CN103034237B - 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 attitude maneuver control method of two single-gimbal control momentum gyro

[technical field]

The invention belongs to technical field of spacecraft attitude control, be specifically related to the spacecraft attitude maneuver control method of a kind of use two single-gimbal control momentum gyro.The total angular momentum of celestial body and gyro be zero or less time, this control method can utilize the single-gimbal control momentum gyro of two parallel installations, by the targeted attitude of spacecraft maneuver to any desired.

[background technology]

Along with the development of aerospace industry, the requirement of modern spacecraft to the precision of attitude control system, life-span and reliability is more and more higher.Spacecraft in-orbit gesture stability is mainly realized by topworks's output control moment.

Single-gimbal control momentum gyro belongs to a kind of angular momentum exchange device, and it changes the angular momentum direction of the rotor of constant rotational speed by frame member, thus produces the moment reacting on spacecraft continuously.In all kinds of attitude control actuators of spacecraft, single-gimbal control moment gyros (Single Gimbal Control Moment Gyros, SGCMGs) amplitude control moment can not only be exported, also have that structure is simple, reliability is high, the advantage such as 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, such as, Mir space station (MIR), the Pleiades-HR satellite of No. one, Heavenly Palace and France all have employed SGCMGs as gesture stability main actuating mechanism.On the other hand, under same moment exports requirement, the quality of SGCMGs is light, volume is little, power consumption is little, SGCMGs is applicable to again need harsher small-sized spacecraft to quality, volume, such as, osmanli micro-satellite BILSAT-1 employs two small-sized SGCMGs to control to realize single-axis attitude.

Use a key issue of SGCMGs to be design appropriate manipulation rule, overcome the singular problem of gyro.The configuration singularity of SGCMGs refers to when being in the combination of some frame corners, the moment output matrix contraction of SGCMGs, anti-solution frame corners speed of can not inverting.The manipulation rule design of the gyro group formed for the SGCMGs by more than three or three has had more solution, but the manipulation rule scheme for only two SGCMGs is more rare.On the other hand, due to long-time operation on orbit, one or more single SGCMGs that spacecraft uses inevitably breaks down or lost efficacy, when the number of the SGCMGs of normal work is less than three, spacecraft becomes under-actuated systems, cannot realize the gesture stability of three axles in any case.On the other hand, for micro-thermoelectric generator, due to the restriction of quality and volume, often can not back up unnecessary topworks, therefore, expect to adopt less topworks to realize gesture stability function.

For this active demand, this patent proposes a kind of spacecraft attitude maneuver control method only using the SGCMGs of two parallel installations, both can tackle part SGCMGs to lose efficacy, improve the reliability of spacecraft attitude control system, how apply two SGCMGs for micro-thermoelectric generator again and carry out gesture stability a solution is provided.

[summary of the invention]

The present invention is directed to the spacecraft of the SGCMGs with two parallel installations, the total angular momentum of spacecraft and gyrosystem be zero or less time, realize any reorientation of spacecraft to inertial space, and in control procedure, evade the unusual of two SGCMGs.The present invention both can be used for the Spacecraft Attitude Control in the SGCMGs of two parallel configuration after certain a pair inefficacy, was applicable to again the gesture stability directly using the micro-thermoelectric generator of two parallel installations.

The spacecraft attitude maneuver control method of a kind of use of the present invention two single-gimbal control momentum gyro comprises three control stages:

In the stage one, gyro is initially unusual evades the stage, and it is made up of the unusual decision logic of gyro and the unusual disengaging controller of gyro.Whether the error size of inspection initial time spacecraft and expectation attitude and two SGCMGs are close to unusual.Make m ₀>0 represents initial time attitude error threshold value, and its occurrence can be selected in actual applications.If attitude error is less than m ₀, or gyro is away from unusual, then directly enter the stage two.If attitude error is greater than m ₀, and gyro is close to unusual, then the speed driver framework that utilization etc. are reverse greatly rotates regular hour T ₀>0, gyro is departed from unusual, expression formula is such as formula shown in (1):

$\begin{array}{c}{\stackrel{\·}{\mathrm{\δ}}}_1=b_0\\ {\stackrel{\·}{\mathrm{\δ}}}_2=-b_0\end{array}---\left(1\right)$

Wherein, with it is the framework rotating speed of two SGCMGs; b ₀for positive constant, generally select less, in order to avoid cause larger frame corners velocity jump after being switched to follow-up attitude maneuver control model.

