CN102566578B - Singular value decomposition-based coordination control method of single gimbal control moment gyros (SGCMGs) - Google Patents

Abstract

The invention relates to a singular value decomposition-based coordination control method of single gimbal control moment gyros (SGCMGs). The singular value decomposition-based coordination control method comprises the following steps of: distributing instruction moment required for controlling an entire spacecraft to two sets of SGCMGs according to a certain proportion; decomposing the instruction moment distributed to the set A of SGCMGs again by using a singular value decomposition method; distributing an instruction moment component in the singular direction of the set A of SGCMGs to the set B of SGCMGs; still distributing an instruction moment component perpendicular to the singular direction of the set A of SGCMGs to the set A of SGCMGs; after distribution, solving instruction gimbal angular velocities of the two sets of SGCMGs respectively; operating according to the respective instruction gimbal angular velocity; and acting the sum of output moment on the spacecraft to finish accurate attitude control. According to the singular value decomposition-based coordination control method, the gyros can still accurately and effectively output control moment to control the attitude of the spacecraft while a part of gyros fails and the gyros are singular and the probability of premature saturation of a single set of SGCMGs is also avoided to the greatest extent without configuring an extra execution mechanism.

Description

Single-gimbal control moment gyros control method for coordinating based on svd

Technical field

The present invention relates to a kind of attitude control method of spacecraft, be specifically related to a kind of control method of single-gimbal control moment gyros.

Background technology

Along with the development of aerospace industry, modern spacecraft is more and more higher to the requirement of precision, life-span and the reliability of attitude control system.It is mainly to export control moment by topworks to realize that spacecraft is controlled in the rail attitude.

The attitude control actuator of spacecraft employing at present mainly contains jet thrust device, angular momentum exchange device, magnetic torquer etc.Wherein the angular momentum exchange device has can provide continuous attitude control moment, non-consume fuel, do not pollute optical device and flight environment of vehicle, the advantages such as vibration of not easy excitated spacecraft flexible appendage, thereby as the main actuating mechanism of spacecraft attitude control system and be widely used in high precision, long-life spacecraft.

The principle of work of angular momentum exchange device is based upon on the basis of the conservation of angular momentum, when the size of its angular momentum or direction change according to certain rules, act on the spacecraft body producing the continuous moment of reaction, thereby reach the purpose of controlling spacecraft attitude.In all kinds of angular momentum exchange devices, single-gimbal control moment gyros (Single Gimbal Control Moment Gyros, SGCMGs) can not only export the amplitude control moment, also has simple in structure, the advantage such as reliability is high, faster system response, control are more accurate, become the first-selected attitude control actuator of the actual medium-and-large-sized long-life spacecraft of engineering, all adopted SGCMGs to control main actuating mechanism as attitude as the large-scale space telescope (LST) of the U.S. and the Mir space station (MIR) of USSR (Union of Soviet Socialist Republics) emission.China starts late about the research of CMGs, and Beijing Control Engineering Inst. began to develop mechanical bearing SGCMGs in 1999, and is successfully applied to first target aircraft of Heavenly Palace of in September, 2011 emission.

When using SGCMGs to carry out attitude control to spacecraft, need at first design the manipulation rule of SGCMGs, determine gyro gimbal angular velocity by the instruction control moment, make the gyro output torque consistent with the instruction moment of spacecraft attitude control system requirement.Yet the intrinsic configuration singularity problem of SGCMGs is but given to handle to restrain to design and has been brought very large difficulty.The configuration singularity of SGCMGs refers to when being in some frame corners combination, the output torque vector of each gyro is coplanar, be that the moment of requirement can't be provided on unusual direction and make in the direction perpendicular to this plane, particularly when having the part gyro to lose efficacy in SGCMGs, quantity corresponding to unusual frame corners combination can sharply increase, and makes singular problem more serious.Although many scholars have carried out large quantity research to this, still there are some problems in designed manipulation rule, handles rule as zero motion and can't avoid aobvious singular point, and approach when unusual at the SGCMGs configuration, and the frame corners velocity solution is excessive even without solution; Robust pseudoinverse and broad sense robust pseudoinverse are handled rule all can introduce the moment error, and attitude control accuracy is descended.

