CN109388906A - A kind of Flexible spacecraft dynamic model and modeling method based on magnetic suspension bearing - Google Patents
A kind of Flexible spacecraft dynamic model and modeling method based on magnetic suspension bearing Download PDFInfo
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Abstract
The present invention relates to spacecraft dynamics modeling technique fields, specifically a kind of Flexible spacecraft dynamic model and modeling method based on magnetic suspension bearing, it is equipped with satellite body, solar battery windsurfing, attitude control flywheel and useful load, the two sides of satellite body are symmetrically arranged in solar battery windsurfing, solar battery windsurfing is driven through stepper motor, attitude control flywheel is connected on the satellite platform, it is characterized in that the useful load is connected through magnetic suspension bearing with satellite body, steps are as follows for modeling method: Step 1: basic configuration describes；Step 2: basic assumption；Step 3: coordinate system defines；Step 4: each component kinematics description；Step 5: fictitious power calculates；Step 6: deriving whole star system kinetics equation, have modeling method easy, modeling process is easily understood, the advantages of convenient for computer programming and realization.
Description
Technical field
The present invention relates to spacecraft dynamics modeling technique field, specifically a kind of modeling method is easy, models
Journey is easily understood, Flexible spacecraft dynamic model and modeling side convenient for computer programming and realization based on magnetic suspension bearing
Method.
Background technique
It is well known that further increasing the control precision of remote sensing satellite payload with the development of China's Aerospace Technology
Become the important content of satellite technology development with stability.An important factor for influencing control precision and stability is exactly axis
The performance held.Traditional mechanical bearing there are fit clearance, relative positional accuracy between bearing movable accessory element by processing and
Assembly precision guarantees, and with the aggravation of bearing wear, operating accuracy is reduced, and can generate vibration, thus serious shadow
Ring the control precision and stability for arriving Satellite Payloads.
Currently, magnetic suspension bearing makes rotor be in suspended state using electromagnetic force compared with mechanical bearing, without mechanical damage
Consumption, because not lubricating without rubbing；Adjust electromagnetic force and rotor-position can be realized and controlled, rotor can be made axial and
Radial accurate movement；And the uneven interference for causing low-vibration noise can be actively controlled.These of magnetic suspension bearing are excellent
Point can effectively improve the control precision and stability of Satellite Payloads, but magnetic suspension bearing is not yet applied at present
In the connection of Satellite Payloads.
Summary of the invention
Present invention aim to address above-mentioned the deficiencies in the prior art, provide a kind of modeling method simplicity, modeling process letter
It is single understandable, convenient for computer programming and the Flexible spacecraft dynamic model and modeling method based on magnetic suspension bearing of realization.
The technical solution adopted by the present invention to solve the technical problems is:
A kind of Flexible spacecraft dynamic model based on magnetic suspension bearing, be equipped with satellite body, solar battery windsurfing,
The two sides of satellite body, solar battery windsurfing warp is symmetrically arranged in attitude control flywheel and useful load, solar battery windsurfing
Stepper motor is driven, and attitude control flywheel is connected on the satellite platform, it is characterised in that the useful load is through magnetcisuspension
Floating axle is held to be connected with satellite body.
A kind of modeling method of the Flexible spacecraft dynamic based on magnetic suspension bearing, it is characterised in that modeling method step
It is as follows:
Step 1: basic configuration describes: being broken down into satellite body, solar-electricity according to the design feature of whole star system
Pond windsurfing, attitude control flywheel and useful load, and satellite body, solar battery windsurfing, attitude control flywheel and useful load are carried out
It describes one by one；
Step 2: basic assumption: according to the track and structure feature of satellite, providing the basic assumption of Dynamic Modeling；
Step 3: coordinate system defines: establishing Centroid orbit coordinate system and satellite body, solar battery windsurfing, attitude control fly
Take turns body coordinate system corresponding with useful load；
Step 4: each component kinematics description: to satellite body, solar battery windsurfing, attitude control flywheel and useful load
Carry out kinematics description, find out satellite body, solar battery windsurfing, in attitude control flywheel and useful load any point position
Shifting, speed, acceleration and speed variation；
Step 5: fictitious power calculates: on this basis, calculating separately satellite body, solar battery windsurfing, attitude control flywheel
With the fictitious power of useful load；
Step 6: deriving whole star system kinetics equation: deriving the dynamics of whole star system using speed variation principle
Equation.
Useful load of the present invention is camera, antenna, scanner or other each components.
