CN105867401A - Spacecraft posture fault tolerance control method of single gimbal control moment gyroscope groups - Google Patents

Abstract

A spacecraft posture fault tolerance control method of single gimbal control moment gyroscope groups includes the following steps that firstly, a kinetic equation and a kinematical equation are established when partial failures exist in the single gimbal control moment gyroscope groups (SGCMGs), wherein a coordinate system is defined, and a control system state equation is established; secondly, on the basis of in-orbit operation characteristics of a spacecraft, the spacecraft posture fault tolerance control method of the single gimbal control moment gyroscope groups is adopted; thirdly, the sliding mode control law is designed, wherein a sliding mode face is designed, the control law is primarily designed and the control law is improved. The method has the advantages that the designed control law is also applicable to fault tolerance control of aircrafts with flywheels as execution mechanisms; people do not need to learn about prior information of faults, real-time estimation of fault information and interference information is achieved through self-adaptation control, and fault time varying is allowed; the method is applicable to SGCMGs of any structure or partial failure modes of flywheels; the method is used in aircrafts of the SGCMGs, the rotation speed of a gyroscope frame serves as direct control amount, and the method conforms to engineering practice.

Description

The spacecraft attitude fault tolerant control method of single-gimbal control moment gyros

[technical field]

The present invention use single-gimbal control moment gyros (Single Gimbal Control Moment Gyros, SGCMGs) it is the three axis stabilized spacecraft of executing agency, the attitude faults-tolerant control when executing agency occurs part failure of removal Method (Fault-Tolerant Control, FTC), has stronger robustness realizing spacecraft, belongs to space flight fault Device gesture stability field.

[background technology]

Along with the development of space technology, space mission is increasingly sophisticated, thus security, stability and the control to spacecraft Precision it is also proposed higher requirement.From the development history of space technology it can be seen that a lot of accident be all one small Fault causes, and the Lewis satellite failure of NASA transmitting in such as 1997 causes all of thruster to lose efficacy, and finally this is defended Star crashes into atmosphere, brings about great losses.How avoiding risk, allowing spacecraft have fault tolerance, to become now a lot of space flight special One emphasis of family's research.At present, fault diagnosis and faults-tolerant control have become as maintenance the reliability of spacecraft, maintainability and One important channel of validity.

The thought of faults-tolerant control is to be proposed in 1971 by Niederlinski the earliest, and faults-tolerant control theory obtains fast subsequently The development of speed.According to the feature of method for designing, faults-tolerant control is generally divided into active tolerant control and passive fault tolerant control.Actively hold Wrong control is after fault occurs, and redesigns a control system according to desired characteristic, and at least can make whole system Reach stable.Passive fault tolerant control uses fixing controller to guarantee that closed-loop system is insensitive to specific fault, keeps system Stablize.Comparing active tolerant control, the system failure is detected or diagnoses owing to need not by passive fault tolerant control, is also not required to Wanting the fault reaction time, therefore simple in construction, fast response time and design difficulty are relatively low.

In attitude faults-tolerant control field, current achievement in research is mainly using control moment as controlled quentity controlled variable and fault modeling Object.But in practical engineering application, when using angular momentum exchange device as attitude control actuator, actual control The rotating speed of executing agency often.Such as, the spacecraft with flywheel as executing agency, control moment is determined by Speed of Reaction Wheels.Separately On the one hand, it is relevant that the moment output of angular momentum exchange device is often also possible to the attitude current to gyro, such as, when using control When moment gyro group (CMG) is executing agency, its singularity problem having and the feature of gyro transverse matrix time-varying, therefore Control moment is affected by frame corners and framework rotating speed simultaneously.

The existence of the problems referred to above makes current achievement in research be difficult in Practical Project to be difficult to apply, especially for CMG is the spacecraft attitude faults-tolerant control field of executing agency, there is no that preferable engineer applied method realizes at present.

[summary of the invention]

The present invention proposes a kind of for the spacecraft with single-gimbal control moment gyros SGCMGs as executing agency, passes through Sliding-mode control and self-adaptation control method, it is achieved executing agency is existed partial failure fault (each gyro of SGCMGs Moment exports) the pose stabilization control of spacecraft.

For the problems referred to above, technical solution of the present invention is as follows:

There is kinetics equation and the kinematical equation of the spacecraft of partial failure fault according to executing agency, utilize Euler The quantity of state such as angle and Euler angle rate sets up sliding-mode surface, and utilizes the fault of self-adaptation control method On-line Estimation spacecraft to believe Breath, by designing sliding mode control strategy and suitably controlling parameter so that spacecraft can realize attitude under non-failure conditions Stable, then this set control parameter can make, under spacecraft executing agency partial failure failure condition, to remain to realize attitude steady equally Fixed.Concrete operating procedure is as follows

Step 1: set up the kinetics equation when single-gimbal control moment gyros SGCMGs exists partial failure fault And kinematical equation.Specifically include following steps:

Step 1.1: definition coordinate system

A. body coordinate system f_b(o_bx_by_bz_b)

This coordinate system is connected with spacecraft, initial point O_bIt is positioned at spacecraft centroid, O_bx_bAxle points to the direction of motion of spacecraft, O_bz_bAxle points to spacecraft above perpendicular to flightpiston, O_by_bAxle, O_bx_bAxle and O_bz_bAxle constitutes right-handed coordinate system.

B. orbital coordinate system f_o(O_ox_oy_oz_o)

Orbital coordinate system initial point is at the barycenter of spacecraft, O_oz_oAxle points to the earth's core, O along local vertical_ox_oAxle is at orbit plane Inside it is perpendicular to O_oz_oAxle, and point to the direction of motion of spacecraft, O_oy_oAxle, O_ox_oAxle and O_oz_oAxle constitutes right-handed coordinate system.This coordinate System is in space with angular velocity omega_oAround O_oy_oAxle rotates.