On the other hand, at present the fit spacecraft of existing large-scale groups mostly adopts the structure of many cabins section in the world, and its attitude control actuator includes two cover pentagonal pyramid configuration SGCMGs at least, is installed on respectively one of application cabin of core cabin and docking.In traditional control program, core cabin SGCMGs is generally used for the attitude of independent core cabin and the rear whole assembly of docking and controls, and only controls for the front attitude of using the cabin of docking and use cabin SGCMGs.The problem of this scheme maximum is, when only utilizing core cabin SGCMGs to carry out assembly when controlling, if the part gyro breaks down, the existing rule of handling can't guarantee that SGCMGs can realize the unusual accurate output of avoiding fully with moment simultaneously.

The present invention proposes a kind of control method for coordinating based on svd that is applied to SGCMGs just for this difficulties, and being intended to provides technical support for the domestic Large Spacecraft attitude control task with future now.

Summary of the invention

The objective of the invention is for the spacecraft with two cover pentagonal pyramid configuration SGCMGs controls, a kind of SGCMGs control method for coordinating is proposed, guarantee when the part gyro lost efficacy and gyro when unusual, still can make gyro export accurately and efficiently control moment to control the attitude of spacecraft.

The invention provides a kind of single-gimbal control moment gyros control method for coordinating based on svd, have two cover pentagonal pyramid configuration SGCMGs at spacecraft, and wherein the part gyro (comprising 1,2 or 3) of A cover lost efficacy, in the situation of B cover normal operation, can be suitable for method of the present invention.

Method of the present invention comprises the following steps:

Step 1, will control the required instruction moment of whole spacecraft distribute to by a certain percentage two the cover SGCMGs;

Step 2, the method for utilizing svd are decomposed again to the instruction moment of distributing to A cover SGCMGs, to wherein distribute to B cover SGCMGs along the instruction moment components of the unusual direction of A cover SGCMGs, and still distribute to A cover SGCMGs perpendicular to the instruction moment components of the unusual direction of A cover SGCMGs;

Step 3, assigned after, A cover SGCMGs utilizes pseudoinverse to handle rule and solves its instruction frame corners speed, B cover SGCMGs utilizes pseudoinverse to add zero motion and handles rule and solve its instruction frame corners speed;

Step 4, two cover SGCMGs press respectively instruction frame corners speed running separately, and the output torque sum acts on spacecraft, completes accurate attitude and controls.

Beneficial effect

In the situation that need not to configure extra topworks, the inventive method takes full advantage of the control ability of two cover SGCMGs, coordination by two cover SGCMGs is controlled, well solved insurmountable problem when utilizing separately a cover SGCMGs to carry out Spacecraft Attitude Control, guarantee when the part gyro lost efficacy and gyro when unusual, still can make gyro export accurately and efficiently control moment to control the attitude of spacecraft, also avoid to the full extent the possibility of single cover SGCMGs Premature saturation.

Description of drawings

Fig. 1 is the structural representation of single frame control-moment gyro (SGCMG).

Fig. 2 is the configuration schematic diagram of two cover SGCMGs.

Fig. 3 is two cover SGCMGs control method for coordinating schematic diagrams based on svd.

Fig. 4 is the assembly spacecraft attitude control system based on two cover SGCMGs.

Fig. 5 is the unusual tolerance figure as a result of A cover SGCMGs.

Fig. 6 is the actual frame angular velocity figure as a result of A cover SGCMGs.

Fig. 7 is the error result figure of the actual output torque and instruction control moment of two cover SGCMGs.

Embodiment

Below in conjunction with accompanying drawing, describe the preferred embodiment of the present invention in detail.

Be the clearer the present embodiment of introducing, the principle of simple declaration SGCMG output torque at first, then in conjunction with the enforcement of SGCMGs explanation this method of two cover pentagonal pyramid configurations.It is emphasized that the method only needs the SGCMGs of two cover pentagonal pyramid configurations, and and do not rely on concrete mounting means.

Referring to Fig. 1, SGCMG is by the rotor of a constant revolution and the system framework of support rotor,

Be rotor spin axis direction,

Be the gimbal axis rotary speed direction,

With output control moment opposite direction.Rotor spin axis and gimbal axis quadrature are installed, and are driven by rotor electric machine and frame motor respectively.Rotor electric machine drives rotor around the spin axis constant speed rotary, produces a constant angle momentum.Frame motor according to steering order make framework around the gimbal axis that is fixed on the spacecraft body with angular velocity

Turn over frame corners δ.Due to the rotation of gimbal axis, cause rotor spin axis direction to change, the angular momentum of rotor is changed, thereby export a gyroscopic couple.For single SGCMG, according to the principle of work of above introduction, can obtain its control moment of exporting and be

$\stackrel{\&RightArrow;}{T}=-\left(\stackrel{\&CenterDot;}{\mathrm{\&delta;}}\stackrel{\&RightArrow;}{g}\right)\&times;\left(h_0\stackrel{\&RightArrow;}{s}\right)=-{\mathrm{<figure-callout\; id="0"\; label="h"\; filenames="HDA0000130508730000031.png,HDA0000130508730000041.png"\; state="\{\{state\}\}">h</figure-callout>}}_0\stackrel{\&CenterDot;}{\mathrm{\&delta;}}\stackrel{\&RightArrow;}{t}---\left(1\right)$

Wherein,

The moment vector that represents single SGCMG output, h ₀Nominal angular momentum for gyrorotor.

