r, resulting in r13bIs also influenced by r, in combination with the previous assumptions, for r13bThe value is limited to R ═ R3And R ═ R6Two groups;
after obtaining the electromagnetic acting force expressions of the magnetic pole pairs of the left radial bearing, the right radial bearing and the axial bearing, the control principle of the magnetic gap is specified to be proportional differential control, the expected control target is that the magnetic gap of each magnetic pole changes to zero and the magnetic gap change rate is zero, and the control current i is obtained as follows:
wherein: k is a radical ofp1And kd1Proportional control parameters and differential control parameters of four magnetic pole pairs of radial bearings (a left radial bearing and a right radial bearing) (namely the proportional control parameters of the four magnetic pole pairs are the same, and the differential control parameters of the four magnetic pole pairs are the same), and kp2And kd2Respectively proportional control parameters and differential control parameters of the axial bearing magnetic pole pairs,
is to calculate the time derivative, K, of the h matrixpAnd KdAre all intermediate variables; the electromagnetic forces f of the magnetic pole pairs AC, BD, EG, FH, and MN are obtained by combining equations (9), (11), and (12) as follows:
obtaining an electromagnetic resultant force vector F of the equivalent of the electromagnetic acting force F of each magnetic pole pair (AC, BD, EG, FH and MN) to the center of the magnetic suspension bearing according to a formula (13)mProjecting F under the system of satellite platformmbComprises the following steps:
the additional torque generated by the translation of the electromagnetic acting force of the left radial bearing and the right radial bearing to the center of the magnetic suspension bearing and the radial interference torque T of the axial bearing are combinedzbObtaining the electromagnetic resultant moment vector T equivalent to the center of the magnetic suspension bearing of the electromagnetic acting force f of each magnetic pole pairmProjecting T under satellite platform systemmbComprises the following steps:
wherein: t iszbIs the radial disturbance moment of the axial bearing.
Thus, an expression of the projection of the electromagnetic resultant force and resultant moment equivalent to the center of the magnetic suspension bearing by each magnetic pole pair of the magnetic suspension bearing under the satellite platform system is obtained.
The sixth specific implementation mode: the fifth embodiment is different from the fifth embodiment in that: the concrete process of the step five is as follows:
displacement-dependent component f in the electromagnetic force f of the pole pairs of a magnetic bearingkComprises the following steps:
resultant electromagnetic force vector FmProjecting F under the system of satellite platformmbOf (2) a displacement dependent component FmbkComprises the following steps: fmbk＝CvfkElectromagnetic resultant moment vector TmProjecting T under satellite platform systemmbMiddle cause fkElectromagnetic torque T generated by translationmbkComprises the following steps:
wherein: t iszbkIs TzbOf a displacement-related quantity, TzbkAs shown in the following formula:
wherein: fzφkIs FzφA displacement-related quantity;
according to TmbkThe expression of (2) indicates that f iskThe electromagnetic torque generated by translation consists of two parts: radial bearing moment TrakAnd axial bearing disturbance torque Tzbk；
Defining the rigidity of the magnetic suspension bearing as follows: fmbkChange r of central displacement of magnetic suspension bearing5b＝[δx δy δz]TThe ratio of (A) to (B) is the displacement stiffness, TmbkAngle of relative attitude
The ratio of (a) to (b) is angular stiffness;
Fmbksystem x in satellite platformbAxial component FkxComprises the following steps:
according to the formulas (2) and (4) at the same time, the method obtains
Thus, xbAxial displacement stiffness kxComprises the following steps:
in the same way, ybAxial displacement stiffness kyComprises the following steps:
solving for FmbkIn the satellite platform body system zbThe direction component, and then deltazMaking a ratio to obtain zbAxial displacement stiffness kzComprises the following steps:
synthesizing formulas (19) to (21) to obtain a displacement stiffness model of the magnetic suspension bearing;
the angular stiffness of the magnetic suspension bearing is provided by the angular stiffness of the left radial bearing, the angular stiffness of the right radial bearing and the angular stiffness of the axial bearing together; wherein the angular stiffness of the left and right journal bearings is determined by journal bearing torque TrakProviding that the angular stiffness of the axial bearing is disturbed by the axial bearing disturbance torque TzbkProviding;
arrangement solving TrakSystem x in satellite platformbAxial moment component TrakxComprises the following steps:
x is thenbAxial angular stiffness kraxComprises the following steps:
in the same way, ybAxial angular stiffness krayComprises the following steps:
according to TzbkExpression to obtain the electromagnetic interference torque T of the axial bearingzbkGenerated xbAxial angular stiffness kzaxAnd ybAxial angular stiffness kzayRespectively as follows:
the magnetic suspension bearing angular stiffness model obtained by integrating the formulas (23) to (25) is as follows:
according to the obtained displacement rigidity model and the angular rigidity model, the rigidity of the magnetic suspension bearing is determined by the electromagnetic parameters of the bearing: the current rigidity and the displacement rigidity are influenced by the parameters of the controller, the bearing structure parameter L and the relative motion relation between the load and the platform, and the strong nonlinearity and the time-varying property are presented.