In the stage two, error attitude converged state, it is primarily of error attitude convergence controller composition.The Z being parallel to spacecraft body for the gimbal axis of two SGCMGs illustrates this controller algorithm, and practical application is not limited thereto, and two SGCMGs can install arbitrarily in spacecraft body, only needs to carry out coordinate conversion to the corresponding entry in this algorithm.Make that { X Y Z} represents that the body of spacecraft is connected coordinate system, J=diag (J ₁j ₂j ₃) inertia matrix of system that forms for spacecraft when gyro locks and gyro, wherein diag () represents and gets diagonal matrix, ω=[ω ₁ω ₂ω ₃] ^trepresent three components of angular velocity in body coordinate system of spacecraft.

First, calculation expectation attitude angular velocity, expression formula is such as formula shown in (2):

$\left[\begin{array}{c}{\mathrm{\ω}}_{d1}\\ {\mathrm{\ω}}_{d2}\end{array}\right]=-k\left[\begin{array}{c}{\mathrm{\ρ}}_1\\ {\mathrm{\ρ}}_2\end{array}\right]+g\left[\begin{array}{c}\mathrm{sat}({\mathrm{\Δ}}_2,a)\\ -\mathrm{sat}({\mathrm{\Δ}}_1,a)\end{array}\right]---\left(2\right)$

Wherein, ω _d1with ω _d2represent the expectation attitude angular velocity along X and Y-axis; ρ=[ρ ₁ρ ₂ρ ₃] ^tfor describing the Rodrigues parameter of spacecraft attitude; Ride gain g and k is positive constant, for ensureing Δ in the process that attitude error is restrained ₁and Δ ₂receipts pour into zero, make their selection meet g>2k; Sat (x, a) for such as formula the saturation function shown in (3):

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

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

Then, according to angular velocity tracing control rule, computations control moment, expression formula is such as formula shown in (4) and 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 ₂for normal number, select in working control; T _cfor instruction control moment;

Finally, computations frame corners speed, expression formula is such 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 (at this, assuming that the angular momentum equal and opposite in direction of two gyrorotors) of gyrorotor; For calculating need moment output matrix to be described, 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 ₂for the frame corner of gyro; Svd is carried out such as formula shown in (8) to matrix D:

D=USV ^T(8)

U and V is orthogonal matrix; S=diag (σ ₁σ ₂), σ ₁and σ ₂for two singular values of matrix D, and meet σ ₁>=σ ₂>=0; computing method such 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 constant value, specify in control procedure; λ _dfor controlling the positive number of specifying in implementation process, λ represents the unusual tolerance of D, calculates by formula (11):

λ＝det(DD ^T) (11)

Make m _s>0 represents the attitude error threshold value of expectation, and its occurrence can be specified in actual applications, judges whether attitude error converges in the threshold range of specifying, 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, then the control in stage three is entered.

In the stage three, stable state controls the stage, and it forms primarily 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 _vfor positive constant, selected in working control; a ₁=m _x/ J ₁and a ₂=m _x/ J ₂; V represents selected intermediate variable, from expression formula above, expression be the projection of angular momentum on the angle separated time of two rotor vectors of spacecraft; for the time-derivative of v; And v _drepresent the expectation value of intermediate variable.In addition, ε is positive a small amount of, can select according to actual conditions, its introducing be in order to avoid time, larger frame corners speed may be caused.

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

The present invention is the spacecraft attitude maneuver control method of a kind of use two single-gimbal control momentum gyro, has the following advantages:

(1) the present invention is when only using two SGCMGs, achieves the three-axis attitude maneuver autopilot to spacecraft.In the gesture stability of conventional aerospace device, controlling for realizing three-axis attitude, at least needing three SGCMGs, when part SGCMGs lost efficacy, only remaining two when normally working, normal gesture stability function cannot be realized.Adopt method of the present invention, the spacecraft that normally can work to only surplus two parallel SGCMGs, when the total angular momentum of system is zero, carry out attitude reorientation, ensure the normal attitude controlling functions of spacecraft, improve the reliability of attitude control system, extend the lifetime of satellite.On the other hand, for the micro-thermoelectric generator being only provided with two SGCMGs, generally only utilize two SGCMGs to realize the gesture stability of single shaft, adopt method of the present invention, micro-thermoelectric generator can be made to realize better three-axis attitude controlling functions.