The gyroscopic couple that single SGCMG produces and is controlled for spacecraft being carried out three axles only on the plane vertical with its gimbal axis, generally need to be no less than 3 SGCMG and form gyro groups, adjusts direction and the size of output torque by different frames angle array mode.For the SGCMGs system that is made of a plurality of gyros, simple for making steering logic, the single gyro in gyro group is in quality, and identical value is got in the parameter such as rotor speed and moment of inertia aspect, therefore single the angular momentum amplitude h that gyro provides ₀All identical.If gyro group is comprised of n gyro, the gimbal axis direction unit vector of i gyro is

Rotor angular momentum direction unit vector is

Gyro output torque unit vector in the other direction is

The total angular momentum of gyro group can be expressed as

${\stackrel{\&RightArrow;}{h}}_c={\mathrm{<figure-callout\; id="0"\; label="h"\; filenames="HDA0000130508730000031.png,HDA0000130508730000041.png"\; state="\{\{state\}\}">h</figure-callout>}}_0\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{\stackrel{\&RightArrow;}{s}}_i---\left(2\right)$

Wherein,

Be the total angular momentum vector of system, it is write as at spacecraft body coordinate system f _b(o _bx _by _bz _b) under component array form be

h _c＝A _sh ₀ (3)

Wherein, A _s=[s ₁s ₂S _n], s _iAngular momentum direction unit vector for i SGCMG of correspondence

At f _bIn the component array.

In like manner, according to formula (1), the resultant couple vector that can obtain gyro group output is

${\stackrel{\&RightArrow;}{T}}_c={-\mathrm{<figure-callout\; id="0"\; label="h"\; filenames="HDA0000130508730000031.png,HDA0000130508730000041.png"\; state="\{\{state\}\}">h</figure-callout>}}_0\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{\stackrel{\&CenterDot;}{\mathrm{\&delta;}}}_i\stackrel{\&RightArrow;}{t_i}---\left(4\right)$

Wherein,

Be the resultant moment vector of n gyro generation,

Be the frame corners speed of i gyro.It is write as at f _b(o _bx _by _bz _b) under component array form be

$T_c={-h}_0{A}_t\stackrel{\&CenterDot;}{\mathrm{\&delta;}}---\left(5\right)$

Wherein, A _t=[t ₁t ₂T _n], t _iBe the output torque of i SGCMG of correspondence unit vector in the other direction

At f _bIn the component array, $\stackrel{\&CenterDot;}{\mathrm{\&delta;}}={\left[\begin{array}{cccc}{\stackrel{\&CenterDot;}{\mathrm{\&delta;}}}_1& {\stackrel{\&CenterDot;}{\mathrm{\&delta;}}}_2& \&CenterDot;\&CenterDot;\&CenterDot;& {\stackrel{\&CenterDot;}{\mathrm{\&delta;}}}_n\end{array}\right]}^T$ Be frame corners speed column vector.

In formula (3) and formula (5), A _sAnd A _tBe variable, change with gyro gimbal angle δ, can be written as

A _s＝A _s0d[cosδ]+A _t0d[sinδ] (6)

A _t＝A _t0d[cosδ]-A _s0d[sinδ] (7)

In formula, A _s0And A _t0Be respectively A _sAnd A _tInitial value, cos δ=[cos δ ₁Cos δ ₂... cos δ _n] ^T, sin δ=[sin δ ₁Sin δ ₂... sin δ _n] ^TTo any n-dimensional vector x=[x ₁x ₂X _n] ^T, operator d[x] and be defined as following diagonal matrix

d[x]＝diag(x ₁ x ₂ … x _n) (8)

The equation of angular momentum (3) and the momental equation (5) of the SGCMGs of n gyro composition have below been obtained respectively.