Beneficial effects of the present invention and advantage:
1. present invention mainly solves fine Dynamic Modeling of the magnetic suspension bearing when applying on Satellite Payloads to ask
Topic, and provide a kind of Flexible spacecraft dynamic modeling method based on magnetic suspension bearing.
2. being connected between spacecraft payload and satellite body by magnetic suspension bearing in the present invention, useful load is used
Magnetic suspension bearing support, organic load rotor portion through magnetic suspension bearing, the stationary part of magnetic suspension bearing and star sheet respectively
Body consolidation.
3. the present invention connects fine modeling process to magnetic suspension bearing, consider that magnetic suspension bearing includes 6 freedom degrees, wherein
1 rotational freedom around optical axis, the characteristics of motion is it is known that other 5 directions are constrained using magnetic suspension force.
4. supporting compared to mechanical bearing, the pointing accuracy and stability of payload can be effectively improved.
5. modeling method of the invention is easy, it is convenient for computer programming and realization, and it is flat in emulation to facilitate control algolithm
Verifying on platform.
6. the present invention has stronger versatility, payload is also possible to other components, such as antenna, scanner
Deng as long as modeling method is identical, and kinetics equation is identical by the camera replacement in the present invention at corresponding assembly.
Detailed description of the invention
Fig. 1 is satellite body of the present invention and and part coordinates system definition figure.
Fig. 2 is position vector schematic diagram.
Specific embodiment
The following further describes the present invention with reference to the drawings:
As shown in the picture, a kind of Flexible spacecraft dynamic model based on magnetic suspension bearing is equipped with satellite body, the sun
The two sides of satellite body, solar energy is symmetrically arranged in energy battery windsurfing, attitude control flywheel and useful load, solar battery windsurfing
Battery windsurfing is driven through stepper motor, and attitude control flywheel, the structure of above-mentioned each component part are connected on the satellite platform
And the interconnected relationship between them is same as the prior art, this is not repeated, it is characterised in that the useful load is through magnetic
Suspension bearing is connected with satellite body, and steps are as follows for modeling method: Step 1: according to the design feature of whole star system by its point
Solution is satellite body, solar battery windsurfing, attitude control flywheel and useful load, and to satellite body, solar battery windsurfing, appearance
Control flywheel and useful load are described one by one；Step 2: providing Dynamic Modeling according to the track and structure feature of satellite
Basic assumption；Step 3: establishing Centroid orbit coordinate system and satellite body, solar battery windsurfing, attitude control flywheel and effective lotus
Carry corresponding body coordinate system；Step 4: being moved to satellite body, solar battery windsurfing, attitude control flywheel and useful load
Learn description, find out satellite body, solar battery windsurfing, the displacement at any point in attitude control flywheel and useful load, speed plus
Speed and speed variation；Step 5: on this basis, calculating separately satellite body, solar battery windsurfing, attitude control flywheel and having
Imitate the fictitious power of load；Step 6: the kinetics equation of whole star system is derived using speed variation principle, effective lotus
Carrying is camera, antenna, scanner or other each components, passes through magnetic suspension between spacecraft payload and star ontology in the present invention
Bearing connection, connects relative to mechanical bearing, can effectively improve the pointing accuracy and stability of payload；And this hair
Bright modeling method is easy, and modeling process is easily understood, and is convenient for computer programming and realization；Furthermore modeling method of the invention has
Certain versatility can be the components such as camera, antenna, scanner by the payload that magnetic suspension is connect with star ontology,
Modeling process and final kinetics equation form having the same.
Embodiment:
Modeling method of the invention has certain versatility, and payload can be the groups such as camera, antenna, scanner
Part, payload used in present invention specific implementation is camera, when using other type components, modeling process and final dynamic
Mechanical equation is all identical.
One, basic configuration describes
According to the design feature of whole star, which is mainly made of following components:
(1) satellite body (centerbody): rigid bodies including satellite and the camera body for being fixedly mounted on rigid bodies
(predominantly magnetic suspension bearing stationary part structure), each electronic equipment etc..
(2) camera: the camera is driven according to given regular uniform rotation using counteraction flyback, realizes that high-precision is high
The imaging of stability.
The camera optical axis is supported using magnetic suspension bearing, and the rotor portion of camera lens and magnetic suspension bearing is affixed, magnetic suspension shaft
The stationary part and star ontology held consolidates.