C. geocentric inertial coordinate system f_i(O_ix_iy_iz_i)

The initial point of geocentric inertial coordinate system is connected in the earth's core O_iPlace, O_ix_iAxle plane under the line and point to the first point of Aries, O_iz_i It is perpendicular to equatorial plane and consistent with rotational-angular velocity of the earth direction, O_iy_iIn axle plane under the line, and and O_ix_iAxle, O_iz_i Axle form right angle coordinate system.

D.SGCMGs frame coordinates system f_ci(O_cig_is_it_i)

The initial point of frame coordinates system is at the barycenter O of SGCMG_ciPlace, coordinate system all directions unit vector is respectively along gimbal axis side To unit vectorUnit vector along armature spindle rotary speed directionReciprocal unit vector is exported along gyroscopic couple

Step 1.2 control system state equation is set up

Step 1.2.1 sets up kinetics equation and kinematical equation

Kinetics equation:

$I_b{\stackrel{\·}{\mathrm{\ω}}}_b+{\mathrm{\ω}}_b^{\×}(I_b{\mathrm{\ω}}_b+A_s{I}_{ws}\mathrm{\Ω})=-h_0{A}_t{\stackrel{\·}{\mathrm{\δ}}}_r+T_d---\left(1\right)$

Wherein, I_bIt is whole system inertia matrix, it is believed that I_bIt it is a constant value inertia matrix；

ω_b=[ω_x ω_y ω_z]^TFor spacecraft absolute angular velocities component array under body series；

h₀Nominal angular momentum for each gyrorotor；

For ω_bAbout the derivative of time,It is defined as form:

${\mathrm{\ω}}_b^{\×}=\left[\begin{array}{ccc}0& -{\mathrm{\ω}}_z& {\mathrm{\ω}}_y\\ {\mathrm{\ω}}_z& 0& -{\mathrm{\ω}}_x\\ -{\mathrm{\ω}}_y& {\mathrm{\ω}}_x& 0\end{array}\right]$

A_s=[s₁ s₂ … s_n] it is SGCMGs rotor speed direction matrix；

I_wsFor SGCMGs rotor axial rotary inertia battle array；

Ω is rotor speed vector；h₀Nominal angular momentum for each gyrorotor；

A_t=[t₁ t₂ … t_n] it is SGCMGs transverse matrix；

δ is gyro gimbal angle；

T_dFor spacecraft experienced interference moment vector；

Kinematical equation:

Wherein, attitude angleθ, ψ are the roll angle of spacecraft, the angle of pitch and yaw angle；Attitude angular velocity Respectively Forθ, ψ are about the derivative of time；ω_oFor track system around body series O_oy_oThe angular speed that axle rotates；

Step 1.2.2 sets up fault mode

${\stackrel{\·}{\mathrm{\δ}}}_r=E\stackrel{\·}{\mathrm{\δ}}+f---\left(3\right)$

It is pointed out that fault modeling here is pro forma, among real system, this fault mode equation is hidden It is contained in the motion of spacecraft.Although the expression of E and f or concrete numerical value cannot be known, but it is easily determined SGCMGs In whether exist gyro stuck and cannot output torque, this is enough.

Wherein,For gyroscopic theory framework rotating speed vector；For gyro actual frame rotating speed vector；

E=diag (e₁ e₂ … e_n) for the property taken advantage of ffault matrix, e_iFailure Factor for i-th gyro；

F=[f₁ f₂ … f_n]^TFor the impact on gyro gimbal rotating speed of the additivity fault,

f_iRotating speed deviation for i-th gyro.

Kinematical equation under step 1.2.3 derivation fault mode and kinetics equation

Wushu (3) substitutes into formula (1), and is defined as follows the equivalence interference of gyrorotor unit nominal angular momentum, Equivalent Rotational Inertia battle array and equivalence gyro group angular momentum: equivalence interference: d=T_d/h₀；

Equivalent moment of inertia matrix: J=I_b/h₀；Equivalence gyro group angular momentum: h_c=A_sI_wsΩ/h₀；

OrderAs the controlled quentity controlled variable of control system, obtain the kinetics equation under fault:

$J{\stackrel{\·}{\mathrm{\ω}}}_b+{\mathrm{\ω}}_b^{\×}({\mathrm{J\ω}}_b+h_c)=-A_{t}Eu-A_{t}f+d---\left(4\right)$

Under low-angle assumed condition, formula (2) can approximate to be write as:

${\mathrm{\ω}}_b\≈\stackrel{\·}{X}+F\left(x\right)---\left(5\right)$

Wherein:

ω_oCalculated by the orbit parameter of spacecraft；Represent the quantity of state of system；

A_s,A_tCan be calculated as follows:

$\begin{array}{c}{s}_i=s_{i0}{\mathrm{cos\δ}}_i+t_{i0}{\mathrm{sin\δ}}_i\\ t_i=t_{i0}{\mathrm{cos\δ}}_i-s_{i0}{\mathrm{sin\δ}}_i\end{array}---\left(6\right)$

s_i0, t_i0Determine according to the configuration that gyro is concrete, for unit vector；s_i0Represent s_iInitial value；t_i0Represent t_iAt the beginning of Value；

Step 2 based on spacecraft actual features in orbit, the application present invention based on an assumption that

Assume 1: experienced interference moment bounded in spacecraft running, it may be assumed that | | d | |≤T_d；And additivity fault is to top The impact of spiral shell framework rotating speed is limited, | | A_tf||≤T_f.Wherein agreement | | | | the 2-norm of representing matrix or vector, T_d,T_fFor Unknown constant.Assume that 1 can be comprehensively for following expression:

||-A_tf+d||≤M_d (7)

Assume 2: spacecraft moment of inertia matrix is positive definite symmetric matrices, i.e. J symmetry and positive definite.