Referring to Fig. 2, the pentagonal pyramid configuration is comprised of 6 SGCMG, and they are mounted respectively on 6 adjacent sides of regular dodecahedron, and the angle on arbitrary neighborhood two sides is 116.51 °, and the gimbal axis of each gyro is symmetrical, respectively perpendicular to its side, place.Consider to have the SGCMGs of A and B two cover pentagonal pyramid configurations to be arranged in spacecraft, supposing has the part gyro to lose efficacy in A cover SGCMGs, the number of the gyro of residue normal operation is n (3≤n≤6), normal operation fully of B cover SGCMGs, and the spacecraft body coordinate system still is designated as f _b(o _bx _by _bz _b).The below is namely concrete implementation step of the present invention.

The first step: will control the required instruction moment of whole spacecraft and distribute to by a certain percentage two cover SGCMGs.Preferred scheme is to carry out moment according to the minimum envelop angular momentum size of two cover SGCMGs and distribute.Suppose that the total instruction control moment that obtains from designed attitude controller is T _c, from avoiding two angles that gyro is saturated, can at first distribute total instruction control moment according to the minimum envelop angular momentum size of two cover SGCMGs, wherein, the instruction control moment of distributing to A cover inefficacy SGCMGs is T _ca, be expressed as

$T_{\mathrm{ca}}=\frac{h_{\mathrm{an}}}{h_{\mathrm{an}}+4.4719}{T}_c---\left(9\right)$

The instruction control moment of distributing to B cover SGCMGs is T _cb, be expressed as

$T_{\mathrm{cb}}=\frac{4.4719}{h_{\mathrm{an}}+4.4719}{T}_c---\left(10\right)$

Wherein, h _anEqual the minimum angular momentum that A overlaps the envelope of the individual SGCMGs of n (3≤n≤6) that works, can utilize numerical method to calculate (reference: Zhang Renwei from formula (3), " satellite orbit and attitude dynamics and control ", publishing house of BJ University of Aeronautics ﹠ Astronautics, 281-285).

Second step is based on the moment reallocation of svd theory.Utilize the theory of svd to T _caCarry out sub-distribution again, obtain respectively the moment components T perpendicular to the unusual direction of A cover SGCMGs _ca1With the moment components T along the unusual direction of A cover SGCMGs _ca2For describing the implementation process of the present embodiment in detail, the below will describe how to obtain T in detail _ca1And T _ca2Expression formula.

Referring to Fig. 3,

Overlap the unit vector of the unusual direction of SGCMGs for A, order (i=1,2 ..., n) the output torque opposite direction unit vector of remaining n normal gyro in the unusual moment A cover of (3≤n≤6) expression SGCMGs.For right

Sub-distribution again determines that unusual direction is crucial.Output torque matrix of coefficients C to inefficacy SGCMGs _aCarry out svd, obtain

C _a＝h ₀A _at＝USV ^T (11)

In formula, A _at=A _at0D[cos δ _a]-A _as0D[sin δ _a], U ∈ R ^{3 * 3}, V ∈ R ^{N * n}, be unitary matrix.S ∈ R ^{3 * n}Can be written as following form

S＝[S ₁ 0 _3×(n-3)] (12)

In formula

S ₁＝diag(σ ₁ σ ₂ σ ₃) (13)

σ wherein ₁, σ ₂And σ ₃Be C _aSingular value, and satisfy σ ₁〉=σ ₂〉=σ ₃V also can be written as

V＝[V ₁ V ₂] (14)

V in formula ₁∈ R ^{N * 3}, V ₂∈ R ^{N * (n-3)}U and V ₁Can be expressed as U=[U by its column vector ₁U ₂U ₃], V ₁=[V ₁₁V ₁₂V ₁₃], the output torque equation for inefficacy SGCMGs can be written as

$C_a{\stackrel{\&CenterDot;}{\mathrm{\&delta;}}}_a={\mathrm{US}}_1{V}_1^T{\stackrel{\&CenterDot;}{\mathrm{\&delta;}}}_a=\underset{i=1}{\overset{3}{\mathrm{\&Sigma;}}}{\mathrm{\&sigma;}}_i{U}_i{V}_{1i}^T{\stackrel{\&CenterDot;}{\mathrm{\&delta;}}}_a=-T_{\mathrm{ca}1}---\left(15\right)$

T in formula _ca1Be the instruction moment perpendicular to unusual direction of distributing to inefficacy SGCMGs.When SGCMGs is absorbed in when unusual fully, σ ₃=0, as can be known this moment U ₃The direction output torque is zero, and U also is described ₃Be the unusual direction of SGCMGs.And as SGCMGs when unusual, σ ₃Also close to zero, U at this moment ₃Also just near unusual direction, can be described as accurate unusual direction.In case determined unusual direction U ₃, just can with SGCMGs when unusual instruction moment at U ₃On the part component and SGCMGs complete when unusual instruction moment at U ₃On whole components distribute to B cover SGCMGs, by B cover SGCMGs output, with the A cover SGCMGs that avoids losing efficacy σ when unusual ₃→ 0 causes the frame corners velocity solution excessive or occur without the phenomenon of separating.

