CN105204513A - Gradually varied inertia liquid filling execution mechanism and method for controlling high-accuracy attitude of spacecraft - Google Patents

Gradually varied inertia liquid filling execution mechanism and method for controlling high-accuracy attitude of spacecraft Download PDF

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CN105204513A
CN105204513A CN201510595474.XA CN201510595474A CN105204513A CN 105204513 A CN105204513 A CN 105204513A CN 201510595474 A CN201510595474 A CN 201510595474A CN 105204513 A CN105204513 A CN 105204513A
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inertia
moment
flywheel
topping
topworks
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CN105204513B (en
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关宏
朱琦
曹荣向
赵江涛
姚宁
吕高见
蔡建
王绍凯
雷拥军
刘洁
李晶心
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Beijing Institute of Control Engineering
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Beijing Institute of Control Engineering
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Abstract

The invention relates to a gradually varied inertia liquid filling execution mechanism and a method for controlling a high-accuracy attitude of a spacecraft. The gradually varied inertia liquid filling execution mechanism comprises a vacuum container (1) for fixing and installing a whole flywheel structure, a flywheel bearing (2), a flywheel motor (3) and a flywheel. The control method comprises the steps that a laminar flow boundary layer equation is established, velocity distribution in a boundary layer is calculated, and an attitude kinetic equation of the spacecraft in the inertia changing process of the execution mechanism is established to obtain control toque Tc required by attitude change and provided by the execution mechanism. By the adoption of the gradually varied inertia liquid filling execution mechanism and the method for controlling the high-accuracy attitude of the spacecraft, the executing capacity of the attitude control execution mechanism is improved in the attitude control process, the output torque coverage range is widened, and meanwhile the problems of dynamic unbalance, too large resistance and the like brought by structure and process design problems during high-frequency rotation of a rotation part are decreased.

Description

A kind of gradual change inertia topping up topworks and the method that spacecraft high-precision attitude is controlled
Technical field
The present invention relates to a kind of method that spacecraft high-precision attitude controls, for gradual change inertia topping up topworks and the method to the control of spacecraft high-precision attitude thereof.
Background technology
Angular momentum exchange topworks, especially reaction wheel, momenttum wheel and control-moment gyro, control the topworks adopted, in engineering reality, obtain sufficient application as spacecraft active attitude.Wherein, the technology of reaction wheel, momenttum wheel is very ripe, is widely used in the high precision high stability degree gesture stability of domestic and international Multiple Type satellite.Constant speed control-moment gyro is the advantage such as structure is simple, reliability is high, faster system response owing to having, and has become the first-selected attitude control actuator of long-life spacecraft in engineering reality.
Spacecraft in orbit in, reaction wheel, momenttum wheel and control-moment gyro are as attitude control actuator likely partial failure, mostly the reason wherein lost efficacy is the defect due to mechanism's physical construction aspect, as the dead band, power limit, vibration interference etc. of motor.On the other hand, just start from the sixties in last century for the tank fuel storage of gas ejecting system and the research of stability analysis, but there is a large amount of quality redundancies and space waste in spacecraft bunkering all the time, the situation remaining tens kilograms of fuel after task completes is very general, this have impact on the payload mass of spacecraft and the accounting in space to a certain extent, and increases the possibility influencing each other and disturb to a great extent.
Summary of the invention
Technology of the present invention is dealt with problems and is: overcome the deficiencies in the prior art, a kind of method gradual change inertia topping up topworks being provided and spacecraft high-precision attitude is controlled, improve in gesture stability process, the executive capability of attitude control actuator, improve the scope that output torque covers, the problems such as the unbalance dynamic brought due to structure, Process Problems when simultaneously reducing rotatable parts high frequency rotational, resistance are excessive, the technical matters of solution utilizes this topworks to realize the large angular velocity quick adjustment of spacecraft and high precision high stability degree control problem.