(2) the unusual bypassing method of combination that the present invention proposes has incorporated attitude error information, when attitude error is comparatively large, two SGCMGs pair is in unusual, two SGCMGs can be made to depart from outer unusual and interior unusual, when attitude error is restrained, higher moment output accuracy can be ensured.

(3) the attitude kinematics equations stability controller form based on 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 gives the ride gain alternative condition avoiding controller unusual.

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

[accompanying drawing explanation]

Fig. 1 is the structural representation of single-gimbal control momentum gyro (SGCMG).

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

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

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

Fig. 5 attitude maneuver control flow schematic diagram.

The unusual tolerance of Fig. 6 two SGCMGs.

Fig. 7 skeleton instruction angular velocity.

The error attitude Rodrigues parameter of Fig. 8 spacecraft.

The angular velocity of Fig. 9 spacecraft.

In figure, symbol description is as follows:

In Fig. 1, s is rotor spin axis direction, and g is gimbal axis direction, and t is contrary with output control moment direction, and they are unit vector.

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

M in Fig. 5 ₀represent the initial time attitude error threshold value of specifying, m _a(0) initial time attitude error tolerance is represented, λ ₀for the unusual metric threshold of initial time gyro of specifying, λ (0) is the unusual tolerance of initial time gyro, with be respectively the framework rotating speed of two gyros, b ₀for positive constant, t and T ₀all represent the time, m _srepresent the attitude error threshold value expected.

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

In Fig. 6 with be respectively the framework rotating speed of two gyros.

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

[ω in 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 the preferred embodiment of the present invention in detail.

Introduce the present embodiment for clearer, first the principle of simple declaration SGCMG output torque, then in conjunction with an attitude kinematics with the spacecraft of two parallel SGCMGs and kinetics equation, attitude control method of the present invention is described.It is emphasized that the method only needs the SGCMGs of two parallel installations, and do not require the concrete orientation of the gimbal axis of two SGCMGs in spacecraft body.

Be made up of the rotor of a constant revolution and the framework of support rotor see Fig. 1, SGCMG, s is rotor spin axis direction, and g is gimbal axis direction, and t is contrary with output control moment direction, and they are unit vector.The installation orthogonal with gimbal axis of rotor spin axis, is driven by rotor electric machine and frame motor respectively.Rotor electric machine drives rotor around spin axis constant speed rotary, produces a constant angular momentum.Frame motor makes framework around being fixed on the gimbal axis of spacecraft body with angular velocity according to steering order 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, thus export a gyroscopic couple.For single SGCMG, according to the above principle of work introduced, its control moment exported can be obtained such as formula shown in (17):

$T=-\left(\stackrel{\&CenterDot;}{\mathrm{\&delta;}}g\right)\&times;\left(h_{0}s\right)={-h}_0\stackrel{\&CenterDot;}{\mathrm{\&delta;}}t---\left(17\right)$

Wherein, T represents the moment vector that single SGCMG exports, h ₀for the nominal angular momentum of gyrorotor.

Referring to Fig. 2, spacecraft is with the SGCMGs of two parallel installations, and wherein X, Y, Z represent that the body of spacecraft is connected three change in coordinate axis direction of coordinate system, the gimbal axis g of two SGCMGs ₁with g ₂all be parallel to Z axis.So the output torque of two SGCMGs all drops in XY plane, and is zero at the control moment of Z-direction, and therefore, Z axis is drive lacking axle.Make J=diag (J ₁j ₂j ₃) represent the inertia matrix of the system that spacecraft and gyro form when gyro locks, so the total angular momentum of spacecraft and gyro is such 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 the angular velocity expression under body series of spacecraft relative to inertial system, s ₁with s ₂be respectively the spin axis unit vector of two gyros.Assuming that the total angular momentum of spacecraft and gyrosystem is zero, formula (18) can be write as component form such 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 frame corner of two gyros.As can be seen from formula (19), because system angle momentum is zero, the angular velocity component ω of drive lacking axle ₃perseverance is zero, therefore, does not need to control the angular velocity of drive lacking axle.