Assume 3: the present invention does not consider the situation that gyro is entirely ineffective, i.e. assume to there is unknown constant e₀Meet:

$0<e_0\&le;\underset{1\&le;i\&le;n}{\min }\left(e_i\right)---\left(8\right)$

Wherein, the number of gyro during n is SGCMGs.

Step 3 sliding formwork design of control law.Specifically include following steps:

Step 3.1 sliding-mode surface designs

Selection sliding-mode surface is:

$s=\stackrel{\&CenterDot;}{x}+kx---\left(9\right)$

Wherein k ＞ 0, gives constant for designer.Then when s → 0, x → 0, For by appearance The column vector of state angle composition, represents the quantity of state of system,Represent the state vector derivative to the time.

Step 3.2 control law Preliminary design

Select following sliding formwork control law:

$u=-A_t^T{\left(A_t{A}_t^T\right)}^{-1}\{{\mathrm{\&omega;}}_b^{\&times;}\&lsqb;{\mathrm{J\&omega;}}_b+h_c\&rsqb;-Jk\stackrel{\&CenterDot;}{x}+J\stackrel{\&CenterDot;}{F}\left(x\right)-\mathrm{\&gamma;}\left(t\right)\frac{s}{||s||}-{\hat{M}}_d\frac{s}{||s||}\}---\left(10\right)$

In above-mentioned control law, value and the meaning of each parameter are as follows:

A_t=[t₁ t₂ … t_n] it is SGCMGs transverse matrix,For A_tTransposed matrix；

J、h_cEquivalent moment of inertia battle array defined in step 1.2.3 and equivalence gyro group angular momentum；

For F (x) in step 1.2.3 about the derivative of time；S is sliding-mode surface；

M in expression (10)_dEstimate, take adaptive updates rule be:

$\stackrel{\&CenterDot;}{\hat{M}}=c_0||s||---\left(11\right)$

One parameter of γ (t): introducing, takes

$\mathrm{\&gamma;}\left(t\right)=-\sqrt{n}\mathrm{\&upsi;}+\sqrt{n}\mathrm{\&upsi;}\widehat{\mathrm{\&xi;}}+{\mathrm{\&epsiv;}}_0---\left(12\right)$

$\mathrm{\&upsi;}=\frac{||u||}{\widehat{\mathrm{\&xi;}}}---\left(13\right)$

$\stackrel{\&CenterDot;}{\widehat{\mathrm{\&xi;}}}=\sqrt{n}{c}_1\mathrm{\&upsi;}||s||---\left(14\right)$

Defined variableWherein c₀,c₁,ε₀Being a normal number, n is the number of gyro under certain configuration, and u is control Amount processed,For the estimate of ξ, υ is intermediate variable,ForDerivative to the time.

Taking Lyapunov function is

$V=\frac{1}{2}{s}^{T}Js+\frac{1}{2c_0}{\tilde{M}}_d^2+\frac{e_0}{2c_1}{\widetilde{\mathrm{\&xi;}}}^2---\left(15\right)$

Wherein Remaining parameter has been given by above, and note Δ E=I-E, I are unit Battle array, E is the property taken advantage of ffault matrix.

Above-mentioned Lyapunov function against time is differentiated, and utilizes formula (10)～(14), can obtain:

$\stackrel{\&CenterDot;}{V}\&le;-{\mathrm{\&epsiv;}}_0||s||---\left(16\right)$

Formula (16) shows, function V at least will not monotonic increase, therefore can obtain sup_t≥0V (t)≤V (0), wherein sup () Represent supremum, i.e.Bounded, therefore,ThusExist and have Boundary, according to Barbalat lemma, hasTherefore there is x → 0,

The improvement of step 3.3 control law

Above-mentioned control law there are in fact buffeting problem and singularity problem, it is therefore desirable on the basis of above-mentioned control law Improve.

Buffeting problem: owing to sliding formwork control has the discontinuity of control, therefore there is chattering phenomenon.According to sliding formwork control Theory, the present invention uses s/ (| | s | |+τ) approximation to replace sign function s/ | | s | |, and wherein τ is a less positive number, generally Give according to actual conditions, be typically selected in 10^-3～10^-1Between.

Singularity problem: when each gyro output torque coplanar (or conllinear), the normal direction of moment plane (or moment side To Normal plane) direction cannot output torque, now SGCMGs transverse matrix A_tNot full rank, formula (9) cannot solve, therefore Formula (9) is made improvement by the method solved with reference to robust pseudoinverse.

Therefore obtain improving control strategy and be:

$u=-A_t^T{\&lsqb;A_t{A}_t^T+\mathrm{\&lambda;}(I_{3\&times;3}+E_{3\&times;3})\&rsqb;}^{-1}\{{\mathrm{\&omega;}}_b^{\&times;}\&lsqb;{\mathrm{J\&omega;}}_b+h_1\&rsqb;-Jk\stackrel{\&CenterDot;}{x}+J\stackrel{\&CenterDot;}{F}\left(x\right)-\mathrm{\&gamma;}\left(t\right)\frac{s}{||s||+\mathrm{\&tau;}}-{\hat{M}}_d\frac{s}{||s||+\mathrm{\&tau;}}\}---\left(17\right)$

Wherein: λ is a less positive number, it usually needs by real work situation value, typically can be taken at 10^-3~ 10^-1Between；I_3×3It is three rank unit matrixs, E_3×3For diagonal matrix, form is:

$E_{3\&times;3}=\left[\begin{array}{ccc}0& {\mathrm{\&epsiv;}}_3& {\mathrm{\&epsiv;}}_2\\ {\mathrm{\&epsiv;}}_3& 0& {\mathrm{\&epsiv;}}_1\\ {\mathrm{\&epsiv;}}_2& {\mathrm{\&epsiv;}}_1& 0\end{array}\right],$

In matrix, each element is: ε_j=0.01 (0.5 π t+ φ_j) (j=1,2,3), φ_j=π (j-1)/2.