The seventh embodiment: the sixth embodiment is different from the sixth embodiment in that: the concrete process of the sixth step is as follows:
because the bearing parameters are often fixed, the rigidity active regulation and control are mainly realized by regulating the controller parameters, however, the rigidity model obtained in the fifth step is complex and is not beneficial to being directly used in engineering, the motion characteristics of a satellite platform (stator) are considered,
simplifying the displacement rigidity model and the angular rigidity model of the magnetic bearing in the step five into the following forms:
designing a radial bearing proportional control parameter k according to the formula (27)p1To regulate and control the displacement rigidity k of the magnetic suspension bearingx、kyAnd angular stiffness kax、kayDesigning the axial bearing proportional control parameter kp2To regulate and control the displacement rigidity k of the magnetic suspension bearingz；
The rigidity of the magnetic suspension bearing is actively regulated and controlled through design parameters, and the stable control of the rotating load is realized.
The invention applies the magnetic suspension bearing to a rotary load satellite system to connect a rotary load and a satellite platform, and the lower rigidity of the magnetic suspension bearing ensures that the control result of the attitude angular velocity of the load relative to an inertial system is smooth and stable, so that the bearing angular rigidity k is used for improving the attitude stability of the loadaxAnd kayThe design result needs to be a little smaller. E.g. at 146mm, kxr＝8.2355e5N/m,kzz′＝8.5373e5N/m,kir＝5.1471e2N/A，kizWhen the angle rigidity is 2.6823e3N/A, the angle rigidity needs to be regulated to kax＝kay2450Nm/rad, the controller parameter design result is k according to equation (27)p1＝3000。
The above-described calculation examples of the present invention are merely to explain the calculation model and the calculation flow of the present invention in detail, and are not intended to limit the embodiments of the present invention. It will be apparent to those skilled in the art that other variations and modifications of the present invention can be made based on the above description, and it is not intended to be exhaustive or to limit the invention to the precise form disclosed, and all such modifications and variations are possible and contemplated as falling within the scope of the invention.