The technology of the present invention solution: a kind of gradual change inertia topping up topworks, comprising: vacuum tank (1), flywheel bearing (2), fly-wheel motor (3), the flywheel (4) of fixing and install whole flywheel structure; Flywheel (4) comprises solid rotor part (41), bell housing (42), topping up chamber (43), radial conduit (44) and axial pipe (45), barrier (46) and prefill valve (47), tapping valve (48) and barrier valve (49); The position of flywheel bearing (2), fly-wheel motor (3) fixed by vacuum tank (1), flywheel bearing (2) is arranged on the rotating shaft two ends of flywheel (4), plays effect that is fixing and support flying wheel (4); Fly-wheel motor (3) coordinates with the rotating shaft of flywheel (4), plays the effect of drive shaft; Be filled with liquid working substance in flywheel topping up chamber (43), injected from prefill valve (47) by axial pipe (45) and radial conduit (44), emptying by tapping valve (48); Liquid in the rotating speed of fly-wheel motor (3) and topping up chamber (43) injects and the emptying calculating according to control algolithm regulates, and is realized by the opening and closing work of barrier valve (49), prefill valve (47) and tapping valve (48).
Utilize gradual change inertia topping up topworks to carry out a method for spacecraft high-precision attitude control, it is characterized in that performing step is as follows
The first step, sets up each laminar flow face laminar sublayer equation in flywheel topping up chamber (43)
∂ V L w ∂ L w + ∂ V R w R w = 1 V L w ∂ V L w ∂ R w + V R w ∂ V L w ∂ R w = - 1 ρ ∂ p ∂ L w + ν ∂ 2 V L w ∂ R w 2 1 ρ ∂ p ∂ R w = V L w 2 ∂ R w
V lwrepresent the flow velocity along bell housing (42) cavity wall face, suppose the velocity distribution V in boundary-layer lw=f (R w) be a function polynomial expression, V lw=a 0+ a 1r w+ a 2r w 2+ a 3r w 3+ ..., a 0, a 1, a 2, a 3for multinomial coefficient, V rwrepresent the flow velocity in vertical bell housing (42) cavity wall face, L wrepresent the length of flowing, R wpresentation layer stream interface radius, ρ represents fluid density, and p represents the pressure differential that change in flow causes, and ν represents the viscosity of fluid, according to the boundary condition of boundary-layer, can be obtained by laminar sublayer equation, and bell housing (42) wall meets non-slip condition, V rw=0, V lw=0, at boundary-layer outer boundary δ place, V lw=V f, and
Second step, according to the V on bell housing (42) wall that the first step draws rw=0, V lw=0, obtain a 0=0; At boundary-layer outer boundary δ place, V lw=V f, obtain δ represents the thickness of boundary-layer, V fthe flowing velocity of presentation layer stream interface, then the flowing velocity in boundary-layer V L w = 2 V f δ R w - V f δ 2 R w 2 ;
3rd step, according to the flowing velocity of second step formula, can obtain flowing velocity V in boundary-layer lwwith laminar flow face flowing velocity V fdifference, V lw<V f, namely there is flow velocity loss in boundary-layer, the loss of flow velocity be equivalent to the loss of inertia, obtain with laminar flow face flowing velocity V ffor the moment of inertia I of topping up chamber (43) equivalent flow velocity wf;
4th step, obtains the moment of inertia I of equivalent flow velocity according to the 3rd step wf, obtain the angular momentum h of flywheel (4) f, h f=I wfβ f, β frepresent that the flow field, center of cavity fluid is around z wthe rotational angular velocity of axle, β fwith V fpass be V f=R wβ f, by rotational angular velocity β fwith moment of inertia I wfset up the attitude dynamic equations of spacecraft in topworks's inertia change procedure, obtain the control moment T that attitudes vibration needs topworks to provide c;
5th step, according to the control moment T that above-mentioned attitudes vibration needs topworks to provide c, consider the friction factor of motor, set up topworks's motor low speed Controlling model, design is applicable to topworks's manipulation rule that high precision high stability degree controls, and the rotating speed β of rule coefficient G and topworks handled by the plus-minus moment of inertia switch of design topworks fcontrol planning, obtain by adjustment moment of inertia I wfwith rotating speed β f, be met the control moment T that high stability requires ccontrol method:
β fstart tapping valve (48) when being less than discharge opeing critical value and close prefill valve (47) reducing mechanism moment of inertia;
β fstart prefill valve (47) when being greater than topping up critical value and close tapping valve (48), open barrier valve (49) simultaneously, improve the filling amount in topping up chamber (43), make moment of inertia I wfincrease, meet the requirements of I wfduring value, prefill valve (47) cuts out;
Moment of inertia I is improved when not continuing topping up wftime, tapping valve (48) is opened, and the flowing groove that flow direction diameter is large, makes moment of inertia I wfincrease;
Realize maximum rotation inertia I wftime, prefill valve (47), barrier valve (49) are all opened, and topping up chamber (43) is full of;
By adjustment moment of inertia I wfwith rotating speed β f, be met the control moment T that high stability requires c.The present invention's advantage is compared with prior art:
(1) with use not Variable inertia topworks simulation result compared with, the attitude parameter change curve of spacecraft is more level and smooth.Sensing convergence result is carried out contrast can find, after using Variable inertia mechanism, the final convergence precision of spacecraft has brought up to 0.001 ° from 0.01 °; Convergence curve is more level and smooth simultaneously, and the process of convergence is also more stable.