(3) solar battery windsurfing: the satellite uses double-vane solar battery windsurfing, is symmetrically installed, using stepper motor
Driving (is driven) using torque, with fixed angular speed rotation, realizes Direct to the sun.
(4) attitude control flywheel: this satellite uses the three-axle steady platform of zero momentum control mode, installs 4 altogether on satellite platform
A counteraction flyback (three orthogonal, an angle mount).In modeling process, it is thought of as rigid body.
Two, basic assumption
According to the track and structure feature of satellite, the derivation of whole star kinetics equation based on an assumption that
(1) satellite body (centerbody) is assumed to be rigid body in Dynamic Modeling and analysis.
(2) solar battery windsurfing is thought of as flexible body, is rigid connection between windsurfing and satellite body, ignores hinge
Gap, damping etc. influence.
(3) camera structure is thought of as rigid body, connects between camera and star ontology for magnetic suspension bearing, is thought of as empty containing gap
Between hinge, magnetic suspension force constraint.
(4) attitude dynamics are studied, since the time of analysis is shorter, it can be assumed that the orbital coordinate system of satellite is former
Point makees linear uniform motion, it is believed that the coordinate system is inertial coodinate system.
(5) ignore the influence of atmospheric drag.
Three, coordinate system defines
Description to each component for convenience introduces following several coordinate systems, as shown in Figure 1:
(1) for nominal Centroid orbit coordinate system OXYZ: origin O on the mass center of satellite platform system, OZ axis is directed toward the earth's core, OX
Axis perpendicular to OZ axis and is directed toward satellite motion direction in satellite orbit plane, and OY axis and OX and OZ axis constitute right-handed scale (R.H.scale)
System.
(2) centerbody coordinate system OcXcYcZc: origin OcAt certain point on satellite platform centerbody, when centerbody is opposite
When three azimuths of orbital coordinate system are zero, it is consistent that each axis is directed toward each axis direction corresponding with orbital coordinate system OXYZ
(3) camera coordinates system OnXnYnZn: coordinate origin is located on camera mirror at certain point, (i.e. magnetic suspension bearing rotor
Certain point on part), when camera coordinates system is zero relative to the azimuth of centerbody coordinate system, each axis is directed toward to be sat with centerbody
The corresponding each axis O of mark systemcXcYcZcIt is directed toward consistent.
(4) windsurfing coordinate system OpiXpiYpiZpi, (i=1,2): coordinate origin is located in solar battery windsurfing and satellite
The junction of heart body, OpZpFor the normal direction of windsurfing, OpXpYpConstitute windsurfing plane.
(5) attitude control flywheel coordinate system OwjXwjYwjZwj, (j=1,2,3,4): coordinate origin is defined in momenttum wheel rotation
The heart, shaft ZwjAxis.
Four, each component kinematics description
On the basis of being given above system configuration and coordinate system and defining, any matter in each component can be determined on satellite
Measure position, the velocity and acceleration of unit.
1. the definition of position vector
According to position vector as shown in Figure 2, position vector as shown in Table 1 is defined.
1 position vector symbol table of table
2. centerbody
The position vector of any one mass unit on centerbody are as follows:
Rc0=Rc+rc0 (1)
In turn, the velocity and acceleration corresponding to the mass unit relative to inertial coodinate system is respectively as follows:
Corresponding speed variation are as follows:
3. camera
Any one mass unit is about the position vector in nominal Centroid orbit coordinate system on camera lens are as follows:
Rn=Rc+rcn+rn (5)
In turn, the velocity and acceleration corresponding to the mass unit relative to inertial coodinate system is respectively as follows:
Corresponding speed variation are as follows:
4. windsurfing
Any one mass unit is about the position vector of nominal Centroid orbit coordinate system on elastic windsurfing
Rp=Rc+rcp+rp+up (9)
Wherein,Mp is the mode number of the elastic vibration intercepted,For the i-th rank of the point
The modal vector of mode, qpiFor the i-th rank modal displacement.For modal displacement array,For modal matrix.
In turn, the velocity and acceleration corresponding to the mass unit relative to inertial coodinate system is respectively as follows:
Corresponding speed variation are as follows:
5. attitude control flywheel
Any one mass unit is about the position vector in nominal Centroid orbit coordinate system on attitude control flywheel are as follows:
Rw=Rc+rcw+rw (13)
In turn, the velocity and acceleration corresponding to the mass unit relative to inertial coodinate system is respectively as follows:
Corresponding speed variation are as follows:
Five, fictitious power calculates
1. inertia force fictitious power
The calculation formula of inertia force fictitious power are as follows:
In sports immunology above, the angular speed of each component and the detailed expressions of speed variation have been obtained, it will
Each section can be calculated in its substitution formula (18) and obtain inertia force fictitious power.
