CN103034237A - Spacecraft attitude maneuver control method using two single-frame control moment gyroscopes - Google Patents

Abstract

A spacecraft attitude maneuver control method using two single-frame control moment gyroscopes comprises three control stages. A first stage is a gyroscope initial singularity dodging stage which is composed of a gyroscope stage judgment logic and a gyroscope singularity separation controller and enables two single-frame control torque gyroscopes to break away of possible inner singularity and outer singularity at an initial moment of controlling, and the control of a second stage is entered. The second stage is an error attitude convergence stage which is composed of an error attitude convergence controller and aims to enable the attitude error convergence of a spacecraft to be restrained within a specified attitude error convergence stage, and the control of a third stage is entered. The third stage is a steady state control stage which is composed of a steady state controller, aims to conduct further attitude convergence and ensures that the convergence of a frame indication rotating speed stably reaches zero. The spacecraft attitude maneuver control method of using two single frame control torque gyroscopes is capable of being used under the condition that part of a control torque gyroscope group in the spacecraft losses efficiency and further used for attitude control of the spacecraft which is provided with only two parallel single frame control torque gyroscopes.

Description

Use the Spacecraft During Attitude Maneuver control method of two single frame control-moment gyros

[technical field]

The invention belongs to the Spacecraft Attitude Control technical field, be specifically related to the Spacecraft During Attitude Maneuver control method of two single frame control-moment gyros of a kind of use.Be zero or hour, this control method can be utilized the single frame control-moment gyro of two parallel installations in the total angular momentum of celestial body and gyro, with spacecraft maneuver to any targeted attitude of expectation.

[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.Spacecraft mainly is to realize by topworks's output control moment in the control of rail attitude.

The single frame control-moment gyro belongs to a kind of angular momentum exchange device, and it rotates the angular momentum direction of the rotor that changes constant rotational speed by framework, thereby produces the moment that reacts on continuously spacecraft.In all kinds of attitude control actuators of spacecraft, single-gimbal control moment gyros (Single Gimbal Control Moment Gyros, SGCMGs) can not only export the amplitude control moment, also have simple in structure, the advantage such as reliability is high, faster system response, control are more accurate.Therefore, SGCMGs is specially adapted to the large-scale long-life spacecraft of the larger control moment of demand, quick satellite, for example, Mir space station (MIR), the Pleiades-HR satellite of No. one, Heavenly Palace and France has all adopted SGCMGs to control main actuating mechanism as attitude.On the other hand, under same moment output requires, the quality of SGCMGs is light, volume is little, power consumption is little, SGCMGs is applicable to again quality, volume are needed harsh small-sized spacecraft, for example, used two small-sized SGCMGs to realize the control of single shaft attitude on the osmanli micro-satellite BILSAT-1.

A key issue using SGCMGs is the appropriate manipulation rule of design, overcomes the singular problem of gyro.The configuration singularity of SGCMGs refers to when being in some frame corners combination, the moment output matrix contraction of SGCMGs, the anti-frame corners speed of separating of can not inverting.Design has had more solution for the manipulation of the gyro group that is comprised of the SGCMGs more than three or three rule, and is still, more rare for the manipulation rule scheme of two SGCMGs only.On the other hand, because long-time operation on orbit, employed one or more the single SGCMGs of spacecraft inevitably breaks down or lost efficacy, when the number of the SGCMGs that works is less than three, spacecraft becomes owes drive system, can't realize in any case the attitude control of three axles.On the other hand, for the microminiature satellite, because the restriction of quality and volume often can not be backed up unnecessary topworks, therefore, expectation adopts less topworks to realize attitude control function.

For this active demand, this patent proposes a kind of Spacecraft During Attitude Maneuver control method of only using the SGCMGs of two parallel installations, both can tackle part SGCMGs lost efficacy, improve the reliability of spacecraft attitude control system, can how to use two SGCMGs for the microminiature satellite again and carry out attitude control a solution is provided.

[summary of the invention]

The present invention is directed to the spacecraft with the SGCMGs of two parallel installations, is zero or hour in the total angular momentum of spacecraft and gyrosystem, realizes directed more arbitrarily to inertial space of spacecraft, and evade the unusual of two SGCMGs in control procedure.The present invention both can be used for the Spacecraft Attitude Control after certain a pair of inefficacy among the SGCMGs of two parallel configuration, was applicable to again directly to use the attitude of the microminiature satellite of two parallel installations to control.

The Spacecraft During Attitude Maneuver control method of two single frame control-moment gyros of a kind of use of the present invention comprises three control stages:

In the stage one, initial unusual evading the stage of gyro, it is comprised of the unusual decision logic of gyro and the unusual disengaging controller of gyro.Whether the error size of check initial time spacecraft and expectation attitude and two SGCMGs are near unusual.Make m ₀0 expression initial time attitude error threshold value, its occurrence can be selected in actual applications.If attitude error is less than m ₀, perhaps gyro then directly enters the stage two away from unusual.If attitude error is greater than m ₀, and gyro is near unusual, the large reverse speed driver framework such as then utilizes to rotate regular hour T ₀0, it is unusual that gyro is broken away from, and expression formula is suc as formula shown in (1):

$\begin{array}{c}{\stackrel{\&CenterDot;}{\mathrm{\&delta;}}}_1={\mathrm{<figure-callout\; id="0"\; label="b"\; filenames="HDA00002667030100042.png,HDA00002667030100043.png"\; state="\{\{state\}\}">b</figure-callout>}}_0\\ {\stackrel{\&CenterDot;}{\mathrm{\&delta;}}}_2=-b_0\end{array}---\left(1\right)$

Wherein,

With

It is the framework rotating speed of two SGCMGs; b ₀Be positive constant, generally select littlely, in order to avoid after switching to follow-up attitude maneuver control model, cause larger frame corners velocity jump.

Stage two, error attitude converged state, it mainly is comprised of error attitude convergence controller.The Z that is parallel to the spacecraft body take the gimbal axis of two SGCMGs illustrates this controller algorithm as example, and practical application is not limited to this, and two SGCMGs can install arbitrarily in the spacecraft body, only need to carry out coordinate conversion to the corresponding entry in this algorithm and get final product.Make that { X Y Z} represents the body of the spacecraft coordinate system that is connected, J=diag (J ₁J ₂J ₃) inertia matrix of the system that spacecraft and gyro form when locking for gyro, wherein diagonal matrix, ω=[ω are got in diag () expression ₁ω ₂ω ₃] ^TThe angular velocity of expression spacecraft is at three components of body coordinate system.