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

ρ=[ρ ₁ρ ₂ρ 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 to obtain with the attitude dynamics of the spacecraft of two parallel SGCMGs and kinetics equation such as formula shown in (21) and formula (22):

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

$\left[\begin{array}{c}{J}_1{\stackrel{\&CenterDot;}{\mathrm{\&omega;}}}_1\\ J_2{\stackrel{\&CenterDot;}{\mathrm{\&omega;}}}_2\end{array}\right]=T_c---\left(22\right)$

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

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

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

, ρ might as well be established namely to illustrate spacecraft and the error expecting attitude here, so namely the target that attitude maneuver controls is design appropriate framework rotary speed instruction, makes ρ converge to zero.In gesture stability process, need from instruction control moment T _cthe frame corners speed of reverse gyro, but, as can be seen from formula (24), when the order of D is 1, i.e. rank(D)=1, D irreversible, the instruction frame corners speed of gyro cannot be obtained, or the frame corners speed obtained by inverting is for infinitely great.Referring to Fig. 3 and Fig. 4, this rotor vector that correspond to two SGCMGs in the same way with reverse situation, wherein, if s ₁=s ₂, then the unusual of gyro appearance is outer unusual, also claims saturated unusual, there is not zero motion and makes gyro disengaging unusual, if s ₁=-s ₂, then gyro is unusual in occurring, there is zero motion, but it is unusual that zero motion can not make gyro depart from.In order to also frame corners speed can be solved at gyro close to time unusual, can adopt as follows based on the method for svd, specifically such as formula shown in (25):

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

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

D=USV ^T(26)

Wherein, U and V is orthogonal matrix; S=diag (σ ₁σ ₂), σ ₁and σ ₂for two singular values of matrix D, and meet σ ₁>=σ ₂>=0; computing method such as formula shown in (27):

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

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 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 _dfor controlling the positive number of specifying in 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 close to unusual, the instruction frame corners speed then calculated by the inversion technique of formula (25-29) also can be large especially, in order to address this problem further, the framework rotating speed that size equidirectional can be adopted contrary drives two SGCMGs motion regular hour T ₀, make two gyros away from very, namely framework rotary speed instruction is now such as formula shown in (30):

$\begin{array}{c}{\stackrel{\&CenterDot;}{\mathrm{\&delta;}}}_1=b_0\\ {\stackrel{\&CenterDot;}{\mathrm{\&delta;}}}_2=-b_0\end{array}---\left(30\right)$

Wherein, b ₀for positive constant, generally select less, in order to avoid cause larger frame corners velocity jump after being switched to follow-up attitude maneuver control model.At gyro away from after unusual, then carry out gesture stability.

Referring to Fig. 5, whole steering logic is divided into three phases, and the first stage, to be that the gyro of initial time is unusual evaded the stage.Subordinate phase is attitude error converged state, corresponding attitude error convergence controller.The last stage is that stable state controls the stage, corresponding steady-state controller.Just specific embodiment of the invention step is described in detail below.

First stage, whether the error of inspection initial time spacecraft and expectation attitude and two SGCMGs are close to unusual.Definition attitude error metric function is such as formula shown in (31):

m _a=k _ρρ ^Tρ+k _wω ^Tω (31)

Wherein, k _ρwith k _wfor two positive numbers of specifying in control procedure.Make m ₀>0 represents the initial time attitude error threshold value of specifying, λ ₀>0 is the unusual metric threshold of initial time gyro of specifying, if m _a(0) >m ₀and λ < λ ₀, then at time t ∈ [0, T ₀) within, the instruction frame corners speed that (30) produce with the formula drives gyro to rotate, and makes gyro away from unusual, wherein, and T ₀be two SGCMGs with the time span of constant value rotary speed movement, specifically can according to expecting selecting away from unusual degree of reaching of gyro.If m _ado not meet above-mentioned condition with λ, then directly enter attitude error convergence controller, its enforcement comprises subordinate phase below.