The same formula of remaining parameter (11)～(14).

λ, τ obtain too big, and above-mentioned improvement cannot ensure the stability of system；In theory, as long as ensureing that the value of λ, τ is enough Little, formula (17) is although remaining to meet the robustness of failure system.But it practice, if λ, τ obtain too small, it is impossible to play elimination strange The opposite sex and the effect of chattering phenomenon.Therefore, choosing of λ, τ must be adjusted according to the parameter of real system, typically can be from 10^-3～10^-1Based on selecting a parameter, it is adjusted according to Actual Control Effect of Strong.

It addition, the control law of present invention design is equally applicable to the spacecraft using flywheel as angular momentum exchange device, only Will be by the gyro relative angular momentum h of kinetic model (4)_cIt is changed to the relative angular momentum h of flywheel_w, transverse matrix A_tIt is changed to flywheel Matrix C is installed, then uses same control law (17) to control the moment of each flywheel, ensure that the steady of failure system equally Fixed.

The present invention devises the attitude fault tolerant control method of the spacecraft of a kind of actuator failure, and its advantage is main such as Under:

1) although the sliding formwork control law of present invention design is designed with SGCMGs for background, but due to the power of gyro Learning characteristic similar to flywheel, design control law the most of the present invention is equally applicable to the fault-tolerant control of the spacecraft with flywheel as executing agency System.

2) present invention need not have any actual knowledge of the prior information of fault, but come fault message by Self Adaptive Control and Interference information carries out real-time estimation, therefore allows fault time-varying, as long as it is entirely ineffective to ensure to there is not certain gyro.

3) not for concrete SGCMGs configuration or flywheel configuration during the present invention relates to, simply stability is being proved In used transverse matrix A_tOr the 2-norm installing each column vector of Matrix C is 1 this feature, and this is in Practical Project Being easily met, therefore the present invention is suitable for the SGCMGs of arbitrary configuration or the partial failure pattern of flywheel.

4) present invention is for in the spacecraft of SGCMGs, is using gyro gimbal rotating speed as direct controlled quentity controlled variable, meets work Cheng Shiji, and be the spacecraft of executing agency to flywheel, although the directly output torque of each flywheel of control, but the output of flywheel Moment and rotating speed are directly proportional, and are the most also equivalent to control Speed of Reaction Wheels, agree with engineering equally actual.

[accompanying drawing explanation]

Fig. 1 is attitude stabilization faults-tolerant control schematic diagram.

Fig. 2 is spacecraft body coordinate system schematic diagram.

Fig. 3 is spacecraft orbit coordinate system schematic diagram.

Fig. 4 is spacecraft inertial coodinate system schematic diagram.

Fig. 5 is SGCMG frame coordinates system schematic diagram.

Fig. 6 is design of control law schematic flow sheet.

Fig. 7 is the SGCMGs schematic diagram of pyramid configuration.

[detailed description of the invention]

Below in conjunction with the accompanying drawings shown in 1-7, as a example by the spacecraft of certain model, illustrate the implementing procedure of the present invention.Boat The parameter of it device is as follows:

Spacecraft moment of inertia matrix is:

$I_b=\left[\begin{array}{ccc}15349.895& -213.77562& -87.759063\\ -213.77562& 71376.093& 84.478260\\ -87.759063& 84.478260& 74260.183\end{array}\right](kg\&CenterDot;m^2)$

Selecting the SGCMGs of pyramid configuration, wherein the nominal angular momentum of gyro is 200Nms；Initial attitude angle is:θ (0)=1.5 °, ψ (0)=1.5 °；ω_bInitial value be ω_b(0)=[0 0 0]^T；Spacecraft flight track is Circular orbit, flight track radius is 26600km, and environmental disturbances moment considers terrestrial gravitational perturbation, solar light pressure moment, too Sun radiation pressure disturbances etc., use following outer interference mode, for

$\left\{\begin{array}{c}{T}_{d1}=A_0\left(3cos\right({\mathrm{\&omega;}}_{0}t)+1)\\ T_{d2}=A_0\left(1.5\sin \right({\mathrm{\&omega;}}_{0}t)+3cos({\mathrm{\&omega;}}_{0}t\left)\right)\\ T_{d3}=A_0\left(3\sin \right({\mathrm{\&omega;}}_{0}t)+1)\end{array}\right.$

Wherein A₀For disturbance torque amplitude, take A₀=1.5 × 10^-5N·m。

Assume the spacecraft property taken advantage of fault simultaneously and additivity fault.

The property taken advantage of fault parameter is:

$e_i\left(t\right)=0.7+0.15rand\left(t\right)+0.1sin(0.5t+\frac{i\mathrm{\&pi;}}{5}),(i=1,2,3,4,t\&GreaterEqual;t_i)$

Wherein rand () represents that amplitude is the random function of 1, t₁=150s, t₂=180s, t₃=200s, t₄=240s

Additivity fault parameter is:

f_i(t)=-0.01 (i=1,2,3,4, t >=t_i)

Provide fault parameter and outer interference expression formula simply emulates needs.

Start setting up control law below the attitude of spacecraft is controlled.

1, the kinetics equation when SGCMGs exists partial failure fault and kinematical equation are set up.Specifically include as follows Step:

1.1 definition coordinate systems: according to relative coordinate system defined in step 1.1.