At first, the calculation expectation attitude angular velocity, expression formula is suc as formula shown in (2):

$\left[\begin{array}{c}{\mathrm{\&omega;}}_{\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="HDA00002667030100021.png,HDA00002667030100031.png"\; state="\{\{state\}\}">d</figure-callout>}1}\\ {\mathrm{\&omega;}}_{\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="HDA00002667030100021.png,HDA00002667030100022.png"\; state="\{\{state\}\}">d</figure-callout>}2}\end{array}\right]=-k\left[\begin{array}{c}{\mathrm{\&rho;}}_1\\ {\mathrm{\&rho;}}_2\end{array}\right]+g\left[\begin{array}{c}\mathrm{sat}({\mathrm{\&Delta;}}_2,a)\\ -\mathrm{sat}({\mathrm{\&Delta;}}_1,a)\end{array}\right]---\left(2\right)$

Wherein, ω _D1With ω _D2Expression is along the expectation attitude angular velocity of X and Y-axis;

ρ=[ρ ₁ρ ₂ρ ₃] ^TFor describing the Rodrigues parameter of spacecraft attitude; Ride gain g and k are positive constant, are Δ in the process that guarantees the attitude error convergence ₁And Δ ₂Receipts pour into zero, make their selection satisfy g〉2k; Sat (x is suc as formula the saturation function shown in (3) a):

$\mathrm{sat}(x,a)=\begin{array}{c}\left\{\begin{array}{cc}x,& -a\&le;x\&le;a\\ a,& x>a\\ -a,& x<a\end{array}\right.---\left(3\right)\end{array}$

Wherein, x is aleatory variable; A is saturation boundary, is positive constant, can select according to actual needs.

Then, follow the tracks of control law according to angular velocity, the computations control moment, expression formula is suc as formula shown in (4) and the formula (5):

$\begin{array}{c}{\stackrel{\&CenterDot;}{\mathrm{\&omega;}}}_1=k_1({\mathrm{\&omega;}}_{d1}-{\mathrm{\&omega;}}_1)\\ {\stackrel{\&CenterDot;}{\mathrm{\&omega;}}}_2=k_1({\mathrm{\&omega;}}_{d2}-{\mathrm{\&omega;}}_2)\end{array}---\left(4\right)$

$T_c=\left[\begin{array}{c}{\mathrm{<figure-callout\; id="1"\; label="J"\; filenames="HDA00002667030100021.png,HDA00002667030100031.png"\; state="\{\{state\}\}">J</figure-callout>}}_1{\stackrel{\&CenterDot;}{\mathrm{\&omega;}}}_1\\ {\mathrm{<figure-callout\; id="2"\; label="J"\; filenames="HDA00002667030100021.png,HDA00002667030100022.png"\; state="\{\{state\}\}">J</figure-callout>}}_2{\stackrel{\&CenterDot;}{\mathrm{\&omega;}}}_2\end{array}\right]---\left(5\right)$

Wherein, k ₁And k ₂Be normal number, in working control, select; T _cBe the instruction control moment;

At last, computations frame corners speed, expression formula is suc as formula shown in (6):

$\stackrel{\&CenterDot;}{\mathrm{\&delta;}}=\frac{1}{h_0}{D}_s^{-1}{T}_c---\left(6\right)$

Wherein, $\stackrel{\&CenterDot;}{\mathrm{\&delta;}}={\left[\begin{array}{cc}{\stackrel{\&CenterDot;}{\mathrm{\&delta;}}}_1& {\stackrel{\&CenterDot;}{\mathrm{\&delta;}}}_2\end{array}\right]}^T,$ h ₀Angular momentum (at this, supposing the angular momentum equal and opposite in direction of two gyrorotors) for gyrorotor; For calculating

Need explanation moment output matrix, shown in (7):

$D=\left[\begin{array}{cc}\sin {\mathrm{\&delta;}}_1& \sin {\mathrm{\&delta;}}_2\\ -\cos {\mathrm{\&delta;}}_1& -{\cos \mathrm{\&delta;}}_2\end{array}\right]---\left(7\right)$

Wherein, δ ₁And δ ₂Framework corner for gyro; Matrix D is carried out svd suc as formula shown in (8):

D=USV ^T (8)

U and V are orthogonal matrix; S=diag (σ ₁σ ₂), σ ₁And σ ₂Be two singular values of matrix D, and satisfy σ ₁〉=σ ₂〉=0; Computing method suc as formula shown in (9):

$D_s^{-1}={\mathrm{VS}}_{\mathrm{\&gamma;}}^{-1}{U}^T---\left(9\right)$

Wherein, $S_{\mathrm{\&gamma;}}^{-1}=\mathrm{<figure-callout\; id="1"\; label="diag"\; filenames="HDA00002667030100021.png,HDA00002667030100031.png"\; state="\{\{state\}\}">diag</figure-callout>}\left(\begin{array}{cc}1/{\mathrm{\&sigma;}}_1& 1/({\mathrm{\&sigma;}}_2+\mathrm{\&gamma;})\end{array}\right),$ γ chooses according to formula (10):

$\mathrm{\&gamma;}=\left\{\begin{array}{cc}0,& \mathrm{\&lambda;}\&GreaterEqual;{\mathrm{\&lambda;}}_D\\ k_D{(1-\frac{\mathrm{\&lambda;}}{{\mathrm{\&lambda;}}_D})}^2,& \mathrm{\&lambda;}\&le;{\mathrm{\&lambda;}}_D\end{array}\right.---\left(10\right)$

Wherein, k _DFor positive normal value, in control procedure, specify; λ _DBe the positive number of appointment in the control implementation process, λ represents the unusual tolerance of D, calculates by formula (11):

λ＝det(DD ^T) (11)

Make m _sThe attitude error threshold value of 0 expression expectation, its occurrence can be specified in actual applications, judges whether attitude error converges in the threshold range of appointment, if attitude error is greater than m _s, then continue use error attitude convergence controller and control; If attitude error is less than or equal to m _s, the control that then enters the stage three.