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

$\left[\begin{array}{c}{\mathrm{\&omega;}}_{d1}\\ {\mathrm{\&omega;}}_{d2}\end{array}\right]=-k\left[\begin{array}{c}{\mathrm{\&rho;}}_1\\ {\mathrm{\&rho;}}_2\end{array}\right]+g\left[\begin{array}{c}\mathrm{sat}({\mathrm{\&Delta;}}_2,a)\\ -\mathrm{sat}({\mathrm{\&Delta;}}_1,a)\end{array}\right]---\left(32\right)$

Wherein, ride gain g and k is positive constant, for ensureing Δ in the process that attitude error is restrained ₁and Δ ₂receipts pour into zero, and their selection meets g>2k; Sat (x, a) for such as formula the saturation function shown in (33):

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

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

Drawing of the expectation angular velocity that represented by formula (32) and ride gain condition is below described.First consider as shown in the formula the expectation angular velocity control law shown in (34):

$\left[\begin{array}{c}{\mathrm{\&omega;}}_{d1}\\ {\mathrm{\&omega;}}_{d2}\end{array}\right]=-k\left[\begin{array}{c}{\mathrm{\&rho;}}_1\\ {\mathrm{\&rho;}}_2\end{array}\right]+g\left[\begin{array}{c}{\mathrm{\&Delta;}}_2\\ {-\mathrm{\&Delta;}}_1\end{array}\right]---\left(34\right)$

Under the control law effect represented by formula (34), the error attitude ρ of spacecraft converges to zero.This can by choosing the Lyapunov function shown in 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 error attitude converges to zero, due to singular term Δ in formula (34) ₁and Δ ₂infinity may be become.This situation can solve by selecting appropriate ride gain g and k, examines or check such as formula the function shown in (36):

$V_0=\frac{{\mathrm{\&rho;}}_3^2}{{({\mathrm{\&rho;}}_1^2+{\mathrm{\&rho;}}_2^2)}^2}---\left(36\right)$

In formula (36), assume initial time to V ₀seeking time derivative can obtain formula (37):

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

As selection g>2k, there is g-2k>0.On the other hand, from above to the explanation of the stability of error attitude ρ, 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 formula (34) ₁and Δ ₂can not infinity be become, and zero can be converged in time.

On the other hand, in order to avoid initial time cause Δ ₁and Δ ₂formula (34) can be modified to the saturated form shown in formula (32) by infinity.

Then, computations control moment.Adopt such as formula the angular velocity tracing control rule 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 ₂for normal number, select in working control.Formula (38) is substituted into following formula and can try to achieve instruction control moment such as formula shown in (39):

$T_c=\left[\begin{array}{c}{J}_1{\stackrel{\&CenterDot;}{\mathrm{\&omega;}}}_1\\ J_2{\stackrel{\&CenterDot;}{\mathrm{\&omega;}}}_2\end{array}\right]---\left(39\right)$

Finally, the instruction control moment obtained by formula (39) is substituted into formula (25) computations framework rotating speed.

Phase III, judge whether to be switched to steady-state controller.Make m _srepresent the steady-state attitude errors threshold value of specifying, if m _a>m _s, then the operation of subordinate phase is repeated; If m _a≤ m _s, be then switched 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, $m=\frac{s_1+s_2}{\left|\right|s_1+s_2\left|\right|}=\left[\begin{array}{c}{m}_x\\ m_y\\ 0\end{array}\right],$ $\stackrel{\&OverBar;}{m}=\left[\begin{array}{c}{m}_x\\ m_y\end{array}\right]---\left(41\right)$

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 _vfor positive constant, selected in working control; a ₁=m _x/ J ₁and a ₂=m _x/ J ₂.V represents selected intermediate variable, for the time-derivative of v; And v _drepresent the expectation value of intermediate variable.In addition, ε is positive a small amount of in the formula (40), can select according to actual conditions, its introducing be in order to avoid time, larger frame corners speed may be caused.