Claims (2)
1. A rotating load stable control method based on magnetic suspension bearing active stiffness regulation is characterized by comprising the following steps:
step one, determining the composition and the working mode of a rotating load satellite system, and defining an earth center equatorial coordinate system oxyz and an orbit coordinate system ooxoyozoCenter of mass coordinate system o of rotating load satellite systemsxsyszsSatellite platform body coordinate system obxbybzbAnd a rotational load body coordinate system opxpypzp；
The specific process of the step one is as follows:
the structure of the rotary load satellite system comprises a satellite platform subsystem, a load subsystem and a rotary joint; the satellite platform subsystem in turn comprises: the system comprises a satellite platform, a platform three-axis orthogonal flywheel and platform bilateral solar sailboards; the load subsystem in turn comprises: a rotating load and a load inner flywheel; the rotary joint is a magnetic suspension bearing, the magnetic suspension bearing consists of a left radial bearing, a right radial bearing, an axial bearing and a rotating shaft, a stator part of the magnetic suspension bearing is fixedly connected with the satellite platform subsystem, and a rotor part of the magnetic suspension bearing is fixedly connected with the load subsystem;
operating mode of the rotating load satellite system: the satellite platform keeps the earth orientation through a three-axis orthogonal flywheel of the platform, solar sailboards on two sides of the platform are driven by single shafts to keep the sun orientation, a rotary joint is provided with a magnetic suspension bearing for connection, a rotary load is controlled by a flywheel in the load to keep constant-speed rotation, and a magnetic torquer and a driving motor are required to provide an unloading scheme when the angular momentum of the flywheel in the load is saturated;
the coordinate system is defined as follows:
establishing an earth center equatorial coordinate system oxyz by taking the earth center as a coordinate origin o, wherein the x axis of the earth center equatorial coordinate system points to a vernalization point at the moment J2000 from the earth center in a J2000 earth plane equatorial plane, the z axis is a normal line of the J2000 earth plane equatorial plane and points to the north pole direction, and the y axis, the x axis and the z axis form a right-handed system;
using the center of mass of the rotating load satellite system as the origin of coordinates ooEstablishing a track coordinate system ooxoyozoX of said orbital coordinate systemoThe axis being in the orbital plane and pointing in the direction of advance, z, of the satellite system carrying the rotary loadsoThe axis points from the center of mass of the satellite system to the center of the earth, yoAxis is same as xoAxis and zoThe shaft constitutes a right-hand system;
using the center of mass of the rotating load satellite system as the origin of coordinates osEstablishing a centroid coordinate system o of the rotating load satellite systemsxsyszsZ of the rotating load satellite system centroid coordinate systemsThe axis points to the satellite platform axial direction, xsAxis and ysThe axis being located within the axial section, x, of the satellite platformsAxis, ysAxis and zsThe shaft constitutes a right-hand system;
using the center of mass of the satellite platform as the origin of coordinates obEstablishing a body coordinate system o of the satellite platformbxbybzbThree-axis pointing same-rotation load satellite system centroid coordinate system o of satellite platform body coordinate systemsxsyszs；
Using the center of mass of the rotating load as the origin of coordinates opEstablishing a body coordinate system o of the rotary loadpxpypzpZ of the rotational load body coordinate systempWith axis directed in the direction of the rotary load axial, xpAxis and ypThe axis lying in the axial section of the rotary load, xpAxis, ypAxis and zpThe shaft constitutes a right-hand system; when the connection error of the rotary joint is zero and the self-rotation angle of the rotary load is zero, the coordinate system o of the rotary load bodypxpypzpThree-axis pointing same-rotation load satellite system centroid coordinate system osxsyszs；
Solving the magnetic gap change of the magnetic poles of the left radial bearing and the right radial bearing according to the space relative attitude information of the satellite platform and the rotating load and the central displacement information of the magnetic suspension bearing;
the specific process of the second step is as follows:
definition vector r5A vector r representing the position of the desired center of the magnetic bearing pointing to the current center of the magnetic bearing6A position vector representing the point at which the current center of the magnetic suspension bearing points to the action point of the left radial bearing, a vector r7A position vector representing the desired center of the magnetic bearing pointing to the action point of the left radial bearing, vector r8A position vector representing the point at which the current center of the magnetic bearing points to the right radial bearing, vector r9Representing a position vector of the expected center of the magnetic suspension bearing pointing to the action point of the right radial bearing;
wherein: r is5bIs a vector r5The lower component of the system in the satellite platform is denoted as r5b＝[δx δy δz]T，δxIs r5System x in satellite platformbComponent under the shaft, δyIs r5Y of system in satellite platformbComponent under the shaft, δzIs rzZ of system in satellite platformbA down-axis component; the upper corner mark T is the transposition operation of the matrix; r is7bIs a vector r7The lower component of the system in the satellite platform is denoted as r7b＝[Δxl Δyl -L]TL is half the span from the left radial bearing to the right radial bearing, Δ xlAnd Δ ylRespectively representing the change of x and y magnetic gaps at the left radial bearing; r is6pIs a vector r6The lower component of the system in the rotational load, denoted as r6p＝[0 0 z6]T，z6Representing an intermediate variable;
representing an attitude transformation matrix of the rotating load body system relative to the satellite platform body system;
describing attitude information of the rotating load relative to the satellite platform by using an xyz sequence, and recording a rotated relative attitude angle theta as:
satellite platform body coordinate system obxbybzbAround xbAngle of rotation of the shaft
To the intermediate system 1, the intermediate system 1 rotates around its own y-axis by an angle theta to the intermediate system 2, and the intermediate system 2 rotates around z of the rotating load body coordinate systempAxis passing angle psi to rotational load body coordinate system opxpypzp；
Solving equation (1) to obtain the x and y two-way magnetic gap variation at the left radial bearing:
r8pis a vector r8The lower component of the system in the rotational load, denoted as r8p＝[0 0 z8]T，z8Representing an intermediate variable;
r9bis a vector r9The lower component of the system in the satellite platform is denoted as r9b＝[Δxr Δyr L]T(ii) a Wherein: Δ xrAnd Δ yrRespectively representing the change of x and y two-way magnetic gaps at the right radial bearing;
solving equation (3) to obtain the x and y two-way magnetic gap variation at the right radial bearing:
arranging the formulas (2) and (4) into the following matrix form:
solving the magnetic gap change of the magnetic pole of the axial bearing according to the space relative attitude information of the satellite platform and the rotating load and the central displacement information of the magnetic suspension bearing;
the specific process of the third step is as follows:
definition vector r10A vector r representing the position of the center of expectation of the magnetic bearing pointing to a certain balance point of the axial bearing11A vector r representing the position of the current center of the magnetic suspension bearing pointing to a certain balance point of the axial bearing12A position vector representing the point at which a balance point of the axial bearing points to the current point of action of the axial bearing, vector r13Representing the position vector of the current action point of the magnetic suspension bearing pointing to the axial bearing at the current center;
wherein: r is10bIs a vector r10The system lower component, r, in the satellite platform10b＝[rcosφ rsinφ 0]TR represents a certain radius corresponding to the axial bearing, and phi represents a certain angle corresponding to the axial bearing; the value range of r is: inner ring [ R ]1,R2]Outer ring [ R ]4,R5](ii) a Phi is in the range of [0,2 pi ]]；r12bIs a vector r12The system lower component, r, in the satellite platform12b＝[0 0 Δzrφ]T，ΔzrφThe magnetic gap change of the magnetic poles of the axial bearing at the radius r and the angle phi is shown; r is13pIs a vector r13The lower component of the system in the rotational load, r13p＝[x13 y13 0]TWherein: x is the number of13And y13Are all intermediate variables; solving equation (6) yields:
wherein: beta is [ 001 ]]TI is a three-dimensional identity matrix, and zeta (theta) is an intermediate variable; r is13bIs a vector r13In the satellite platform, the system has
If true;
step four, setting the magnetic bearing magnetic gap control principle as PD control, and calculating the electromagnetic force of each magnetic pole pair of the left radial bearing and the right radial bearing and the electromagnetic force of the magnetic pole pair of the axial bearing according to the magnetic gap change of the magnetic poles of the left radial bearing and the right radial bearing solved in the step two and the magnetic gap change of the magnetic poles of the axial bearing solved in the step three by combining a Maxwell electromagnetic force equation;