(2) with use not Variable inertia topworks simulation result compared with, present invention effectively avoids the angular velocity concussion in control procedure, in the concussion region using the topworks of not Variable inertia to produce, topworks enters that time in dead band is long, dead zone range large, and this can affect the precision of output torque.After adopting design of the present invention, by stable regulation moment of inertia, improve the rotating speed in little moment output situation, reduce the impact in motor dead band, thus improve attitude control accuracy.
(3), compared with changing the simulation result of discontinuous topworks with use inertia, the present invention changes moment of inertia gradually when rotating speed is reduced to setting, improves the rotating speed of flywheel, makes flywheel quickly through dead band, reduces the time that flywheel moves in dead band.Meanwhile, topworks's output pulsation that the sudden change avoiding moment of inertia causes, improves the stability of high precision high stability degree control procedure.
Accompanying drawing explanation
Fig. 1 is the structural front view of gradual change inertia topworks of the present invention;
Fig. 2 is the A-A cut-open view in Fig. 1;
Fig. 3 is the mass distribution schematic diagram of invention gradual change inertia topworks; Wherein a is that liquid is full of, and b is that water jacket is full of, and c is that inside groove is full of, and d is emptying rate of liquid;
Fig. 4 is that the rotating speed of gradual change inertia topworks of the present invention controls change procedure figure; Wherein upper figure represents the change curve of flow angle speed in the topworks that is arranged in spacecraft X-axis, middle figure represents the change curve of flow angle speed in the topworks that is arranged in spacecraft Y-axis, and figure below represents the change curve of flow angle speed in the topworks that is arranged on spacecraft Z axis.
Fig. 5 is the method control chart that spacecraft high-precision attitude of the present invention controls;
Fig. 6 is the Spacecraft Attitude Control result figure of gradual change inertia topworks of the present invention.
Embodiment
In order to improve in gesture stability process, the executive capability of attitude control actuator, improve the scope that output torque covers, simultaneously reduce rotatable parts high frequency rotational time due to structure, the unbalance dynamic that Process Problems brings, the problems such as resistance is excessive, in conjunction with structure and the work characteristics of jet mechanism and angular momentum exchange topworks, the present invention proposes a kind of novel topping up that utilizes and regulates the topworks of Rotary Inertia of Flywheel, improve configuration and the intrinsic concept of rotor of angular momentum exchange topworks, this topworks changes the fill ratio of liquid working substance by continuous print, realize the consecutive variations of moment of inertia, according to different attitude stabilities, attitude maneuver Capability Requirement, autonomous adjustment actuating mechanism moment of inertia, utilize new configuration, Biological process, too high and the serious wear of angular momentum exchange actuator system rotating speed is in the past avoided to there is dither phenomenon by designing a kind of new topworks, and a kind of method utilizing this topworks to realize the control of spacecraft high-precision attitude is proposed.