The following describes the effect of steady-state controller (40-44).Formula (45) can be obtained as follows by formula (41) and (42):

m _xJ ₁ω ₁+m _yJ ₂ω ₂=v ₂(45)

Due to s ₁-s ₂perpendicular with m, and (s ₁-s ₂) ^tj ω=0, accordingly, the relational expression (46) from below formula (42) and formula (45) can obtain:

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

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

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

Formula (47) represents that attitude error successively decreases, and therefore, after control laws transformation to steady-state controller, can not be switched to the error attitude convergence controller of second step to the 4th step again.So far, can be clear and definite what know that formula (43) represents is to expectation intermediate variable v _dtracing control rule.On the other hand, be the hypothesis of zero according to formula (42) and total angular momentum, formula (48) can be obtained:

v=-h ₀m ^T(h ₁+h ₂) (48)

Formula (49) can be obtained to formula (48) differentiate:

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

As can be seen from formula (49), can have and infinite organize solution more, its least-norm solution can be become such as formula shown in (50) by 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 can obtain the skeleton instruction rotating speed shown in formula (40).

So far, obtained the instruction framework rotating speed at two SGCMGs of different gesture stability stages completely, driven SGCMGs to rotate according to the instruction framework rotating speed of gained and spacecraft maneuver just can be made to arrive targeted attitude.

Attitude maneuver control imitation result below in conjunction with some micro-thermoelectric generator explains this programme.

See Fig. 2, assuming that satellite is 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, assuming that the rotor angular momentum of each SGCMGs is h ₀=50N.m.s.Attitude parameter and the gyro gimbal Angle Position parameter of initial time spacecraft are as follows:

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

The parameter that controller all and of the present invention is relevant is 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,

3rd step: k ₁=k ₂=0.8/s,

4th step: k _d=0.01, D ₀=0.001

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 initial time two SGCMGs is reverse, the unusual tolerance of two SGCMGs is zero, and gyro is in interior unusual.Meanwhile, 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, the lower frame corners speed b specified with frame ₀=0.01rad/s, drives two SGCMGs to rotate backward 20s, two SGCMGs is departed from unusual.As can be seen from Fig. 8 and Fig. 9, after this, steering logic enters second step, and what control spacecraft is tending towards targeted attitude, and two SGCMGs are again close to interior unusual simultaneously, are less than designated value m when attitude error converges to _s=1 × 10 ^-6time (close to emulation moment 170s), steering logic is switched to steady-state controller, and attitude error is reduced further.In the switching of this step, skeleton instruction produces a small size point of discontinuity, but after being switched to steady-state controller, attitude error is restrained further, and whole steering logic can not return previous step.Therefore, the stage that controls from error attitude converged state to stable state only once switches, and there will not be the chatter phenomenon caused owing to switching back and forth between the two controllers.Finally, whole steering logic had both made two SGCMGs depart 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 being applicable to spacecraft with two parallel SGCMGs.Utilize control method of the present invention, according to spacecraft in practical application with the systematic parameter of SGCMGs and attitude error parameter, select suitable controling parameters, just can utilize the targeted attitude that spacecraft maneuver is expected to any one by the SGCMGs of two parallel installations.The present invention may be used for the situation tackling control-moment gyro group partial failure in spacecraft, also can be used for the gesture stability of the spacecraft only using two parallel SGCMGs.

The above is only the preferred embodiment of the present invention; should be understood that; for those skilled in the art; under the premise without departing from the principles of the invention; some improvement can also be made; or carry out equivalent replacement to wherein portion of techniques feature, these improve and replace and also should be considered as protection scope of the present invention.

Claims (2)

1. use a spacecraft attitude maneuver control method for two single-gimbal control momentum gyro, it is characterized in that: the characterization step of the method comprises three phases:

Stage one: gyro is initially unusual evades the stage

Gyro is initially unusual to be evaded the stage and is made up of the unusual decision logic of gyro and the unusual disengaging controller of gyro; Whether inspection initial time spacecraft is unusual with the error and two single-gimbal control moment gyros SGCMGs expecting attitude; Make m ₀> 0 represents initial time attitude error threshold value, m ₀occurrence select in actual applications; If attitude error is less than m ₀, or gyro is away from unusual, then directly enter the stage two; If attitude error is greater than m ₀, and gyro is close to unusual, then the speed driver framework that utilization etc. are reverse greatly rotates regular hour T ₀>0, gyro is departed from unusual, expression formula is such 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 ₀for positive constant, select less, in order to avoid cause large frame corners velocity jump after being switched to follow-up attitude maneuver control model;