Centerbody:
Camera:
Windsurfing:
Attitude control flywheel:
2. active force fictitious power
The calculation formula of active force fictitious power are as follows:
Active force includes the thrust that satellite propulsion unit provides, the control moment that momenttum wheel provides, interference of the environment to satellite
Power and disturbance torque, camera rotate control moment, and windsurfing rotates control moment.Power suffered by each component and torque are substituted into formula
(22) the active force fictitious power of each section can be calculated in.
Centerbody:
Wherein, momenttum wheel control moment Tc；The moment of reaction of windsurfingEnvironmental disturbances torque Tcd；Satellite propulsion unit pushes away
Power Fc；The magnetic suspension force restraining force of magnetic suspension bearing hingeOther spaces external force Fcd。
Camera:
Wherein, the magnetic suspension restraining force F of magnetic suspension bearing hingej；Camera reaction force driving moment Tn。
Windsurfing:
Wherein, windsurfing driving moment Tp；Solar light pressure external force F of the stepless action on solar arrayp。
Attitude control flywheel:
Wherein, flywheel control moment Tw。
3. virtual strain energy change rate
DefinitionFor the generalized Modal stiffness matrix of windsurfing, then the virtual strain energy change rate of windsurfing can use modal coordinate
It indicates are as follows:
Six, whole star system kinetics equation
The model mainly uses Jourdan variation principle (also known as speed variation principle), establishes based on magnetic suspension bearing
Flexible spacecraft dynamic equation.The expression formula of speed variation principle are as follows:
∑δPI+∑δPa-∑δPe=0 (28)
Wherein δ PIFor inertia force fictitious power, δ PaFor active force fictitious power, δ PeFor virtual strain energy change rate, Σ symbol is indicated
It sums to system.
On the basis of each component fictitious power derived above, and then available whole star inertia force fictitious power δ PI, main
Power fictitious power δ PaAnd virtual strain energy change rate δ PeExpression formula, substituted into (28), speed variation side can be obtained
Journey.The equation is the speed variation about each componentδωc、δωn、δωp、δωwLinear expansion,
Each speed variation is mutually indepedent, then available following whole star system kinetics equation:
(1) satellite is with respect to the translation kinetics equation that nominal track moves
(2) Dynamical Attitude Equations
(3) kinetics equation of camera rotation
(4) the translation kinetics equation of camera
(5) kinetics equation of windsurfing rotation
(6) kinetics equation of windsurfing vibration
(7) kinetics equation of attitude control flywheel turns
Through the above steps, by model parameters and drivings such as real satellite mass inertia, accessory structure, magnetic suspension restraining forces
Parameter is brought into the Flexible spacecraft dynamic model based on magnetic suspension bearing of foundation and in formula (29)-(35), can be arrived
The specifically Flexible spacecraft dynamic equation based on magnetic suspension bearing.
Claims (5)
1. a kind of Flexible spacecraft dynamic model based on magnetic suspension bearing is equipped with satellite body, solar battery windsurfing, appearance
The two sides of satellite body are symmetrically arranged in control flywheel and useful load, solar battery windsurfing, and solar battery windsurfing is through step
It is driven into motor, attitude control flywheel is connected on the satellite platform, it is characterised in that the useful load is through magnetic suspension
Bearing is connected with satellite body.
2. a kind of modeling method of the Flexible spacecraft dynamic based on magnetic suspension bearing, it is characterised in that modeling method step is such as
Under:
Step 1: basic configuration describes: being broken down into satellite body, solar battery sail according to the design feature of whole star system
Plate, attitude control flywheel and useful load, and satellite body, solar battery windsurfing, attitude control flywheel and useful load are carried out one by one
Description；
Step 2: basic assumption: according to the track and structure feature of satellite, providing the basic assumption of Dynamic Modeling；
Step 3: coordinate system defines: establish Centroid orbit coordinate system and satellite body, solar battery windsurfing, attitude control flywheel with
The corresponding body coordinate system of useful load；
Step 4: each component kinematics description: being carried out to satellite body, solar battery windsurfing, attitude control flywheel and useful load
Kinematics description finds out satellite body, solar battery windsurfing, the displacement at any point, speed in attitude control flywheel and useful load
Degree, acceleration and speed variation；
Step 5: fictitious power calculates: on this basis, calculating separately satellite body, solar battery windsurfing, attitude control flywheel and have
Imitate the fictitious power of load；
Step 6: deriving whole star system kinetics equation: deriving the kinetics equation of whole star system using speed variation principle.