Order is assigned to the U of B cover SGCMGs ₃Instruction moment on direction is

${\mathrm{<figure-callout\; id="2"\; label="T\; ca"\; filenames="HDA0000130508730000022.png,HDA0000130508730000041.png"\; state="\{\{state\}\}">T</figure-callout>}}_{\mathrm{ca}}=\frac{\mathrm{\&alpha;}}{{\mathrm{\&sigma;}}_3+\mathrm{\&alpha;}}{U}_3{U}_3^T{T}_{\mathrm{ca}}---\left(16\right)$

In formula

$\mathrm{\&alpha;}=\left\{\begin{array}{cc}0& D_a\&GreaterEqual;\mathrm{\&epsiv;}\\ k{(D_a-\mathrm{\&epsiv;})}^2,& \mathrm{\&epsiv;}>D_a\&GreaterEqual;0\end{array}\right.---\left(17\right)$

D wherein _aUnusual tolerance for inefficacy SGCMGs is expressed as

D _a＝det(A _atA _at ^T) (18)

ε is positive threshold value, and k is positive scalar parameter, and both can be selected according to actual conditions.The instruction moment of SGCMGs of losing efficacy is

T _ca1＝T _ca-T _ca2＝US _aU ^TT _ca (19)

Wherein

$S_a=\mathrm{<figure-callout\; id="1"\; label="diag"\; filenames="HDA0000130508730000021.png,HDA0000130508730000022.png"\; state="\{\{state\}\}">diag</figure-callout>}\left(\begin{array}{ccc}1& 1& \frac{{\mathrm{\&sigma;}}_3}{{\mathrm{\&sigma;}}_3+\mathrm{\&alpha;}}\end{array}\right)---\left(20\right)$

By formula (16) and (19) as can be known, work as D _a〉=ε can think A cover SGCMGs away from unusual, α=0, σ ₃＞0, S _a=E ₃, T _ca1=T _ca, T _ca2=0, three axle instruction moment T _caDistribute to A cover SGCMGs fully.And work as D _a＜ε, A cover SGCMGs move closer to when unusual, and α increases, σ ₃Reduce, distribute to B cover SGCMGs at unusual direction U ₃On instruction moment also constantly increase, distribute to simultaneously A cover SGCMGs at unusual direction U ₃On instruction moment constantly reduce.Finally, when SGCMGs is unusual, σ ₃=0,

U ₃On instruction moment distribute to B cover SGCMGs fully, guarantee that topworks still can accurately export three axle instruction moments when unusual.

So far, obtained T fully _ca1And T _ca2Expression formula suc as formula shown in (19) and (16).

In the 3rd step, determine to be finally allocated to two moments of overlapping SGCMGs.After distributing through twice moment, last T _cIn distribute to the instruction control moment component T ' of A cover SGCMGs _caBe expressed as

$T_{\mathrm{ca}}^{\&prime;}={\mathrm{<figure-callout\; id="1"\; label="T\; ca"\; filenames="HDA0000130508730000021.png,HDA0000130508730000022.png"\; state="\{\{state\}\}">T</figure-callout>}}_{\mathrm{ca}}={\mathrm{US}}_a{U}^T{T}_{\mathrm{ca}}=\frac{h_{\mathrm{an}}}{h_{\mathrm{an}}+4.4719}{\mathrm{US}}_a{U}^T{T}_c---\left(21\right)$

Distribute to the instruction control moment component T ' of B cover SGCMGs _cbBe expressed as

$T_{\mathrm{cb}}^{\&prime;}=T_{\mathrm{cb}}+{\mathrm{<figure-callout\; id="2"\; label="T\; ca"\; filenames="HDA0000130508730000022.png,HDA0000130508730000041.png"\; state="\{\{state\}\}">T</figure-callout>}}_{\mathrm{ca}}=\frac{4.4719}{h_{\mathrm{an}}+4.4719}{T}_c+\frac{\mathrm{\&alpha;}}{{\mathrm{\&sigma;}}_3+\mathrm{\&alpha;}}\&CenterDot;\frac{h_{\mathrm{an}}}{h_{\mathrm{an}}+4.4179}{U}_3{U}_3^T{T}_c---\left(22\right)$