In the stage three, in the stable state control stage, it mainly is comprised of steady-state controller, namely according to formula (12) computations frame corners speed:

$\stackrel{\&CenterDot;}{\mathrm{\&delta;}}=\frac{D^T\stackrel{\&OverBar;}{m}}{h_0{\stackrel{\&OverBar;}{m}}^T{\mathrm{DD}}^T\stackrel{\&OverBar;}{m}+\mathrm{\&epsiv;}}\stackrel{\&CenterDot;}{v}---\left(12\right)$

Wherein,

$m=\frac{s_1+s_2}{\left|\right|s_1+s_2\left|\right|}=\left[\begin{array}{c}{m}_x\\ m_{\mathrm{<figure-callout\; id="0"\; label="y"\; filenames="HDA00002667030100042.png,HDA00002667030100043.png"\; state="\{\{state\}\}">y</figure-callout>}}\\ 0\end{array}\right],$ $\stackrel{\&OverBar;}{m}=\left[\begin{array}{c}{m}_x\\ m_y\end{array}\right]---\left(13\right)$

m ^TJω=v (14)

$\stackrel{\&CenterDot;}{v}=k_v(v_d-v)---\left(15\right)$

v _d=-k _d(ρ ₁a ₁+ρ ₂a ₂) (16)

In the equation above, k _dAnd k _vBe positive constant, selected in working control; a ₁=m _x/ J ₁And a ₂=m _x/ J ₂V represents selected intermediate variable, by top expression formula as can be known, expression be the projection of angular momentum on the separated time of the angle of two rotor vectors of spacecraft;

Time-derivative for v; And v _dThe expectation value of expression intermediate variable.In addition, ε is positive a small amount of, can be selected according to actual conditions, its introducing be for fear of

The time, may cause larger frame corners speed.

So far, narrated complete to three phases of the present invention.

The present invention is the Spacecraft During Attitude Maneuver control method of two single frame control-moment gyros of a kind of use, has the following advantages:

(1) the present invention has realized the motor-driven control of the three-axis attitude of spacecraft in the situation of only using two SGCMGs.In the attitude of traditional spacecraft is controlled, for realizing three-axis attitude control, need at least three SGCMGs, when part SGCMGs lost efficacy, when only being left two normal operations, can't realize normal attitude control function.Adopt method of the present invention, can be to the spacecrafts of surplus two parallel SGCMGs normal operations only, be in zero the situation in the total angular momentum of system, it is directed again to carry out attitude, guarantee the normal attitude control function of spacecraft, improve the reliability of attitude control system, prolong the lifetime of satellite.On the other hand, for the microminiature satellite that two SGCMGs only are installed, generally only utilize two SGCMGs to realize the attitude control of single shaft, adopt method of the present invention, can make the microminiature satellite realize better three-axis attitude control function.

(2) the unusual bypassing method of combination of the present invention's proposition has incorporated attitude error information, be in when unusual in that large and two SGCMGs of attitude error are two, it is outer unusual and interior unusual that two SGCMGs are broken away from, and when attitude error is restrained, can guarantee higher moment output accuracy.

(3) the attitude motion equation stability controller form based on the Rodrigues parameter of the present invention's proposition is simpler, and traditional method then needs to carry out complicated coordinate conversion, and the present invention has provided the ride gain alternative condition of avoiding controller unusual.

(4) the present invention proposes the attitude controller of stable state, solved in the Spacecraft During Attitude Maneuver control procedure, along with the convergence of attitude error, two SGCMGs must be tending towards interior unusual contradiction.

[description of drawings]

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

Fig. 2 is the spacecraft synoptic diagram with the SGCMGs of two parallel installations.

The outer unusual synoptic diagram of two parallel SGCMGs of Fig. 3.

The interior unusual synoptic diagram of two parallel SGCMGs of Fig. 4.

Fig. 5 attitude maneuver control flow synoptic diagram.

The unusual tolerance of two SGCMGs of Fig. 6.

Fig. 7 skeleton instruction angular velocity.

The error attitude Rodrigues parameter of Fig. 8 spacecraft.

The angular velocity of Fig. 9 spacecraft.

Symbol description is as follows among the figure:

S is rotor spin axis direction among Fig. 1, and g is the gimbal axis direction, t and output control moment opposite direction, and they are unit vector.

X, Y, Z represent be connected three change in coordinate axis direction of coordinate system of the body of spacecraft, g among Fig. 2, Fig. 3 and Fig. 4 ₁With g ₂Be the gimbal axis direction of two SGCMGs, s ₁With s ₂It is the rotor spin axis direction of two SGCMGs.

M among Fig. 5 ₀The initial time attitude error threshold value of expression appointment, m _a(0) expression initial time attitude error tolerance, λ ₀Be the unusual tolerance threshold value of initial time gyro of appointment, λ (0) is the unusual tolerance of initial time gyro,

With

Be respectively the framework rotating speed of two gyros, b ₀Be positive constant, t and T ₀All represent the time, m _sThe attitude error threshold value of expression expectation.

Among Fig. 6 to Fig. 9, s is chronomere's second.

Among Fig. 6

With

Be respectively the framework rotating speed of two gyros.

[ρ among Fig. 8 ₁ρ ₂ρ ₃] the error attitude Douglas Rodríguez parameter of spacecraft.

[ω among Fig. 9 ₁ω ₂ω ₃] represent that the angular velocity of spacecraft is at three components of body coordinate system.

[embodiment]

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

Be the clearer present embodiment of introducing, at first the principle of simple declaration SGCMG output torque describes attitude control method of the present invention with kinetics equation in conjunction with attitude motion with the spacecraft of two parallel SGCMGs again.It is emphasized that the method only needs the SGCMGs of two parallel installations, and do not require the concrete orientation of gimbal axis in the spacecraft body of two SGCMGs.

Referring to Fig. 1, SGCMG is by the rotor of a constant revolution and the system framework of support rotor, and s is rotor spin axis direction, and g is the gimbal axis direction, t and output control moment opposite direction, and they are unit vector.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.Because the rotation of gimbal axis causes rotor spin axis direction to change, and 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 suc as formula shown in (17):

$T=-\left(\stackrel{\&CenterDot;}{\mathrm{\&delta;}}g\right)\&times;\left(h_{0}s\right)={-\mathrm{<figure-callout\; id="0"\; label="h"\; filenames="HDA00002667030100042.png,HDA00002667030100043.png"\; state="\{\{state\}\}">h</figure-callout>}}_0\stackrel{\&CenterDot;}{\mathrm{\&delta;}}t---\left(17\right)$

Wherein, T represents the moment vector of single SGCMG output, h ₀Nominal angular momentum for gyrorotor.