1.2 control system state equations are set up

First according to the spacecraft relevant parameter used of illustrating, the most following systematic parameter can directly be listed:

Select the SGCMGs of pyramid configuration, then number n=4 of gyro.

Spacecraft moment of inertia matrix is:

$I_b=\left[\begin{array}{ccc}15349.895& -213.77562& -87.759063\\ -213.77562& 71376.093& 84.478260\\ -87.759063& 84.478260& 74260.183\end{array}\right](kg\&CenterDot;m^2)$

The nominal angular momentum h of each gyrorotor₀=200Nms；

T_d=[T_d1 T_d2 T_d3] it is spacecraft experienced interference moment vector；

Below according to pyramid configuration reference view, calculate A_s,A_tExpression formula.

s₁₀=[0-1 0]^T,g₁₀=[-sin β 0 cos β]^T

s₂₀=[-10 0]^T,g₂₀=[0 sin β cos β]^T

s₃₀=[0 1 0]^T,g₃₀=[sin β 0 cos β]^T

s₄₀=[1 0 0]^T,g₄₀=[0-sin β cos β]^T

According to formula (6), can obtain:

$A_s=\left[\begin{array}{cccc}\cos \mathrm{\&beta;}\sin \mathrm{\&delta;}1& -\cos \mathrm{\&delta;}2& -\cos \mathrm{\&beta;}\sin \mathrm{\&delta;}3& \cos \mathrm{\&delta;}4\\ -\cos \mathrm{\&delta;}1& -\cos \mathrm{\&beta;}\sin \mathrm{\&delta;}2& \cos \mathrm{\&delta;}3& \cos \mathrm{\&beta;}\sin \mathrm{\&delta;}4\\ \sin \mathrm{\&beta;}\sin \mathrm{\&delta;}1& \sin \mathrm{\&beta;}\sin \mathrm{\&delta;}2& \sin \mathrm{\&beta;}\sin \mathrm{\&delta;}3& \sin \mathrm{\&beta;}\sin \mathrm{\&delta;}4\end{array}\right]$

$A_t=\left[\begin{array}{cccc}\cos \mathrm{\&beta;}\cos \mathrm{\&delta;}1& \sin \mathrm{\&delta;}2& -\cos \mathrm{\&beta;}\cos \mathrm{\&delta;}3& -\sin \mathrm{\&delta;}4\\ \sin \mathrm{\&delta;}1& -\cos \mathrm{\&beta;}\cos \mathrm{\&delta;}2& -\sin \mathrm{\&delta;}3& \cos \mathrm{\&beta;}\cos \mathrm{\&delta;}4\\ \sin \mathrm{\&beta;}\cos \mathrm{\&delta;}1& \sin \mathrm{\&beta;}\cos \mathrm{\&delta;}2& \sin \mathrm{\&beta;}\cos \mathrm{\&delta;}3& \sin \mathrm{\&beta;}\cos \mathrm{\&delta;}4\end{array}\right]$

Wherein β can be determined by following process,

Three shaft angle momentum under body series are respectively:

H_x=2h₀+2h₀cosβ

H_y=2h₀+2h₀cosβ

H_z=4h₀sinβ

In order to the three shaft angle momentum making pyramid configuration are equal, i.e. H_x=H_y=H_z, try to achieve β=53.1 °.Then h_c=A_s[h₀ h₀ h₀ h₀]^T。

ω_oDetermine based on orbit parameter.Due to spacecraft be radius be the circular orbit of 26600km, therefore:

${\mathrm{\&omega;}}_0=\frac{2\mathrm{\&pi;}}{T}=\sqrt{\frac{\mathrm{\&mu;}}{R^3}}$

Wherein μ is Gravitational coefficient of the Earth, is 3.986005 × 10¹⁴m³/s², R is orbit radius.

It is calculated: ω₀=4.6020 × 10^-4rad/s。

1.2.1 kinetics equation and kinematical equation are set up

Kinetics equation:

$I_b{\stackrel{\&CenterDot;}{\mathrm{\&omega;}}}_b+{\mathrm{\&omega;}}_b^{\&times;}(I_b{\mathrm{\&omega;}}_b+A_s{I}_{ws}\mathrm{\&Omega;})=-h_0{A}_t{\stackrel{\&CenterDot;}{\mathrm{\&delta;}}}_r+T_d---\left(18\right)$

Kinematical equation:

1.2.2 fault mode is set up

${\stackrel{\&CenterDot;}{\mathrm{\&delta;}}}_r=E\stackrel{\&CenterDot;}{\mathrm{\&delta;}}+f---\left(20\right)$

E=diag (e₁ e₂ e₃ e₄) for the property taken advantage of fault compression, f=[f₁ f₂ f₃ f₄]^TFor additivity fault compression.

1.2.3 the kinematical equation under derivation fault mode and kinetics equation

If d=T_d/h₀, J=I_b/h₀,h_c=A_sI_wsΩ/h₀, and makeAs the controlled quentity controlled variable of control system, substitute into fault Pattern, to kinetics equation, obtains the kinetics equation under fault:

$J{\stackrel{\&CenterDot;}{\mathrm{\&omega;}}}_b+{\mathrm{\&omega;}}_b^{\&times;}({\mathrm{J\&omega;}}_b+h_c)=-A_{t}Eu-A_{t}f+d---\left(21\right)$

Under low-angle assumed condition, kinematical equation (2) can approximate to be write as:

${\mathrm{\&omega;}}_b\&ap;\stackrel{\&CenterDot;}{x}+F\left(x\right)---\left(22\right)$

Wherein:

2, based on spacecraft actual features in orbit, the application present invention based on an assumption that

Assume 1: experienced interference moment bounded in spacecraft running, it may be assumed that | | d | |≤T_d；And additivity fault is to top The impact of spiral shell framework rotating speed is limited, | | A_tf||≤T_f.Wherein agreement | | | | the 2-norm of representing matrix or vector, T_d,T_fFor Unknown constant.Assume that 1 can be comprehensively for following expression:

||-A_tf+d||≤M_d (23)

Assume 2: spacecraft moment of inertia matrix is positive definite symmetric matrices, i.e. J symmetry and positive definite.