The 4th step, the manipulation rule design of two cover SGCMGs.For A cover SGCMGs, when it is absorbed in when unusual, only need output perpendicular to the moment of unusual direction, therefore can directly ask the pseudoinverse solution of frame corners speed according to formula (15) and (21), obtain

${\stackrel{\&CenterDot;}{\mathrm{\&delta;}}}_{\mathrm{ca}}=-\frac{h_{\mathrm{an}}}{h_{\mathrm{an}}+4.4719}{V}_1{S}_1^{-1}{S}_a{U}^T{T}_c---\left(23\right)$

For B cover SGCMGs, because its each gyro all works, can its controlled angular momentum body be set to the spheroid take the minimum angular momentum of envelope as radius, hidden singular point is only arranged in this angular momentum body like this, just can effectively use zero motion to handle and restrain.It is unusual to be that convenient A cover SGCMGs is absorbed in, and utilize zero motion to handle rule and also can handle B cover SGCMGs fully and hide singular point, and output is along the moment of the unusual direction of A cover SGCMGs.Zero motion of B cover SGCMGs is handled rule and is designed to

${\stackrel{\&CenterDot;}{\mathrm{\&delta;}}}_{\mathrm{cb}}=-{A_{\mathrm{bt}}}^T{\left(A_{\mathrm{bt}}{A_{\mathrm{bt}}}^T\right)}^{-1}\frac{T_{\mathrm{cb}}^{\&prime;}}{{\mathrm{<figure-callout\; id="0"\; label="h"\; filenames="HDA0000130508730000031.png,HDA0000130508730000041.png"\; state="\{\{state\}\}">h</figure-callout>}}_0}+\mathrm{\&beta;}(I_{6\&times;6}-{A_{\mathrm{bt}}}^T{\left(A_{\mathrm{bt}}{A_{\mathrm{bt}}}^T\right)}^{-1}{A}_{\mathrm{bt}})\frac{{\&PartialD;D}_b\left({\mathrm{\&delta;}}_b\right)}{{\&PartialD;\mathrm{\&delta;}}_b}---\left(24\right)$

In formula, A _bt=A _bt0D[cos δ _b]-A _bs0D[sin δ _b], scalar parameter β chooses as follows,

$\left\{\begin{array}{cc}\mathrm{\&beta;}=0,& D_b>1\\ \mathrm{\&beta;}=5,& D_b\&le;0.5\\ \mathrm{\&beta;}=20{(D_b-1)}^2,& 0.5<D_b\&le;1\end{array}\right.---\left(25\right)$

Wherein, D _b=det (A _btA _bt ^T) be the unusual tolerance of B cover SGCMGs.The concrete theory of this part can with reference to pertinent literature (reference: Zhang Renwei, " satellite orbit and attitude dynamics and control ", publishing house of BJ University of Aeronautics ﹠ Astronautics, 291-293).

So far, A cover and B cover SGCMGs skeleton instruction angular velocity have separately been obtained fully

With

Only need to rotate with the gimbal axis that these two instruction angular speed drive respectively A cover and B cover SGCMGs and just can guarantee when the part gyro lost efficacy and gyro when unusual, control moment is exported accurately and efficiently, and then the attitude of control spacecraft.

Referring to Fig. 4, the solution of the present invention residing position in whole Spacecraft Control loop is dotted line frame part in figure.In figure, (1) is actual attitude angle and angular velocity information; (2) for estimating attitude angle and angular velocity information; (3) be expectation attitude angle and angular velocity information; (4) be the instruction control moment; (5) for distributing to the instruction control moment of inefficacy gyro group; (6) for distributing to the instruction control moment of normal operation gyro group; (7) be perpendicular to the moment components of the unusual direction of inefficacy gyro group in (6); (8) be that (5) are along the moment components of the unusual direction of inefficacy gyro group; (9) for the instruction frame corners speed of inefficacy gyro group; (10) be the instruction frame corners speed of normal operation gyro group; (11) for the actual frame angular velocity of inefficacy gyro group; (12) be the actual frame angular velocity of normal operation gyro group; (13) for the actual output torque of inefficacy gyro group; (14) be the actual output torque of normal operation gyro group; (15) be the two total output torques of cover gyro group; (16) be outer disturbance torque.Spacecraft attitude control system based on two cover SGCMGs consists of close loop control circuit together by attitude sensor, attitude controller, topworks (two cover SGCMGs) and spacecraft body.Attitude sensor is measured and is determined spacecraft with respect to the orientation of some known reference target of space, then determines to determine spacecraft attitude after algorithm is further processed the information that records by attitude.Then determine according to attitude information and the attitude of spacecraft expectation the attitude information that link obtains, select suitable control algorithm design attitude controller, thus the required instruction control moment of controlled spacecraft.Next be exactly to utilize the two cover SGCMGs Coordinated Control Schemes that propose, thereby the frameworks of handling two each gyros of cover SGCMGs move according to certain rules and guarantee that two cover SGCMGs can produce required control moment by steering order.At last, the resultant couple of two cover SGCMGs outputs acts on the spacecraft body, can obtain the attitude response of spacecraft according to the spacecraft attitude dynamics equation of setting up.Because two cover SGCMGs can accurately export control moment, so spacecraft will rotate according to attitude angle and the angular velocity characteristics of motion of expectation.