3. a kind of Flexible spacecraft dynamic model based on magnetic suspension bearing according to claim 1 or 2 and modeling side
Method, it is characterised in that the useful load is camera, antenna, scanner or other each components.
4. a kind of modeling method of Flexible spacecraft dynamic based on magnetic suspension bearing according to claim 2, special
The coordinate system for levying the satellite body being in step 3 is set as OcXcYcZc, the coordinate system of effective carrier is set as OnXnYnZn: effectively carry
The coordinate origin of body is located on effective carrier at certain point, i.e. certain point on magnetic suspension bearing rotor part, works as effective carrier
When coordinate system relative to the azimuth of satellite body coordinate system is zero, each axis is directed toward each axis corresponding with satellite body coordinate system
OcXcYcZcIt is directed toward consistent.
5. a kind of modeling method of Flexible spacecraft dynamic based on magnetic suspension bearing according to claim 2, special
Levy the calculation formula for the active force fictitious power being in step 5 are as follows:
Active force includes the thrust that satellite propulsion unit provides, the control moment that momenttum wheel provides, environment to the perturbed force of satellite and
Disturbance torque, effective carrier rotate control moment, and windsurfing rotates control moment, will be in power suffered by each component and torque substitution formula
State the active force fictitious power that each section can be calculated in formula.
Centerbody:
Wherein, momenttum wheel control moment Tc；The moment of reaction of windsurfingEnvironmental disturbances torque Tcd；Satellite propulsion unit thrust Fc；
The magnetic suspension force restraining force of magnetic suspension bearing hingeOther spaces external force Fcd。
Effective carrier:
Wherein, the magnetic suspension restraining force F of magnetic suspension bearing hingej；Camera reaction force driving moment Tn。
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| CN110045744A (en) * | 2019-05-10 | 2019-07-23 | 哈尔滨工业大学 | The steady control method of spin load based on the regulation of magnetic suspension bearing active stiffness |
| CN110147115A (en) * | 2019-06-21 | 2019-08-20 | 哈尔滨工业大学 | Centered on load, the spin load satellite attitude control method that platform is servo-actuated |
| CN110990949A (en) * | 2019-11-28 | 2020-04-10 | 上海航天控制技术研究所 | Flexible spacecraft dynamics modeling method considering hinge gap |
| CN111506991A (en) * | 2020-04-08 | 2020-08-07 | 武汉大学 | Magnetic force modeling method and system for magnetic suspension turntable and storage medium |
| CN111781939A (en) * | 2020-05-11 | 2020-10-16 | 北京控制工程研究所 | Attitude control method and system based on spacecraft three-super mutual restriction and coupling |
| CN114683285A (en) * | 2022-03-31 | 2022-07-01 | 中国空间技术研究院 | Rapid space robot simulation modeling method and system |
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| CN110045744B (en) * | 2019-05-10 | 2021-11-19 | 哈尔滨工业大学 | Rotating load stability control method based on magnetic suspension bearing active stiffness regulation |
| CN110147115A (en) * | 2019-06-21 | 2019-08-20 | 哈尔滨工业大学 | Centered on load, the spin load satellite attitude control method that platform is servo-actuated |
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| CN111506991A (en) * | 2020-04-08 | 2020-08-07 | 武汉大学 | Magnetic force modeling method and system for magnetic suspension turntable and storage medium |
| CN111506991B (en) * | 2020-04-08 | 2022-04-29 | 武汉大学 | Magnetic force modeling method and system for magnetic suspension turntable and storage medium |
| CN111781939A (en) * | 2020-05-11 | 2020-10-16 | 北京控制工程研究所 | Attitude control method and system based on spacecraft three-super mutual restriction and coupling |
| CN111781939B (en) * | 2020-05-11 | 2023-06-30 | 北京控制工程研究所 | Attitude control method and system based on three-ultrasonic mutual constraint and coupling of spacecraft |
| CN114683285A (en) * | 2022-03-31 | 2022-07-01 | 中国空间技术研究院 | Rapid space robot simulation modeling method and system |
| CN114683285B (en) * | 2022-03-31 | 2024-03-26 | 中国空间技术研究院 | simulation modeling method and system for shortcut space robot |
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