Referring to Fig. 2, spacecraft is with the SGCMGs of two parallel installations, and wherein X, Y, Z represent be connected three change in coordinate axis direction of coordinate system of the body of spacecraft, the gimbal axis g of two SGCMGs ₁With g ₂All be parallel to Z axis.So the output torque of two SGCMGs all drops on the XY plane, and be zero at the control moment of Z-direction, therefore, Z axis is for owing driving shaft.Make J=diag (J ₁J ₂J ₃) be illustrated in the inertia matrix of gyro when locking spacecraft and the system of gyro composition, so the total angular momentum of spacecraft and gyro is suc as formula shown in (18):

H=Jω+h ₀s ₁+h ₀s ₂ (18)

Wherein, H is the total angular momentum of spacecraft and gyro; ω is that spacecraft is with respect to the expression of angular velocity under body series of inertial system, s ₁With s ₂Be respectively the spin axis unit vector of two gyros.The total angular momentum of supposing spacecraft and gyrosystem is zero, formula (18) can be write as the component form suc as formula shown in (19):

J ₁ω ₁+h ₀cosδ ₁+h ₀cosδ ₂=0

J ₂ω ₂+h ₀sinδ ₁+h ₀sinδ ₂=0 (19)

J ₃ω ₃=0

Wherein, δ ₁With δ ₂Be respectively the framework corner of two gyros.Can be found out by formula (19), because the system angle momentum is zero, owe the angular velocity component ω of driving shaft ₃Perseverance is zero, therefore, does not need the angular velocity of owing driving shaft is controlled.

The below is with the attitude of Rodrigues parametric description spacecraft, and it is the attitude describing method that a class derives from hypercomplex number, and it only needs three parameters, and separate between the parameter.The Rodrigues parameter of the body coordinate system relative inertness system of definition spacecraft is suc as formula shown in (20):

ρ=[ρ ₁ ρ ₂ ρ ₃] ^T=ηtan(φ/2) (20)

Wherein, η is the component array of Euler's turning axle under body series, and φ is the angular dimension around Eigenaxis rotation.

So, can obtain with the attitude dynamics of the spacecraft of two parallel SGCMGs and kinetics equation suc as formula shown in (21) and the formula (22):

$\left[\begin{array}{c}{\stackrel{\&CenterDot;}{\mathrm{\&rho;}}}_1\\ {\stackrel{\&CenterDot;}{\mathrm{\&rho;}}}_2\\ {\stackrel{\&CenterDot;}{\mathrm{\&rho;}}}_3\end{array}\right]=\frac{1}{2}\left[\begin{array}{cc}(1+{\mathrm{\&rho;}}_1^2)& ({\mathrm{\&rho;}}_1{\mathrm{\&rho;}}_2-{\mathrm{\&rho;}}_3)\\ ({\mathrm{\&rho;}}_3+{\mathrm{\&rho;}}_1{\mathrm{\&rho;}}_2)& (1+{\mathrm{\&rho;}}_2^2)\\ ({\mathrm{\&rho;}}_1{\mathrm{\&rho;}}_3-{\mathrm{\&rho;}}_2)& \left({\mathrm{\&rho;}}_1{+\mathrm{\&rho;}}_2{\mathrm{\&rho;}}_3\right)\end{array}\right]\left[\begin{array}{c}{\mathrm{\&omega;}}_1\\ {\mathrm{\&omega;}}_2\end{array}\right]---\left(21\right)$

$\left[\begin{array}{c}{\mathrm{<figure-callout\; id="1"\; label="J"\; filenames="HDA00002667030100021.png,HDA00002667030100031.png"\; state="\{\{state\}\}">J</figure-callout>}}_1{\stackrel{\&CenterDot;}{\mathrm{\&omega;}}}_1\\ {\mathrm{<figure-callout\; id="2"\; label="J"\; filenames="HDA00002667030100021.png,HDA00002667030100022.png"\; state="\{\{state\}\}">J</figure-callout>}}_2{\stackrel{\&CenterDot;}{\mathrm{\&omega;}}}_2\end{array}\right]=T_c---\left(22\right)$

Wherein, T _cBe the control moment that two SGCMGs produce, expression formula is suc as formula shown in (23) and the formula (24):

$T_c=h_{0}D\left[\begin{array}{c}{\stackrel{\&CenterDot;}{\mathrm{\&delta;}}}_1\\ {\stackrel{\&CenterDot;}{\mathrm{\&delta;}}}_2\end{array}\right]---\left(23\right)$

$D=\left[\begin{array}{cc}\sin {\mathrm{\&delta;}}_1& \sin {\mathrm{\&delta;}}_2\\ -{\cos \mathrm{\&delta;}}_1& -{\cos \mathrm{\&delta;}}_2\end{array}\right]---\left(24\right)$

Here, might as well establish ρ and namely represent the error of spacecraft with the expectation attitude, so the target of attitude maneuver control namely is the appropriate framework rotary speed instruction of design, so that ρ converges to zero.In the attitude control procedure, need to be from instruction control moment T _cThe counter frame corners speed of asking gyro still, can be found out from formula (24), when the order of D is 1, i.e. and rank(D)=1, D is irreversible, can't obtain the instruction frame corners speed of gyro, and the frame corners speed that perhaps obtains by inverting is for infinitely great.Referring to Fig. 3 and Fig. 4, the rotor vector that this correspondence two SGCMGs in the same way with reverse situation, wherein, if s ₁=s ₂, then gyro occur unusual be outer unusual, also claim saturated unusually, do not have zero motion so that the gyro disengaging is unusual, if s ₁=-s ₂, then gyro is unusual in occurring, and has zero motion, and still, it is unusual that zero motion can not make gyro break away from.In order also to solve frame corners speed at gyro when unusual, can adopt following method based on svd, specifically suc as formula shown in (25):

$\stackrel{\&CenterDot;}{\mathrm{\&delta;}}=\frac{1}{h_0}{D}_s^{-1}{T}_c---\left(25\right)$

Wherein, $\stackrel{\&CenterDot;}{\mathrm{\&delta;}}={\left[\begin{array}{cc}{\stackrel{\&CenterDot;}{\mathrm{\&delta;}}}_1& {\stackrel{\&CenterDot;}{\mathrm{\&delta;}}}_2\end{array}\right]}^T,$ Matrix D is carried out svd suc as formula shown in (26):

D=USV ^T (26)

Wherein, U and V are orthogonal matrix; S=diag (σ ₁σ ₂), σ ₁And σ ₂Be two singular values of matrix D, and satisfy σ ₁〉=σ ₂〉=0; Computing method suc as formula shown in (27):

$D_s^{-1}={\mathrm{VS}}_{\mathrm{\&gamma;}}^{-1}{U}^T---\left(27\right)$

Wherein, $S_{\mathrm{\&gamma;}}^{-1}=\mathrm{<figure-callout\; id="1"\; label="diag"\; filenames="HDA00002667030100021.png,HDA00002667030100031.png"\; state="\{\{state\}\}">diag</figure-callout>}\left(\begin{array}{cc}1/{\mathrm{\&sigma;}}_1& 1/({\mathrm{\&sigma;}}_2+\mathrm{\&gamma;})\end{array}\right);$ γ chooses shown in formula (28)