Below in conjunction with some assembly Spacecraft Attitude Control simulation results, this programme is made specific description.

Referring to Fig. 2, suppose the core cabin in the assembly of space station and use one of cabin a cover pentagonal pyramid configuration SGCMGs all respectively is installed.In figure, o _bx _by _bz _bBe core cabin body coordinate system, initial point o _bBe taken at the barycenter of core cabin module, x _b, y _bAnd z _bBe fixed on the core cabin,

With

Be respectively the gimbal axis direction unit vector of the 1-6 gyro of the A cover SGCMGs that is installed on the core cabin,

With

Be respectively the armature spindle direction unit vector of the 1-6 gyro of A cover SGCMGs.

With

Be respectively the gimbal axis direction unit vector of the 1-6 gyro that is installed on the B cover SGCMGs that uses the cabin,

With

Be respectively the armature spindle direction unit vector of the 1-6 gyro of B cover SGCMGs.Two cover SGCMGs are with respect to installation position such as Fig. 2 of core cabin body coordinate system, the gimbal axis of first gyro in A cover SGCMGs Along

With

The projection that forms the plane with

Direction is consistent, the gimbal axis of first gyro in B cover SGCMGs

Along

With

The projection that forms the plane with

Direction is consistent.Select the reason of this installation position to be that this installation position can guarantee that gyro group has envelope and unusual performance index preferably when two cover SGCMGs work or have the part gyro to lose efficacy.Two cover each gyro initial time rotor angular momentum direction unit vectors of SGCMGs and output torque the component array of unit vector under the body series of core cabin in the other direction are

s _a10＝[1 0 0] ^T，s _a20＝[-sin18° 0 -cos18°] ^T，s _a30＝[-1 0 0] ^T，s _a40＝[-sin18° 0 cos18°] ^T，

s _a50＝[cos36° 0 sin36°] ^T，s _a60＝[cos36° 0 -sin36°] ^T，t _a10＝[0 0 -1] ^T，

t _a20＝[-sin26.57°cos18° -cos26.57° sin26.57°sin18°] ^T，

t _a30＝[0 -cos26.57° sin26.57°] ^T，

t _a40＝[sin26.57°cos18° -cos26.57° sin26.57°sin18°] ^T，

t _a50＝[sin26.57°sin36° -cos26.57° -sin26.57°cos36°] ^T，

t _a60＝[-sin26.57°sin36° -cos26.57° -sin26.57°cos36°] ^T。

s _b10＝[0 0 1] ^T，s _b20＝[0-cos18° -sin18°] ^T，s _b30＝[0 0 -1] ^T，s _b40＝[0cos18° -sin18°] ^T，

s _b50＝[0sin36°cos36°] ^T，s _b60＝[0 -sin36° cos36°] ^T，t _b10＝[0 -1 0] ^T，

t _b20＝[-cos26.57°sin26.57°sin18°-sin26.57°cos18°] ^T，

t _b30＝[-cos26.57°sin26.57°0] ^T，

t _b40＝[-cos26.57°sin26.57°sin18°sin26.57°cos18°] ^T，

t _b50＝[-cos26.57°-sin26.57°cos36°sin26.57°sin36°] ^T，

t _b60＝[-cos26.57°-sin26.57°cos36°-sin26.57°sin36°] ^T。

The nominal angular momentum of supposing each gyro is 180Nms, and the 5th and the 6th the gyro inefficacy of hypothesis A cover SGCMGs, the initial frame corners δ of A cover SGCMGs _a0=[pi/2 00 0] ^T, the initial frame corners δ of B cover SGCMGs _b0=[pi/2 0000 0] ^TIn order to carry out numerical simulation, also need A cover and the final output torque of B cover SGCMGs are synthesized.Specific practice is: the Gimbal servo system of supposing each gyro can realize accurate control, can think that the actual frame angular velocity and instruction frame corners speed of each gyro equates, namely