As shown in Figure 1, 2, the structural drawing of gradual change inertia topworks of the present invention, comprising: vacuum tank 1, flywheel bearing 2, fly-wheel motor 3, the flywheel 4 of fixing and install whole flywheel structure; Flywheel 4 comprises solid rotor part 41, bell housing 42, topping up chamber 43, radial conduit 44 and axial pipe 45, barrier 46 and prefill valve 47, tapping valve 48 and barrier valve 49; The position of flywheel bearing 2, fly-wheel motor 3 fixed by vacuum tank 1, and flywheel bearing 2 is arranged on the rotating shaft two ends of flywheel 4, plays effect that is fixing and support flying wheel 4; Fly-wheel motor 3 coordinates the effect of dynamic rotating shaft with the rotating shaft of flywheel 4; Be filled with liquid working substance in flywheel topping up chamber 43, injected from prefill valve 47 by axial pipe 45 and radial conduit 44, emptying by tapping valve 48; Liquid in the rotating speed of control gear 5 pairs of fly-wheel motors 3 and topping up chamber 43 injects and emptyingly to regulate, the switch of control barrier valve 49, prefill valve 47 and tapping valve 48.The course of work of gradual change mass flywheel comprises rotating speed control and moment of inertia controls two aspects, when carrying out rotating speed control, fly-wheel motor 3 controls the rotating speed that flywheel solid rotor part 41 realizes control method requirement, when carrying out moment of inertia control: control method requires by when in increase topping up chamber 43, liquid quality makes moment of inertia increase, prefill valve 47 is opened, axial pipe 45 and radial conduit 44 inject flywheel topping up chamber 43 from prefill valve 47, barrier valve 49 is opened by hydraulic action according to the amount injecting liquid, after in topping up chamber 43, liquid quality is increased to the value of control method requirement, prefill valve 47 cuts out, control method requires not increase liquid quality in topping up chamber 43, but when moment of inertia increases, maintenance prefill valve 47 cuts out, tapping valve 48 is closed, and barrier valve 49 is opened, and liquid enters in the larger flowing groove of topping up chamber 43 diameter, and moment of inertia increases, when the moment of inertia that control method requires reduces, open tapping valve 48, barrier valve 49, liquid discharges topping up chamber 43, and moment of inertia reduces.
As shown in Figure 3, gradual change inertia topworks of the present invention can realize topping up and emptying different quality distribution, the liquid requiring quality can be filled with as required in flywheel topping up chamber under topping up state, and by the valve in the middle of each layer topping up ring, under the effect of wheel body rotary centrifugal force and pressure, liquid can be distributed within the scope of least radius or maximum radius, meets the flexible control mode of many inertia change combination; When needing discharge opeing, tapping valve is opened, and discharges liquid, reduces moment of inertia;
As shown in Figure 4, can find out, gradual change inertia topworks of the present invention is carrying out in gesture stability process, when the rotating speed of topworks be reduced to critical value once time, owing to triggering the discharge opeing pattern of manipulation rate design, the moment of inertia of topworks reduces, and improves the slewing rate of topworks, make it quickly through Critical Control region, avoid the impact of topworks's non-linear in tribology on control accuracy.Present invention effectively avoids the angular velocity concussion in control procedure, by stable regulation moment of inertia, improve the rotating speed in little moment output situation, reduce the impact in motor dead band, thus improve attitude control accuracy.The present invention changes moment of inertia gradually when rotating speed is reduced to setting, improves the rotating speed of flywheel, makes flywheel quickly through dead band, reduces the time that flywheel moves in dead band.Meanwhile, topworks's output pulsation that the sudden change avoiding moment of inertia causes, improves the stability of high precision high stability degree control procedure.
As shown in Figure 5, the method implementation procedure of spacecraft high-precision attitude control of the present invention is as follows:
The flow field modeling focusing on gradual change inertia topworks of the present invention, gradual change inertia handles factor design, and utilizes gradual change inertia topworks to the manipulation rule design of Spacecraft Control, and other algorithms belong to conventional algorithm.