Assume 3: the present invention does not consider the situation that gyro is entirely ineffective, i.e. assume to there is unknown constant e₀Meet:

$0<e_0\&le;\underset{1\&le;i\&le;4}{\min }\left(e_i\right)---\left(24\right)$

3, sliding formwork design of control law.Specifically include following sub-step:

3.1 sliding-mode surface designs

Selection sliding-mode surface is:

$s=\stackrel{\&CenterDot;}{x}+kx---\left(25\right)$

Wherein k ＞ 0, for permanent number.

Represent for convenience, be defined as follows parameter:

3.2 control law Preliminary design

Select following sliding formwork control law:

$u=-A_t^T{\left(A_t{A}_t^T\right)}^{-1}\{{\mathrm{\&omega;}}_b^{\&times;}\&lsqb;{\mathrm{J\&omega;}}_b+h_1\&rsqb;-Jk\stackrel{\&CenterDot;}{x}+J\stackrel{\&CenterDot;}{F}\left(x\right)-\mathrm{\&gamma;}\left(t\right)\frac{s}{||s||}-{\hat{M}}_d\frac{s}{||s||}\}---\left(26\right)$

In above-mentioned control law, value and the meaning of each parameter are as follows:

M in expression (9)_dEstimate, take adaptive updates rule be:

$\stackrel{\&CenterDot;}{\hat{M}}=c_0||s||---\left(27\right)$

One parameter of γ (t): introducing, takes

$\mathrm{\&gamma;}\left(t\right)=-2\mathrm{\&upsi;}+2\mathrm{\&upsi;}\widehat{\mathrm{\&xi;}}+{\mathrm{\&epsiv;}}_0---\left(28\right)$

$\mathrm{\&upsi;}=\frac{||u||}{\widehat{\mathrm{\&xi;}}}---\left(29\right)$

$\stackrel{\&CenterDot;}{\widehat{\mathrm{\&xi;}}}=2c_1\mathrm{\&upsi;}||s||---\left(30\right)$

Wherein c₀,c₁,ε₀It it is a normal number.

Because concrete time and the parameter that spacecraft breaks down cannot be known a priori by, therefore in executing agency's fault-free work As time adjust it and control parameter, it is ensured that preferably gesture stability performance, select to control parameter as follows:

K=2, c₀=0.5, ε₀=0.5, c₁=10 (31)

The initial value of two auto-adaptive parameters is chosen as follows:

The unknown, is the most directly set as 0.

Owing to it is generally acknowledged that system does not exist fault, therefore, chooses when emulation starts

Taking Lyapunov function is

$V=\frac{1}{2}{s}^{T}Js+\frac{1}{2c_0}{\tilde{M}}_d^2+\frac{e_0}{2c_1}{\widetilde{\mathrm{\&xi;}}}^2---\left(32\right)$

Above-mentioned Lyapunov function against time is differentiated, and utilizes formula (27)～(31), can obtain:

$\stackrel{\&CenterDot;}{V}\&le;-0.5||s||\&le;0---\left(33\right)$

This formula shows, function V at least will not monotonic increase, therefore can obtain sup_t≥0V (t)≤V (0), wherein sup () table Show supremum, i.e.Bounded, therefore,ThusExist and have Boundary, according to Barbalat lemma, hasTherefore there is x → 0,

The improvement of 3.3 control laws

Singularity problem and sliding formwork in view of single-gimbal control momentum gyro control intrinsic buffeting problem, herein will Formula (23) is amended as follows:

$u=-A_t^T{\&lsqb;A_t{A}_t^T+\mathrm{\&lambda;}(I_{3\&times;3}+E_{3\&times;3})\&rsqb;}^{-1}\{{\mathrm{\&omega;}}_b^{\&times;}\&lsqb;{\mathrm{J\&omega;}}_b+h_1\&rsqb;-Jk\stackrel{\&CenterDot;}{x}+J\stackrel{\&CenterDot;}{F}\left(x\right)-\mathrm{\&gamma;}\left(t\right)\frac{s}{||s||+\mathrm{\&tau;}}-{\hat{M}}_d\frac{s}{||s||+\mathrm{\&tau;}}\}---\left(34\right)$

Wherein: λ=0.001；I_3×3It is three rank unit matrixs, E_3×3For diagonal matrix, form is:

$E_{3\&times;3}=\left[\begin{array}{ccc}0& {\mathrm{\&epsiv;}}_3& {\mathrm{\&epsiv;}}_2\\ {\mathrm{\&epsiv;}}_3& 0& {\mathrm{\&epsiv;}}_1\\ {\mathrm{\&epsiv;}}_2& {\mathrm{\&epsiv;}}_1& 0\end{array}\right],$

In matrix, each element is: ε_j=0.01 (0.5 π t+ φ_j) (j=1,2,3), φ_j=π (j-1)/2, τ=0.001.

The same formula of remaining parameter (27)～(31).

In sum, select control law (34) ensure that system (18), (19) though appearance in case of a failure State angle and attitude angular velocity remain to have Global asymptotic stability at initial point, this also indicate that control law (34) to system (18), (19) fault has robustness.