After having arrived the instruction frame corners speed of A cover SGCMGs and each gyro of B cover SGCMGs in the 4th step in implementation step, so again according to gyro output torque equation (5), the actual output torque that can obtain A cover and B cover SGCMGs is respectively

$T_{\mathrm{ra}}={-h}_0{A}_{\mathrm{at}}{\stackrel{\&CenterDot;}{\mathrm{\&delta;}}}_{\mathrm{ra}}---\left(26\right)$

$T_{\mathrm{rb}}={-h}_0{A}_{\mathrm{bt}}{\stackrel{\&CenterDot;}{\mathrm{\&delta;}}}_{\mathrm{rb}}---\left(27\right)$

Finally synthesize by moment, can obtain two cover SGCMGs total output torques and be

T _r＝T _ra+T _rb (28)

Adopt the PID control law to carry out the Large angle maneuver control of assembly spacecraft.As Fig. 5 and Fig. 6 as seen, during to the 2800s left and right, A cover SGCMGs is very near unusual in simulation run, but this moment, its frame corners speed was not undergone mutation, and A overlaps SGCMGs and keeps controlled in whole process.Simultaneously, as shown in Figure 7, in whole process, the two total output torque and instruction of cover SGCMGs control moment errors all maintain in 10-14Nm, and the moment output accuracy is very high.

In sum, the present invention has provided a kind of single-gimbal control moment gyros control method for coordinating based on svd.When a cover pentagonal pyramid configuration SGCMGs who installs on the assembly of space station has 3 gyros to break down at the most, can unite mounted another set of SGCMGs and coordinate to control.Utilize the method for svd to make fault SGCMGs only need to export instruction moment perpendicular to unusual direction, and will distribute to normal SGCMGs along the instruction moment of unusual direction.Adopt this Coordinated Control Scheme, can guarantee the complete controllability of fault SGCMGs when experience is unusual, can guarantee that again total output torque and instruction moments of two cover SGCMGs conform to fully, thereby improved the precision that attitude is controlled.The present invention can be applied in the Large Spacecraft tasks such as space station.

The above is only the preferred embodiment of the present invention; should be understood that; for those skilled in the art; under the prerequisite that does not break away from the principle of the invention; can also make some improvement; perhaps part technical characterictic wherein is equal to replacement, these improvement and replace and also should be considered as protection scope of the present invention.

Claims (1)

1. single-gimbal control moment gyros control method for coordinating based on svd, the method is applicable to spacecraft and has two cover pentagonal pyramid configuration single-gimbal control moment gyros, and wherein the A cover has 1,2 or 3 gyros inefficacies, and the situation of B cover normal operation comprises the following steps:

The minimum envelop angular momentum sizes of step 1, foundation two cover single-gimbal control moment gyros are carried out moment and are distributed: suppose that controlling the required instruction moment of whole spacecraft is T _c, the instruction moment of distributing to A cover inefficacy single-gimbal control moment gyros is T _ca, be expressed as

$T_{\mathrm{ca}}=\frac{h_{\mathrm{an}}}{h_{\mathrm{an}}+4.4719}{T}_c$

The instruction moment of distributing to B cover single-gimbal control moment gyros is T _cb, be expressed as

$T_{\mathrm{cb}}=\frac{4.4719}{h_{\mathrm{an}}+4.4719}{T}_c$

Wherein, h _anOverlap the minimum angular momentum of the envelope of n the single-gimbal control moment gyros that works for A, the span of n is 3≤n≤6;

Step 2, the method for utilizing svd are decomposed again to the instruction moment of distributing to A cover single-gimbal control moment gyros, to wherein distribute to B cover single-gimbal control moment gyros along the instruction moment components of the unusual direction of A cover single-gimbal control moment gyros, and still distribute to A cover single-gimbal control moment gyros perpendicular to the instruction moment components of the unusual direction of A cover single-gimbal control moment gyros;

Step 3, assigned after, A cover single-gimbal control moment gyros utilizes pseudoinverse to handle rule and solves its instruction frame corners speed, B cover single-gimbal control moment gyros utilizes pseudoinverse to add zero motion and handles rule and solve its instruction frame corners speed;

Step 4, two cover single-gimbal control moment gyros are pressed respectively instruction frame corners speed running separately, and the output torque sum acts on spacecraft, completes accurate attitude and controls.

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