$\mathrm{\&gamma;}=\left\{\begin{array}{cc}0,& \mathrm{\&lambda;}\&GreaterEqual;{\mathrm{\&lambda;}}_D\\ k_D{(1-\frac{\mathrm{\&lambda;}}{{\mathrm{\&lambda;}}_D})}^2,& \mathrm{\&lambda;}\&le;{\mathrm{\&lambda;}}_D\end{array}\right.---\left(28\right)$

Wherein, λ _DBe the positive number of appointment in the control implementation process, λ represents the unusual tolerance of D, calculates by formula (29):

λ＝det(DD ^T) (29)

If at initial time, larger and two SGCMGs of the attitude error of spacecraft are again near unusual, the instruction frame corners speed that is then calculated by the method for inverting of formula (25-29) also can be large especially, in order further to address this problem, can adopt the opposite framework rotating speed of big or small equidirectional to drive two SGCMGs motion regular hour T ₀, so that two gyros are away from very, namely the framework rotary speed instruction of this moment is suc as formula shown in (30):

$\begin{array}{c}{\stackrel{\&CenterDot;}{\mathrm{\&delta;}}}_1={\mathrm{<figure-callout\; id="0"\; label="b"\; filenames="HDA00002667030100042.png,HDA00002667030100043.png"\; state="\{\{state\}\}">b</figure-callout>}}_0\\ {\stackrel{\&CenterDot;}{\mathrm{\&delta;}}}_2=-b_0\end{array}---\left(30\right)$

Wherein, b ₀Be positive constant, generally select littlely, in order to avoid after switching to follow-up attitude maneuver control model, cause larger frame corners velocity jump.Away from after unusual, carry out again attitude control at gyro.

Referring to Fig. 5, whole steering logic is divided into three phases, and the phase one, to be that the gyro of initial time is unusual evaded the stage.Subordinate phase is the attitude error converged state, corresponding attitude error convergence controller.The last stage is the stable state control stage, corresponding steady-state controller.Below just implementation step of the present invention is elaborated.

Phase one, whether the error of check initial time spacecraft and expectation attitude and two SGCMGs are near unusual.Definition attitude error metric function is suc as formula shown in (31):

m _a=k _ρρ ^Tρ+k _wω ^Tω (31)

Wherein, k _ρWith k _wTwo positive numbers for appointment in control procedure.Make m ₀0 the expression appointment initial time attitude error threshold value, λ ₀0 be the unusual tolerance threshold value of initial time gyro of appointment, if m _a(0)〉m ₀And λ＜λ ₀, then at time t ∈ [0, T ₀) within, the instruction frame corners speed drive gyro that produces with formula (30) rotates, so that gyro is away from unusual, wherein, T ₀Be two SGCMGs with the time span of normal value rotary speed movement, specifically can select according to the degree away from unusual that reaches of expectation gyro.If m _aDo not satisfy above-mentioned condition with λ, then directly enter attitude error convergence controller, its enforcement comprises following subordinate phase.

Subordinate phase is calculated as the desired angular velocity of attitude maneuver of realizing spacecraft by following formula (32):

$\left[\begin{array}{c}{\mathrm{\&omega;}}_{\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="HDA00002667030100021.png,HDA00002667030100031.png"\; state="\{\{state\}\}">d</figure-callout>}1}\\ {\mathrm{\&omega;}}_{\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="HDA00002667030100021.png,HDA00002667030100022.png"\; state="\{\{state\}\}">d</figure-callout>}2}\end{array}\right]=-k\left[\begin{array}{c}{\mathrm{\&rho;}}_1\\ {\mathrm{\&rho;}}_2\end{array}\right]+g\left[\begin{array}{c}\mathrm{sat}({\mathrm{\&Delta;}}_2,a)\\ -\mathrm{sat}({\mathrm{\&Delta;}}_1,a)\end{array}\right]---\left(32\right)$

Wherein,

Ride gain g and k are positive constant, are Δ in the process that guarantees the attitude error convergence ₁And Δ ₂Receipts pour into zero, and g is satisfied in their selection〉2k; Sat (x is suc as formula the saturation function shown in (33) a):

$\mathrm{sat}(x,a)=\begin{array}{c}\left\{\begin{array}{cc}x,& -a\&le;x\&le;a\\ a,& x>a\\ -a,& x<a\end{array}\right.---\left(33\right)\end{array}$

Wherein, x is aleatory variable; A is saturation boundary, is positive constant, can select according to actual needs.

Below explanation is by the expectation angular velocity of formula (32) expression and drawing of ride gain condition.At first consider as shown in the formula the expectation angular velocity control law shown in (34):

$\left[\begin{array}{c}{\mathrm{\&omega;}}_{\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="HDA00002667030100021.png,HDA00002667030100031.png"\; state="\{\{state\}\}">d</figure-callout>}1}\\ {\mathrm{\&omega;}}_{\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="HDA00002667030100021.png,HDA00002667030100022.png"\; state="\{\{state\}\}">d</figure-callout>}2}\end{array}\right]=-k\left[\begin{array}{c}{\mathrm{\&rho;}}_1\\ {\mathrm{\&rho;}}_2\end{array}\right]+g\left[\begin{array}{c}{\mathrm{\&Delta;}}_2\\ {-\mathrm{\&Delta;}}_1\end{array}\right]---\left(34\right)$

Under the represented control law effect of formula (34), the error attitude ρ of spacecraft converges to zero.This can be by choosing the Lyapunov function shown in the formula (35) and proving in conjunction with LaSalle invariant set principle.

$V={\mathrm{\&rho;}}_1^2+{\mathrm{\&rho;}}_2^2+{\mathrm{\&rho;}}_3^2---\left(35\right)$

But, when the error attitude converges to zero, because Singular term Δ in the formula (34) ₁And Δ ₂May become infinity.This situation can solve by selecting appropriate ride gain g and k, examines or check suc as formula the function shown in (36):

${\mathrm{<figure-callout\; id="0"\; label="V"\; filenames="HDA00002667030100042.png,HDA00002667030100043.png"\; state="\{\{state\}\}">V</figure-callout>}}_0=\frac{{\mathrm{\&rho;}}_3^2}{{({\mathrm{\&rho;}}_1^2+{\mathrm{\&rho;}}_2^2)}^2}---\left(36\right)$

In formula (36), supposed initial time

To V ₀The seeking time derivative can get formula (37):

${\stackrel{\&CenterDot;}{V}}_0=\frac{{-\mathrm{\&rho;}}_3^2((g-2k-k({\mathrm{\&rho;}}_1^2+{\mathrm{\&rho;}}_2^2))({\mathrm{\&rho;}}_1^2+{\mathrm{\&rho;}}_2^2)+{2g}_4{\mathrm{\&rho;}}_3^2)}{{({\mathrm{\&rho;}}_1^2+{\mathrm{\&rho;}}_2^2)}^3}---\left(37\right)$

When selecting g〉2k, g-2k is arranged〉0.On the other hand, by the front to the explanation of the stability of error attitude ρ as can be known, along with the time increases,

Therefore, when the time is fully large, always have

So, when the time is fully large,

After this, V ₀Along with the time increases monotone decreasing, again in V ₀〉=0, therefore, as time t → ∞, V ₀→ 0.So, the singular term Δ in the formula (34) ₁And Δ ₂Can not become infinity, and can converge in time zero.