according to the electromagnetic force of each magnetic pole pair of the left radial bearing and the right radial bearing and the electromagnetic force of the magnetic pole pair of the axial bearing, the electromagnetic resultant force vector F of the electromagnetic acting force of each magnetic pole pair equivalent to the center of the magnetic suspension bearing is obtainedmProjecting F under the system of satellite platformmbAnd the electromagnetic acting force of each magnetic pole pair is equivalent to the electromagnetic resultant torque vector T on the center of the magnetic suspension bearingmProjecting T under satellite platform systemmb；
The specific process of the step four is as follows:
setting the magnetic gap control principle of the magnetic suspension bearing as PD control, wherein the control mode of the magnetic pole adopts differential control; assuming that the number of coil turns, the cross-sectional area of a magnetic circuit and a reference point of each magnetic pole pair of the left radial bearing and the right radial bearing are the same, on the basis of the establishment of an assumed condition, the current rigidity and the displacement rigidity of each channel of the left radial bearing and the right radial bearing are the same, and k is usedirAnd klrThe current stiffness and displacement stiffness of the radial bearing are expressed as follows:
wherein: mu.s0Is air permeability, NrIs the number of turns of the radial bearing coil, ir0Is the radial bearing coil initial current, ArIs the cross-sectional area of the magnetic path of the radial bearing, x0The initial magnetic gap of each magnetic pole pair of the radial bearing is obtained;
the electromagnetic force of each magnetic pole pair of the left radial bearing and the right radial bearing is obtained as follows:
wherein: fACIs the electromagnetic resultant force of the AC magnetic pole pair of the left radial bearing FBDIs the electromagnetic resultant force, F, of the left radial bearing BD magnetic pole pairEGIs the electromagnetic resultant force of EG magnetic pole pair of the right radial bearingFHIs the electromagnetic resultant force of the right radial bearing FH magnetic pole pair; Δ ilx、Δily、ΔirxAnd Δ iryPole pair AC, BD, EG and FH current changes, respectively;
assuming equal pole areas of the inner and outer rings of the axial bearing, R3la＝R6lbIs established, R3Represents R1And R2Average value of (1), R6Represents R4And R5Average value of (d); on the basis of the assumption that the conditions are satisfied, the magnetic pole attraction force of the axial bearing at a certain radius and a certain angle is calculated, length integration is carried out on the radius, and the electromagnetic resultant force F of the magnetic pole pair of the axial bearing MN to the thrust disc at the angle phi is obtained by combining a differential control modezφComprises the following steps:
wherein: laIs the radial thickness of the inner ring magnetic pole, /)bIs the radial thickness of the outer ring magnetic pole, NzIs the number of turns of the axial bearing coil, iz0Is the axial bearing coil initial current, z0Is the initial magnetic gap of the axial bearing magnetic pole, Δ zaφIs the radius R3Magnetic gap variation at angle phi, Δ zbφIs the radius R6The magnetic gap at the angle phi changes;
carrying out angle integral to obtain the electromagnetic force F of the axial bearing magnetic pole pair MNMNAnd electromagnetic torque TzbComprises the following steps:
wherein k isizAnd kzz' Current stiffness and Displacement stiffness, respectively, of an axial bearing, [ Delta ] izIs the change of the magnetic pole to MN current; a. theaIs the axial bearing pole area;
represents a pair of r13bTaking coordinate square matrix operation, r13bIs a vector r13Projection under the system of satellite platform, r13b＝[I+βζ(θ)](r10b-r5b)，β＝[0 0 1]TI is a three-dimensional identity matrix;
the control principle of the specified magnetic gap is proportional differential control, the expected control target is that the magnetic gap of each magnetic pole is changed to be zero, the magnetic gap change rate is zero, and the control current i is obtained as follows:
wherein: k is a radical ofp1And kd1Proportional and differential control parameters, k, of four magnetic pole pairs of a radial bearing, respectivelyp2And kd2Respectively proportional control parameters and differential control parameters of the axial bearing magnetic pole pairs,
is to derive the time derivative from the h matrixThe electromagnetic forces f of the magnetic pole pairs AC, BD, EG, FH, and MN obtained by combining equations (9), (11), and (12) are as follows:
obtaining the electromagnetic acting force F of each magnetic pole pair equivalent to the electromagnetic resultant force vector F on the center of the magnetic suspension bearing according to the formula (13)mProjecting F under the system of satellite platformmbComprises the following steps:
the electromagnetic acting force f of each magnetic pole pair is equivalent to the electromagnetic resultant moment vector T of the center of the magnetic suspension bearingmProjecting T under satellite platform systemmbComprises the following steps:
wherein: t iszbRadial disturbance moment of the axial bearing;
step five, obtaining an electromagnetic resultant force vector F according to the step fourmProjecting F under the system of satellite platformmbAnd electromagnetic resultant torque vector TmProjecting T under satellite platform systemmbSolving and sorting to obtain a displacement stiffness model and an angular stiffness model of the magnetic suspension bearing;
the concrete process of the step five is as follows:
displacement-dependent component f in electromagnetic force f of each magnetic pole pairkComprises the following steps:
resultant electromagnetic force vector FmProjecting F under the system of satellite platformmbOf (2) a displacement dependent component FmbkComprises the following steps: fmbk＝CvfkElectromagnetic resultant moment vector TmProjecting T under satellite platform systemmbMiddle cause fkElectromagnetic torque T generated by translationmbkComprises the following steps:
wherein: t iszbkIs TzbOf a displacement-related quantity, TzbkAs shown in the following formula:
wherein: fzφkIs FzφA displacement-related quantity;
defining the rigidity of the magnetic suspension bearing as follows: fmbkThe ratio of the change of the central displacement of the magnetic suspension bearing is displacement rigidity TmbkThe ratio to the relative attitude angle is the angular stiffness;
Fmbksystem x in satellite platformbAxial component FkxComprises the following steps:
according to the formulas (2) and (4) at the same time, the method obtains
Thus, xbAxial displacement stiffness kxComprises the following steps:
in the same way, ybAxial displacement stiffness kyComprises the following steps:
to obtain zbAxial displacement stiffness kzComprises the following steps:
synthesizing formulas (19) to (21) to obtain a displacement stiffness model of the magnetic suspension bearing;
the angular stiffness of the magnetic suspension bearing is provided by the angular stiffness of the left radial bearing, the angular stiffness of the right radial bearing and the angular stiffness of the axial bearing together; wherein the angular stiffness of the left and right journal bearings is determined by journal bearing torque TrakProviding that the angular stiffness of the axial bearing is disturbed by the axial bearing disturbance torque TzbkProviding;
arrangement solving TrakSystem x in satellite platformbAxial moment component TrakxComprises the following steps:
x is thenbAxial angular stiffness kraxComprises the following steps:
in the same way, ybAxial angular stiffness krayComprises the following steps:
according to TzbkExpression to obtain the electromagnetic interference torque T of the axial bearingzbkGenerated xbAxial angular stiffness kzaxAnd ybAxial angular stiffness kzayRespectively as follows:
the magnetic suspension bearing angular stiffness model obtained by integrating the formulas (23) to (25) is as follows:
and step six, simplifying the displacement stiffness model and the angular stiffness model of the magnetic suspension bearing obtained in the step five, designing the proportional control parameters of the radial bearing and the proportional control parameters of the axial bearing by using the simplified models, and actively regulating and controlling the stiffness of the magnetic suspension bearing through the designed proportional control parameters of the radial bearing and the axial bearing to realize the stable control of the rotating load.
2. The method for controlling the rotating load to be stable based on the active stiffness regulation of the magnetic suspension bearing according to claim 1, wherein the specific process of the sixth step is as follows:
simplifying the displacement rigidity model and the angular rigidity model of the magnetic bearing in the step five into the following forms:
designing a radial bearing proportional control parameter k according to the formula (27)p1To regulate and control the displacement rigidity k of the magnetic suspension bearingx、kyAnd angular stiffness kax、kayDesigning the axial bearing proportional control parameter kp2To regulate and control the displacement rigidity k of the magnetic suspension bearingz；
The rigidity of the magnetic suspension bearing is actively regulated and controlled through design parameters, and the stable control of the rotating load is realized.
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| CN112758359A (en) * | 2021-01-20 | 2021-05-07 | 北京国电高科科技有限公司 | Area coverage control method for bias momentum satellite |
| CN112987579B (en) * | 2021-05-13 | 2021-07-30 | 中国人民解放军国防科技大学 | Method, system and device for measuring suspension stiffness in electromagnetic suspension control system |
| CN114992241B (en) * | 2022-07-31 | 2022-12-20 | 常州明磁卓控智能科技有限公司 | Magnetic suspension motor instability pre-diagnosis method based on dynamic stiffness real-time detection |
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