Stage two: error attitude converged state

Error attitude converged state restrains controller by error attitude and forms; Two SGCMGs install arbitrarily in spacecraft body, only need to carry out coordinate conversion to the corresponding entry in the method; Make that { X, Y, Z} represent that the body of spacecraft is connected coordinate system, J=diag (J ₁j ₂j ₃) inertia matrix of system that forms for spacecraft when gyro locks and gyro;

Wherein diag (J ₁j ₂j ₃) represent (J ₁j ₂j ₃) get diagonal matrix, ω=[ω ₁ω ₂ω ₃] ^trepresent three components of angular velocity in body coordinate system of spacecraft;

First, calculation expectation attitude angular velocity, expression formula is such 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 _d2represent the expectation attitude angular velocity along X and Y-axis; ρ=[ρ ₁ρ ₂ρ ₃] ^tfor describing the Rodrigues parameter of spacecraft attitude; Ride gain g and k is positive constant, for ensureing Δ in the process that attitude error is restrained ₁and Δ ₂converge to zero, make the selection of error attitude converged state meet g > 2k; Sat (x, a) for such as formula the saturation function shown in (3):

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

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

Then, according to angular velocity tracing control rule, computations control moment, expression formula is such as formula shown in (4) and formula (5):

$\begin{array}{c}{\stackrel{\&CenterDot;}{\mathrm{\&omega;}}}_1=k_1({\mathrm{\&omega;}}_{d1}-{\mathrm{\&omega;}}_1)\\ {\stackrel{\&CenterDot;}{\mathrm{\&omega;}}}_2=k_2({\mathrm{\&omega;}}_{d2}-{\mathrm{\&omega;}}_2)\end{array}---\left(4\right)$

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

Wherein, k ₁and k ₂for normal number, select in working control; T _cfor instruction control moment;

Finally, computations frame corners speed, expression formula is such 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, assuming that the angular momentum equal and opposite in direction of two gyrorotors; For calculating need moment output matrix to be described, 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 ₂for the frame corner of gyro; Svd is carried out such as formula shown in (8) to matrix D:

D＝USV ^T(8)

U and V is orthogonal matrix; S=diag (σ ₁σ ₂), σ ₁and σ ₂for two singular values of matrix D, and meet σ ₁>=σ ₂>=0; computing method such 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 constant value, specify in control procedure; λ _dfor controlling the positive number of specifying in implementation process, λ represents the unusual tolerance of D, calculates by formula (11):

λ＝det(DD ^T) (11)

Make m _s> 0 represents the attitude error threshold value expected, m _soccurrence specify in actual applications; Judge whether attitude error converges in the threshold range of specifying, if do not have, then continue use error attitude convergence controller and control; If so, the control in stage three is then entered;

Stage three: stable state controls the stage

The stable state control stage is made up 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 _vfor positive constant, selected in working control; a ₁=m _x/ J ₁and a ₂=m _x/ J ₂; V represents selected intermediate variable, from expression formula above, expression be the projection of angular momentum on the angle separated time of two rotor vectors of spacecraft; for the time-derivative of v; And v _drepresent the expectation value of intermediate variable; In addition, ε is positive a small amount of, selectes according to actual conditions.

2. the spacecraft attitude maneuver control method of use according to claim 1 two single-gimbal control momentum gyro; It is characterized in that: in the stage one, the instruction framework rotating speed that utilization etc. are reverse greatly, two SGCMGs are departed from and is controlling the inside and outside unusual of initial time appearance; In the stage two, attitude is expected by making the attitude convergence of spacecraft based on the expectation angular velocity of Rodrigues parameter, then, passing ratio angular velocity tracing control rule is followed the tracks of and is expected angular velocity, and then obtain instruction control moment, recycle that correction based on svd is inverse solves instruction framework rotating speed; In the stage three, utilize the projection effect intermediate variable of the angular momentum of spacecraft on the angle separated time of two rotor vectors, design expects that intermediate variable and corresponding tracing control are restrained, and the attitude error of spacecraft is restrained further, and obtains instruction framework rotating speed on this basis.