On the other hand, for fear of initial time

Cause Δ ₁And Δ ₂Infinity can be modified to formula (34) saturated form shown in the formula (32).

Then, computations control moment.Employing is followed the tracks of control law suc as formula the angular velocity shown in (36):

$\begin{array}{c}{\stackrel{\&CenterDot;}{\mathrm{\&omega;}}}_1=k_1({\mathrm{\&omega;}}_{d1}-{\mathrm{\&omega;}}_1)\\ {\stackrel{\&CenterDot;}{\mathrm{\&omega;}}}_2=k_2({\mathrm{\&omega;}}_{d2}-{\mathrm{\&omega;}}_2)\end{array}---\left(38\right)$

Wherein, k ₁And k ₂Be normal number, in working control, select.Formula (38) substitution following formula can be tried to achieve the instruction control moment suc as formula shown in (39):

$T_c=\left[\begin{array}{c}{\mathrm{<figure-callout\; id="1"\; label="J"\; filenames="HDA00002667030100021.png,HDA00002667030100031.png"\; state="\{\{state\}\}">J</figure-callout>}}_1{\stackrel{\&CenterDot;}{\mathrm{\&omega;}}}_1\\ {\mathrm{<figure-callout\; id="2"\; label="J"\; filenames="HDA00002667030100021.png,HDA00002667030100022.png"\; state="\{\{state\}\}">J</figure-callout>}}_2{\stackrel{\&CenterDot;}{\mathrm{\&omega;}}}_2\end{array}\right]---\left(39\right)$

At last, instruction control moment substitution formula (25) the computations framework rotating speed that is obtained by formula (39).

Phase III, judge whether to switch to steady-state controller.Make m _sIf the stable state attitude error threshold value of expression appointment is m _aM _s, then repeat the operation of subordinate phase; If m _a≤ m _s, then switch to following steady-state controller, and according to formula (40) computations frame corners speed:

$\stackrel{\&CenterDot;}{\mathrm{\&delta;}}=\frac{D^T\stackrel{\&OverBar;}{m}}{h_0{\stackrel{\&OverBar;}{m}}^T{\mathrm{DD}}^T\stackrel{\&OverBar;}{m}+\mathrm{\&epsiv;}}\stackrel{\&CenterDot;}{v}---\left(40\right)$

Wherein, $m=\frac{s_1+{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA00002667030100021.png,HDA00002667030100022.png"\; state="\{\{state\}\}">s</figure-callout>}}_2}{\left|\right|s_1+{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA00002667030100021.png,HDA00002667030100022.png"\; state="\{\{state\}\}">s</figure-callout>}}_2\left|\right|}=\left[\begin{array}{c}{m}_x\\ m_{\mathrm{<figure-callout\; id="0"\; label="y"\; filenames="HDA00002667030100042.png,HDA00002667030100043.png"\; state="\{\{state\}\}">y</figure-callout>}}\\ 0\end{array}\right],$ $\stackrel{\&OverBar;}{m}=\left[\begin{array}{c}{m}_x\\ m_y\end{array}\right]---\left(41\right)$

m ^TJω=v (42)

$\stackrel{\&CenterDot;}{v}=k_v(v_d-v)---\left(43\right)$

v _d=-k _d(ρ ₁a ₁+ρ ₂a ₂) (44)

In formula (41-44), k _dAnd k _vBe positive constant, selected in working control; a ₁=m _x/ J ₁And a ₂=m _x/ J ₂V represents selected intermediate variable,

Time-derivative for v; And v _dThe expectation value of expression intermediate variable.In addition, ε is positive a small amount of in formula (40), can be selected according to actual conditions, its introducing be for fear of The time, may cause larger frame corners speed.

The following describes the effect of steady-state controller (40-44).It is as follows to get formula (45) by formula (41) and (42):

m _xJ ₁ω ₁+m _yJ ₂ω ₂=v ₂ (45)

Because s ₁-s ₂Perpendicular with m, and (s ₁-s ₂) ^TJ ω=0, accordingly, the relational expression (46) below formula (42) and formula (45) can get:

$\left[\begin{array}{c}{\mathrm{\&omega;}}_1\\ {\mathrm{\&omega;}}_2\end{array}\right]=\left[\begin{array}{c}{a}_1{v}_2\\ a_2{v}_2\end{array}\right]---\left(46\right)$

So, under the effect of the expectation intermediate variable shown in the formula (45), consider that the variation of the attitude error shown in the formula (35) can get:

$\stackrel{\&CenterDot;}{V}=-k_d(1+{\mathrm{\&rho;}}_1^2+{\mathrm{\&rho;}}_2^2+{\mathrm{\&rho;}}_3^2){({\mathrm{\&rho;}}_1{a}_1+{\mathrm{\&rho;}}_2{a}_2)}^2\&le;0---\left(47\right)$

Formula (47) expression attitude error successively decreases, and therefore, after control law switches to steady-state controller, can not switch to the error attitude convergence controller in four steps of second step to the again.So far, can be clear and definite what know formula (43) expression is to expectation intermediate variable v _dThe tracking control law.On the other hand, be zero hypothesis according to formula (42) and total angular momentum, can obtain formula (48):

v=-h ₀m ^T(h ₁+h ₂) (48)

Differentiate can get formula (49) to formula (48):

$\stackrel{\&CenterDot;}{v}=h_0{m}^{T}D\stackrel{\&CenterDot;}{\mathrm{\&delta;}}---\left(49\right)$

Can find out from formula (49),

Can have infinite many groups to separate, its minimum norm solution can be become suc as formula shown in (50) by the Moore-Penrose reciprocal representation:

$\stackrel{\&CenterDot;}{\mathrm{\&delta;}}=\frac{D^T\stackrel{\&OverBar;}{m}}{h_0{\stackrel{\&OverBar;}{m}}^T{\mathrm{DD}}^T\stackrel{\&OverBar;}{m}}\stackrel{\&CenterDot;}{v}---\left(50\right)$

In the denominator of formula (50), add positive a small amount of ε and can obtain the skeleton instruction rotating speed shown in the formula (40).