The first step, sets up each laminar flow face laminar sublayer equation in flywheel topping up chamber (43)
&part; V L w &part; L w + &part; V R w R w = 1 V L w &part; V L w &part; R w + V R w &part; V L w &part; R w = - 1 &rho; &part; p &part; L w + &nu; &part; 2 V L w &part; R w 2 1 &rho; &part; p &part; R w = V L w 2 &part; R w
V lwrepresent the flow velocity along bell housing (42) cavity wall face, suppose the velocity distribution V in boundary-layer lw=f (R w) be a function polynomial expression, V lw=a 0+ a 1r w+ a 2r w 2+ a 3r w 3+ ..., a 0, a 1, a 2, a 3for multinomial coefficient, V rwrepresent the flow velocity in vertical bell housing (42) cavity wall face, L wrepresent the length of flowing, R wpresentation layer stream interface radius, ρ represents fluid density, and p represents the pressure differential that change in flow causes, and ν represents the viscosity of fluid, according to the boundary condition of boundary-layer, can be obtained by laminar sublayer equation, and bell housing (42) wall meets non-slip condition, V rw=0, V lw=0, at boundary-layer outer boundary δ place, V lw=V f, and
Second step, according to the V on bell housing (42) wall that the first step draws rw=0, V lw=0, obtain a 0=0; At boundary-layer outer boundary δ place, V lw=V f, obtain δ represents the thickness of boundary-layer, V fthe flowing velocity of presentation layer stream interface, then the flowing velocity in boundary-layer V L w = 2 V f &delta; R w - V f &delta; 2 R w 2 ;
3rd step, according to the flowing velocity of second step formula, can obtain flowing velocity V in boundary-layer lwwith laminar flow face flowing velocity V fdifference, except boundary-layer outer boundary δ place V lw=V f, V everywhere in boundary-layer lw<V f, namely there is flow velocity loss in boundary-layer, this is the shear stress τ owing to being produced by fluid viscosity in boundary-layer wcause, the shear stress τ produced by fluid viscosity in boundary-layer wbe expressed as
- &tau; w + &part; p &part; L w &delta; = &part; &part; L w ( &Integral; 0 &delta; &rho;V L w 2 dR w ) dL w - V f &part; &part; L w ( &Integral; 0 &delta; &rho;V L w dR w ) dL w
Due to the existence of sticky shearing stress, when fluid flows in boundary-layer, the loss of momentum being produced, in order to simplify calculating, the loss of flow velocity being equivalent to the loss of inertia, obtain with laminar flow face flowing velocity V ffor the moment of inertia I of the equivalent flow velocity in topping up chamber 43 wf, I wfrelevant to the duty of barrier valve 49, prefill valve 47 and tapping valve 48, introduce in the 5th step;
4th step, obtains the moment of inertia I of equivalent flow velocity according to the 3rd step wf, calculate the angular momentum h of flywheel 4 f, β frepresent that the flow field, center of cavity fluid is around z wthe rotational angular velocity of axle, β fwith V fpass be V f=R wβ f, by rotational angular velocity β fwith moment of inertia I wfobtain the angular momentum h of flywheel 4 f, h f=I wfβ f, set up the attitude dynamic equations of spacecraft in topworks's inertia change procedure, obtain required control moment T c, wherein I represents the moment of inertia of spacecraft, and ω represents spacecraft attitude angular velocity, X-axis, Y-axis, and the attitude angular velocity of Z axis is respectively ω x, ω y, ω z;
5th step, consider the friction factor of motor, set up topworks's motor low speed Controlling model, reduce friction during tick-over square T fbe expressed as: T f = T c u s g n ( &beta; f ) + ( T s - T c u ) exp &lsqb; - ( &beta; f &beta; f s b ) 2 &rsqb; + T v &beta; f , β fsbrepresent the dead zone function line of rotating speed, T cu, T s, T vfor friction factor item, in order to the square T that reduces friction as far as possible fimpact, design be applicable to high precision high stability degree control topworks handle rule g is the switching coefficient of prefill valve and tapping valve, and the plus-minus moment of inertia switch manipulation rule of design topworks is as follows: G = ( 1 - &beta; f min / | &beta; f | ) 2 , | &beta; f | > &beta; f min 0 , | &beta; f | &le; &beta; f min , In order to avoid rotating speed to enter nonlinear area as far as possible, require to reduce when moment exports, rotating speed is close to (-β fsb, β fsb) time, by