The attitude stabilization fault tolerant control method of the spacecraft with SGCMGs as executing agency that the present invention is introduced, feature exists In: because the design parameter information of fault cannot be predefined, therefore cannot according to the prior information design control law of fault, because of This use adaptive approach to estimate in real time herein fault message carrys out design control law, more meet engineering actual.On the other hand, this It is entirely ineffective that bright control method does not the most allow to there is gyro, is because when configuration gyro number used is less, if depositing Entirely ineffective at certain gyro, result in gyro the most in configuration unusual, it is possible to always have the direction cannot output torque. The row of the problem that this problem does not solves in the present invention.

Claims (1)

1. the spacecraft attitude fault tolerant control method of a single-gimbal control moment gyros, it is characterised in that include walking as follows Rapid:

Step 1: set up the kinetics equation when single-gimbal control moment gyros SGCMGs exists partial failure fault and fortune Dynamic equation；Specifically include following steps:

Step 1.1: definition coordinate system

A. body coordinate system f_b(o_bx_by_bz_b)

Body coordinate system is connected with spacecraft, initial point O_bIt is positioned at spacecraft centroid, O_bx_bAxle points to the direction of motion of spacecraft, O_bz_b Axle points to spacecraft above perpendicular to flightpiston, O_by_bAxle, O_bx_bAxle and O_bz_bAxle constitutes right-handed coordinate system；

B. orbital coordinate system f_o(O_ox_oy_oz_o)

Orbital coordinate system initial point is at the barycenter of spacecraft, O_oz_oAxle points to the earth's core, O along local vertical_ox_oAxle hangs down in orbit plane Straight in O_oz_oAxle, and point to the direction of motion of spacecraft, O_oy_oAxle, O_ox_oAxle and O_oz_oAxle constitutes right-handed coordinate system；This orbit coordinate System is in space with angular velocity omega_oAround O_oy_oAxle rotates；

C. geocentric inertial coordinate system f_i(O_ix_iy_iz_i)

The initial point of geocentric inertial coordinate system is connected in the earth's core O_iPlace, O_ix_iAxle plane under the line and point to the first point of Aries, O_iz_iVertically In equatorial plane and consistent with rotational-angular velocity of the earth direction, O_iy_iIn axle plane under the line, and and O_ix_iAxle, O_iz_iAxle structure Coordinate system at a right angle；

D.SGCMGs frame coordinates system f_ci(O_cig_is_it_i)

The initial point of frame coordinates system is at the barycenter O of SGCMG_ciPlace, frame coordinates system all directions unit vector is respectively along gimbal axis side To unit vectorUnit vector along armature spindle rotary speed directionReciprocal unit vector is exported along gyroscopic couple

Step 1.2: control system state equation is set up

Step 1.2.1: set up kinetics equation and kinematical equation

Kinetics equation:

$I_b{\stackrel{\&CenterDot;}{\mathrm{\&omega;}}}_b+{\mathrm{\&omega;}}_b^{\&times;}(I_b{\mathrm{\&omega;}}_b+A_s{I}_{ws}\mathrm{\&Omega;})=-h_0{A}_t{\stackrel{\&CenterDot;}{\mathrm{\&delta;}}}_r+T_d---\left(1\right)$

Wherein, I_bIt is whole control system inertia matrix, it is believed that I_bIt it is a constant value inertia matrix；

ω_b=[ω_x ω_y ω_z]^TComponent array for spacecraft absolute angular velocities；

h₀Nominal angular momentum for each gyrorotor；

For ω_bAbout the derivative of time,It is defined as form:

${\mathrm{\&omega;}}_b^{\&times;}=\left[\begin{array}{ccc}0& -{\mathrm{\&omega;}}_z& {\mathrm{\&omega;}}_y\\ {\mathrm{\&omega;}}_z& 0& -{\mathrm{\&omega;}}_x\\ -{\mathrm{\&omega;}}_y& {\mathrm{\&omega;}}_x& 0\end{array}\right]$

A_s=[s₁ s₂ … s_n] it is SGCMGs rotor speed direction matrix；

I_wsFor SGCMGs rotor axial rotary inertia battle array；

Ω is rotor speed vector；h₀Nominal angular momentum for each gyrorotor；

A_t=[t₁ t₂ … t_n] it is SGCMGs transverse matrix；

δ is gyro gimbal angle；

T_dFor spacecraft experienced interference moment vector；

Kinematical equation:

Wherein, attitude angleθ, ψ are the roll angle of spacecraft, the angle of pitch and yaw angle；Attitude angular velocity It is respectively θ, ψ are about the derivative of time；ω_oFor track system around body series O_oy_oThe angular speed that axle rotates；

Step 1.2.2: set up fault mode

${\stackrel{\&CenterDot;}{\mathrm{\&delta;}}}_r=E\stackrel{\&CenterDot;}{\mathrm{\&delta;}}+f---\left(3\right)$

Wherein,For gyroscopic theory framework rotating speed vector；For gyro actual frame rotating speed vector；

E=diag (e₁ e₂ … e_n) for the property taken advantage of ffault matrix, e_iFailure Factor for i-th gyro；

F=[f₁ f₂ … f_n]^TFor the impact on gyro gimbal rotating speed of the additivity fault,

f_iRotating speed deviation for i-th gyro；

Step 1.2.3: the kinematical equation under derivation fault mode and kinetics equation

Wushu (3) substitutes into formula (1), and is defined as follows the equivalence interference of gyrorotor unit nominal angular momentum, equivalent moment of inertia Battle array and equivalence gyro group angular momentum: equivalence interference: d=T_d/h₀；

Equivalent moment of inertia matrix: J=I_b/h₀；Equivalence gyro group angular momentum: h_c=A_sI_wsΩ/h₀；

OrderAs the controlled quentity controlled variable of control system, obtain the kinetics equation under fault:

$J{\stackrel{\&CenterDot;}{\mathrm{\&omega;}}}_b+{\mathrm{\&omega;}}_b^{\&times;}({\mathrm{J\&omega;}}_b+h_c)=-A_{t}Eu-A_{t}f+d---\left(4\right)$