So far, obtained the instruction framework rotating speed at different attitudes control stage two SGCMGs fully, driven SGCMGs according to the instruction framework rotating speed of gained and rotate and just can make spacecraft maneuver arrive targeted attitude.

Attitude maneuver control simulation result below in conjunction with some microminiature satellites is made specific description to this programme.

Referring to Fig. 2, suppose satellite with the SGCMGs of two parallel installations, the gimbal axis of two SGCMGs is along the Z axis of spacecraft body.The inertia matrix of spacecraft and gyrosystem is J=diag (1009050) kg.m ², the rotor angular momentum of supposing each SGCMGs is h ₀=50N.m.s.The attitude parameter of initial time spacecraft and gyro gimbal angle location parameter are as follows:

δ(0)=[0π] ^Trad,ρ(0)=[-13-1] ^T,ω(0)=[-0.5-0.50] ^Trad/s

All parameters relevant with controller of the present invention are as follows:

The first step: k _ρ=1, k _w=1 (s/rad) ², T ₀=20s, m ₀=1 * 10 ^-4, λ ₀=0.01, b ₀=0.01rad/s

Second step: k=0.1rad/s, g=0.21rad/s, a=1,

The 3rd step: k ₁=k ₂=0.8/s,

The 4th step: k _D=0.01, D ₀=0.001

The 5th step: k _d=0.1kg ².m ⁴.s ^-1, k _v=50/s, ε=1 * 10 ^-8N.m.s, m _s=1 * 10 ^-6,

As can be seen from Figure 6, because the rotor Complexor common line of two SGCMGs of initial time is reverse, the unusual tolerance of two SGCMGs is zero, and gyro is in interior unusual.Simultaneously, as can be seen from Figure 7, because the attitude error of initial time is larger, steering logic enters the control of the first step, with the lower frame corners speed b of frame appointment ₀=0.01rad/s drives two SGCMGs backward rotation 20s, so that two SGCMGs disengaging is unusual.Can find out that from Fig. 8 and Fig. 9 after this, steering logic enters second step, control the targeted attitude that is tending towards of spacecraft, two SGCMGs are unusual in again approaching simultaneously, when attitude error converges to less than designated value m _s=1 * 10 ^-6The time (close to emulation 170s constantly), steering logic switches to steady-state controller, so that attitude error further reduces.In the switching in this step, skeleton instruction produces a small size point of discontinuity, and still, because after switching to steady-state controller, attitude error is further restrained, whole steering logic can not returned previous step.Therefore, the control stage only once switches from error attitude converged state to stable state, can not occur owing to switch back and forth the chatter phenomenon that causes between two controllers.Finally, whole steering logic both so that two SGCMGs have broken away from the hidden unusual of initial time, made again spacecraft maneuver arrive targeted attitude.

In sum, the present invention proposes a kind of attitude maneuver control method that is applicable to the spacecraft of two parallel SGCMGs.Utilize control method of the present invention, according to spacecraft in the practical application and systematic parameter SGCMGs and attitude error parameter, select suitable control parameter, just can utilize the SGCMGs of two parallel installations with the targeted attitude of spacecraft maneuver to any one expectation.The present invention can be used for the situation of reply spacecraft control-moment gyro group partial failure, also can be used for only using the attitude control of the spacecraft of two parallel SGCMGs.

The above only is preferred implementation 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 (2)

1. Spacecraft During Attitude Maneuver control method of using two single frame control-moment gyros, it is characterized in that: the characterization step of the method comprises three phases:

Stage one: initial unusual evading the stage of gyro

It is comprised of the unusual decision logic of gyro and the unusual disengaging controller of gyro; Whether check initial time spacecraft is unusual with error and two single-gimbal control moment gyros SGCMGs of expectation attitude; Make m ₀0 expression initial time attitude error threshold value, its occurrence is selected in actual applications; If attitude error is less than m ₀, perhaps gyro then directly enters the stage two away from unusual; If attitude error is greater than m ₀, and gyro is near unusual, the large reverse speed driver framework such as then utilizes to rotate regular hour T ₀0, it is unusual that gyro is broken away from, and expression formula is suc as formula shown in (1):

$\begin{array}{c}{\stackrel{\&CenterDot;}{\mathrm{\&delta;}}}_1=b_0\\ {\stackrel{\&CenterDot;}{\mathrm{\&delta;}}}_2=-b_0\end{array}---\left(1\right)$

Wherein, With

It is the framework rotating speed of two SGCMGs; b ₀Be positive constant; Select littlely, in order to avoid after switching to follow-up attitude maneuver control model, cause large frame corners velocity jump;

Stage two: error attitude converged state

It mainly is comprised of error attitude convergence controller; Two SGCMGs install arbitrarily in the spacecraft body, only need to carry out coordinate conversion to the corresponding entry in this algorithm and get final product; Make that { X Y Z} represents the body of the spacecraft coordinate system that is connected, J=diag (J ₁J ₂J ₃) inertia matrix of the system that spacecraft and gyro form when locking for gyro, wherein diag (J ₁J ₂J ₃) represent (J ₁J ₂J ₃) get diagonal matrix, ω=[ω ₁ω ₂ω ₃] ^TThe angular velocity of expression spacecraft is at three components of body coordinate system;

At first, the calculation expectation attitude angular velocity, expression formula is suc as formula shown in (2):

$\left[\begin{array}{c}{\mathrm{\&omega;}}_{d1}\\ {\mathrm{\&omega;}}_{d2}\end{array}\right]=-k\left[\begin{array}{c}{\mathrm{\&rho;}}_1\\ {\mathrm{\&rho;}}_2\end{array}\right]+g\left[\begin{array}{c}\mathrm{sat}({\mathrm{\&Delta;}}_2,a)\\ -\mathrm{sat}({\mathrm{\&Delta;}}_1,a)\end{array}\right]---\left(2\right)$

Wherein, ω _D1With ω _D2Expression is along the expectation attitude angular velocity of X and Y-axis;

ρ=[ρ ₁ρ ₂ρ ₃] ^TFor describing the Rodrigues parameter of spacecraft attitude; Ride gain g and k are positive constant, are Δ in the process that guarantees the attitude error convergence ₁And Δ ₂Receipts pour into zero, make their selection satisfy g〉2k; Sat (x is suc as formula the saturation function shown in (3) a):