the emptying rate of liquid in wheel, only use solid rotor, improve rotating speed, the Stability and veracity that holding torque exports, β fminfor rotation speed threshold values, when the rotating speed of topworks | β f| > β fmintime, flywheel topping up, realizes large angular momentum exchange requirement with larger inertia; When | β f|≤β fmintime, think that spacecraft enters the pose stabilization control stage, flywheel emptying rate of liquid, reduce wheel speed when little angular momentum exports and be absorbed in (-β fsb, β fsb) possibility in district.The course of work of gradual change mass flywheel comprises rotating speed control and moment of inertia controls two aspects:
Carry out rotating speed β fduring control, fly-wheel motor 3 controls the rotating speed β that flywheel solid rotor part 41 realizes control method requirement f;
Carry out moment of inertia I wfduring control:
β fwhen being greater than topping up critical value, control method requires to make moment of inertia I by increasing liquid quality in topping up chamber 43 wfduring increase, prefill valve 47 is opened, and axial pipe 45 and radial conduit 44 inject flywheel topping up chamber 43 from prefill valve 47, and barrier valve 49 is opened by hydraulic action according to the amount injecting liquid, and in topping up chamber 43, liquid quality increases, and makes moment of inertia I wfincrease, meet the requirements of I wfduring value, prefill valve 47 cuts out, and reduces β fspeedy carding process requirement, alleviate fly-wheel motor 3 burden;
Control method requires not increase liquid quality in topping up chamber 43, but improves moment of inertia I wftime, maintenance prefill valve 47 cuts out, tapping valve 48 is closed, and barrier valve 49 is opened, and liquid enters in the larger flowing groove of topping up chamber 43 diameter, make moment of inertia I wfincrease;
Requirement realizes maximum rotation inertia I wftime, prefill valve 47, barrier valve 49 are all opened, and topping up chamber 43 is full of;
β fwhen being less than discharge opeing critical value, the moment of inertia I that control method requires wfreduce, then keep prefill valve 47 to close, open tapping valve 48, barrier valve 49, by rotary centrifugal force effect, liquid discharges topping up chamber 43, moment of inertia I wfreduce, the requirement rotating speed β of output fcorresponding increase, quickly through (-β fmin, β fmin) region, reduce the Nonlinear friction torque of fly-wheel motor 3 to the impact controlled,
By adjustment moment of inertia I wfwith rotating speed β f, be met the control moment T that high stability requires c.
As shown in Figure 6, use topworks of the present invention, the attitude angular velocity Parameters variation curve of spacecraft is more level and smooth, the X-axis attitude angular velocity ω of spacecraft x, Y-axis attitude angular velocity ω y, Z axis attitude angular velocity ω z, final convergence precision has brought up to 0.001 °; Convergence curve is more level and smooth simultaneously, and the process of convergence is also more stable, improves the stability of high precision high stability degree control procedure.

Claims (2)

1. a gradual change inertia topping up topworks, is characterized in that: comprising: vacuum tank (1), flywheel bearing (2), fly-wheel motor (3), the flywheel (4) of fixing and install whole flywheel structure; Flywheel (4) comprises solid rotor part (41), bell housing (42), topping up chamber (43), radial conduit (44) and axial pipe (45), barrier (46), prefill valve (47), tapping valve (48) and barrier valve (49); The position of flywheel bearing (2), fly-wheel motor (3) fixed by vacuum tank (1), flywheel bearing (2) is arranged on the rotating shaft two ends of flywheel (4), plays effect that is fixing and support flying wheel (4); Fly-wheel motor (3) coordinates with the rotating shaft of flywheel (4), plays the effect of drive shaft; Be filled with liquid working substance in flywheel topping up chamber (43), injected from prefill valve (47) by axial pipe (45) and radial conduit (44), emptying by tapping valve (48); Control gear (5) injects the liquid in the rotating speed of fly-wheel motor (3) and topping up chamber (43) and emptyingly to regulate, the switch of control barrier valve (49), prefill valve (47) and tapping valve (48).