$\mathrm{sat}(x,a)=\begin{array}{c}\left\{\begin{array}{cc}x,& -a\&le;x\&le;a\\ a,& x>a\\ -a,& x<a\end{array}\right.---\left(3\right)\end{array}$

Wherein, x is aleatory variable; A is saturation boundary, is positive constant, and is selected according to actual needs;

Then, follow the tracks of control law according to angular velocity, the computations control moment, expression formula is suc as formula shown in (4) and the formula (5):

$\begin{array}{c}{\stackrel{\&CenterDot;}{\mathrm{\&omega;}}}_1=k_1({\mathrm{\&omega;}}_{d1}-{\mathrm{\&omega;}}_1)\\ {\stackrel{\&CenterDot;}{\mathrm{\&omega;}}}_2=k_1({\mathrm{\&omega;}}_{d2}-{\mathrm{\&omega;}}_2)\end{array}---\left(4\right)$

$T_c=\left[\begin{array}{c}{J}_1{\stackrel{\&CenterDot;}{\mathrm{\&omega;}}}_1\\ J_2{\stackrel{\&CenterDot;}{\mathrm{\&omega;}}}_2\end{array}\right]---\left(5\right)$

Wherein, k ₁And k ₂Be normal number, in working control, select; T _cBe the instruction control moment;

At last, computations frame corners speed, expression formula is suc as formula shown in (6):

$\stackrel{\&CenterDot;}{\mathrm{\&delta;}}=\frac{1}{h_0}{D}_s^{-1}{T}_c---\left(6\right)$

Wherein, $\stackrel{\&CenterDot;}{\mathrm{\&delta;}}={\left[\begin{array}{cc}{\stackrel{\&CenterDot;}{\mathrm{\&delta;}}}_1& {\stackrel{\&CenterDot;}{\mathrm{\&delta;}}}_2\end{array}\right]}^T,$ h ₀For the angular momentum of gyrorotor, at this, suppose the angular momentum equal and opposite in direction of two gyrorotors; For calculating

Need explanation moment output matrix, shown in (7):

$D=\left[\begin{array}{cc}\sin {\mathrm{\&delta;}}_1& \sin {\mathrm{\&delta;}}_2\\ -\cos {\mathrm{\&delta;}}_1& -{\cos \mathrm{\&delta;}}_2\end{array}\right]---\left(7\right)$

Wherein, δ ₁And δ ₂Framework corner for gyro; Matrix D is carried out svd suc as formula shown in (8):

D=USV ^T (8)

U and V are orthogonal matrix; S=diag (σ ₁σ ₂), σ ₁And σ ₂Be two singular values of matrix D, and satisfy σ ₁〉=σ ₂〉=0;

Computing method suc as formula shown in (9):

$D_s^{-1}={\mathrm{VS}}_{\mathrm{\&gamma;}}^{-1}{U}^T---\left(9\right)$

Wherein, $S_{\mathrm{\&gamma;}}^{-1}=\mathrm{diag}\left(\begin{array}{cc}1/{\mathrm{\&sigma;}}_1& 1/({\mathrm{\&sigma;}}_2+\mathrm{\&gamma;})\end{array}\right),$ γ chooses according to formula (10):

$\mathrm{\&gamma;}=\left\{\begin{array}{cc}0,& \mathrm{\&lambda;}\&GreaterEqual;{\mathrm{\&lambda;}}_D\\ k_D{(1-\frac{\mathrm{\&lambda;}}{{\mathrm{\&lambda;}}_D})}^2,& \mathrm{\&lambda;}\&le;{\mathrm{\&lambda;}}_D\end{array}\right.---\left(10\right)$

Wherein, k _DFor positive normal value, in control procedure, specify; λ _DBe the positive number of appointment in the control implementation process, λ represents the unusual tolerance of D, calculates by formula (11):

λ＝det(DD ^T) (11)

Make m _sThe attitude error threshold value of 0 expression expectation, its occurrence is specified in actual applications; Judge whether attitude error converges in the threshold range of appointment, if do not have, then continue use error attitude convergence controller and control; If, the control that then enters the stage three;

Stage three: stable state control stage

It mainly is comprised of steady-state controller, namely according to formula (12) computations frame corners speed:

$\stackrel{\&CenterDot;}{\mathrm{\&delta;}}=\frac{D^T\stackrel{\&OverBar;}{m}}{h_0{\stackrel{\&OverBar;}{m}}^T{\mathrm{DD}}^T\stackrel{\&OverBar;}{m}+\mathrm{\&epsiv;}}\stackrel{\&CenterDot;}{v}---\left(12\right)$

Wherein,

$m=\frac{s_1+s_2}{\left|\right|s_1+s_2\left|\right|}=\left[\begin{array}{c}{m}_x\\ m_y\\ 0\end{array}\right],$ $\stackrel{\&OverBar;}{m}=\left[\begin{array}{c}{m}_x\\ m_y\end{array}\right]---\left(13\right)$

m ^TJω=v (14)

$\stackrel{\&CenterDot;}{v}=k_v(v_d-v)---\left(15\right)$

v _d=-k _d(ρ ₁a ₁+ρ ₂a ₂) (16)

In the equation above, k _dAnd k _vBe positive constant, selected in working control; a ₁=m _x/ J ₁And a ₂=m _x/ J ₂V represents selected intermediate variable, by top expression formula as can be known, expression be the projection of angular momentum on the separated time of the angle of two rotor vectors of spacecraft;

Time-derivative for v; And v _dThe expectation value of expression intermediate variable; In addition, ε is positive a small amount of, and is selected according to actual conditions.

2. the Spacecraft During Attitude Maneuver control method of two single frame control-moment gyros of use according to claim 1; It is characterized in that: in the stage one, the large reverse instruction framework rotating speed such as utilization is being controlled inside and outside unusual that initial time occurs so that two SGCMGs break away from; In the stage two, so that restraining, the attitude of spacecraft expects attitude by the expectation angular velocity based on the Rodrigues parameter, then, passing ratio angular velocity is followed the tracks of control law and is followed the tracks of expectation angular velocity, and then obtaining the instruction control moment, niche is in the contrary instruction framework rotating speed of finding the solution of the correction of svd again; In the stage three, utilize the projection effect intermediate variable of angular momentum on the separated time of the angle of two rotor vectors of spacecraft, design expectation intermediate variable is followed the tracks of control law with corresponding, so that the attitude error of spacecraft further restrains, and obtains on this basis instruction framework rotating speed.

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