2. utilize gradual change inertia topping up topworks to carry out a method for spacecraft high-precision attitude control, it is characterized in that performing step is as follows:
The first step, sets up each laminar flow face laminar sublayer equation in flywheel topping up chamber (43)
&part; V L w &part; L w + &part; V R w &part; R w = 1 V L w &part; V L w &part; L w + V R w &part; V L w &part; R w = - 1 &rho; &part; p &part; L w + v &part; 2 V L w &part; R w 2 1 &rho; &part; p &part; R w = V L w 2 &part; R w
V lwrepresent the flow velocity along bell housing (42) cavity wall face, suppose the velocity distribution V in boundary-layer lw=f (R w) be a function polynomial expression, V lw=a 0+ a 1r w+ a 2r w 2+ a 3r w 3+ ..., a 0, a 1, a 2, a 3for multinomial coefficient, V rwrepresent the flow velocity in vertical bell housing (42) cavity wall face, L wrepresent the length of flowing, R wpresentation layer stream interface radius, ρ represents fluid density, and p represents the pressure differential that change in flow causes, and ν represents the viscosity of fluid, according to the boundary condition of boundary-layer, can be obtained by laminar sublayer equation, and bell housing (42) wall meets non-slip condition, V rw=0, V lw=0, at boundary-layer outer boundary δ place, V lw=V f, and
Second step, according to the V on bell housing (42) wall that the first step draws rw=0, V lw=0, obtain a 0=0; At boundary-layer outer boundary δ place, V lw=V f, obtain δ represents the thickness of boundary-layer, V fthe flowing velocity of presentation layer stream interface, then the flowing velocity in boundary-layer V L w = 2 V f &delta; R w - V f &delta; 2 R w 2 ;
3rd step, according to the flowing velocity of second step formula, can obtain flowing velocity V in boundary-layer lwwith laminar flow face flowing velocity V fdifference, V lw<V f, namely there is flow velocity loss in boundary-layer, the loss of flow velocity be equivalent to the loss of inertia, obtain with laminar flow face flowing velocity V ffor the moment of inertia I of topping up chamber (43) equivalent flow velocity wf;
4th step, obtains the moment of inertia I of equivalent flow velocity according to the 3rd step wf, obtain the angular momentum h of flywheel (4) f, h f=I wfβ f, β frepresent that the flow field, center of cavity fluid is around z wthe rotational angular velocity of axle, β fwith V fpass be V f=R wβ f, by rotational angular velocity β fwith moment of inertia I wfset up the attitude dynamic equations of spacecraft in topworks's inertia change procedure, obtain the control moment T that attitudes vibration needs topworks to provide c;
5th step, according to the control moment T that above-mentioned attitudes vibration needs topworks to provide c, consider the friction factor of motor, set up topworks's motor low speed Controlling model, design is applicable to topworks's manipulation rule that high precision high stability degree controls, and the rotating speed β of rule coefficient G and topworks handled by the plus-minus moment of inertia switch of design topworks fcontrol planning, obtain by adjustment moment of inertia I wfwith rotating speed β f, be met the control moment T that high stability requires ccontrol method:
β fstart tapping valve (48) when being less than discharge opeing critical value and close prefill valve (47) reducing mechanism moment of inertia;
β fstart prefill valve (47) when being greater than topping up critical value and close tapping valve (48), open barrier valve (49) simultaneously, improve the filling amount in topping up chamber (43), make moment of inertia I wfincrease, meet the requirements of I wfduring value, prefill valve (47) cuts out;
Moment of inertia I is improved when not continuing topping up wftime, tapping valve (48) is opened, and the flowing groove that flow direction diameter is large, makes moment of inertia I wfincrease;
Realize maximum rotation inertia I wftime, prefill valve (47), barrier valve (49) are all opened, and topping up chamber (43) is full of;
By adjustment moment of inertia I wfwith rotating speed β f, be met the control moment T that high stability requires c.
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