Under low-angle assumed condition, formula (2) is write as:

${\mathrm{\&omega;}}_b\&ap;\stackrel{\&CenterDot;}{x}+F\left(x\right)---\left(5\right)$

Wherein:

ω_oCalculated by the orbit parameter of spacecraft；Represent the quantity of state of control system；

A_s,A_tIt is calculated as follows:

$\begin{array}{c}{s}_i=s_{i0}\cos {\mathrm{\&delta;}}_i+t_{i0}\sin {\mathrm{\&delta;}}_i\\ t_i=t_{i0}\cos {\mathrm{\&delta;}}_i-s_{i0}\sin {\mathrm{\&delta;}}_i\end{array}---\left(6\right)$

s_i0, t_i0Determine according to the configuration that gyro is concrete, for unit vector；s_i0Represent s_iInitial value；t_i0Represent t_iInitial value；

Step 2: based on spacecraft feature in orbit, the fault-tolerant control of spacecraft attitude of application single-gimbal control moment gyros Method processed, based on an assumption that

Assume 1: experienced interference moment bounded in spacecraft running, it may be assumed that | | d | |≤T_d；And additivity fault is to gyro gimbal The impact of rotating speed is limited, | | A_tf||≤T_f；Wherein agreement | | | | the 2-norm of representing matrix or vector, T_d,T_fNormal for the unknown Number；Assume 1 comprehensively for following expression:

||-A_tf+d||≤M_d (7)

Assume 2: spacecraft moment of inertia matrix is positive definite symmetric matrices, i.e. J symmetry and positive definite；

Assume 3: in the situation not considering that gyro is entirely ineffective, i.e. assume to there is unknown constant e₀Meet:

$0<e_0\&le;\underset{1\&le;i\&le;n}{\min }\left(e_i\right)---\left(8\right)$

Wherein, the number of gyro during n is SGCMGs；

Step 3: sliding formwork design of control law；Specifically include following steps:

Step 3.1: sliding-mode surface designs

Selection sliding-mode surface is:

$s=\stackrel{\&CenterDot;}{x}+kx---\left(9\right)$

Wherein k ＞ 0, gives constant for designer；Then when s → 0, x → 0, For by attitude angle group The column vector become, represents the quantity of state of control system,Represent the state vector derivative to the time；

Step 3.2: control law Preliminary design

Select following sliding formwork control law:

$u=-A_t^T{\left(A_t{A}_t^T\right)}^{-1}\{{\mathrm{\&omega;}}_b^{\&times;}\&lsqb;{\mathrm{J\&omega;}}_b+h_c\&rsqb;-Jk\stackrel{\&CenterDot;}{x}+J\stackrel{\&CenterDot;}{F}\left(x\right)-\mathrm{\&gamma;}\left(t\right)\frac{s}{\left|\right|s\left|\right|}-{\hat{M}}_d\frac{s}{\left|\right|s\left|\right|}\}---\left(10\right)$

In above-mentioned control law, value and the meaning of each parameter are as follows:

A_t=[t₁ t₂ … t_n] it is SGCMGs transverse matrix,For A_tTransposed matrix；

J、h_cEquivalent moment of inertia battle array defined in step 1.2.3 and equivalence gyro group angular momentum；

For F (x) in step 1.2.3 about the derivative of time；S is sliding-mode surface；

M in expression (10)_dEstimate, take adaptive updates rule be:

${\stackrel{\&CenterDot;}{\hat{M}}}_d=c_0\left|\right|s\left|\right|---\left(11\right)$

One parameter of γ (t): introducing, takes

$\mathrm{\&gamma;}\left(t\right)=-\sqrt{n}\mathrm{\&upsi;}+\sqrt{n}\mathrm{\&upsi;}\widehat{\mathrm{\&xi;}}+{\mathrm{\&epsiv;}}_0---\left(12\right)$

$\mathrm{\&upsi;}=\frac{\left|\right|u\left|\right|}{\widehat{\mathrm{\&xi;}}}---\left(13\right)$

$\stackrel{\&CenterDot;}{\widehat{\mathrm{\&xi;}}}=\sqrt{n}{c}_1\mathrm{\&upsi;}\left|\right|s\left|\right|---\left(14\right)$

Defined variableWherein c₀,c₁,ε₀Being a normal number, n is the number of gyro under certain configuration, and u is controlled quentity controlled variable,For the estimate of ξ, υ is intermediate variable,ForDerivative to the time；

Taking Lyapunov function is

$V=\frac{1}{2}{s}^{T}Js+\frac{1}{2c_0}{\tilde{M}}_d^2+\frac{e_0}{2c_1}{\widetilde{\mathrm{\&xi;}}}^2---\left(15\right)$

WhereinRemaining parameter has been given by above, and note Δ E=I-E, I are unit battle array, E For the property taken advantage of ffault matrix；

Above-mentioned Lyapunov function against time is differentiated, and utilizes formula (10)～(14), obtain:

$\stackrel{\&CenterDot;}{V}\&le;-{\mathrm{\&epsiv;}}_0\left|\right|s\left|\right|---\left(16\right)$

Formula (16) shows, function V at least will not monotonic increase, therefore obtain sup_t≥0V (t)≤V (0), wherein sup () represents Supremum, i.e.Bounded, therefore,ThusExist and bounded, According to Barbalat lemma, haveTherefore there is x → 0,

Step 3.3: the improvement of control law

There is buffeting problem and singularity problem in above-mentioned control law, it is therefore desirable to improves on the basis of control law；

Buffeting problem: owing to sliding formwork control has the discontinuity of control, therefore there is chattering phenomenon；Reason is controlled according to sliding formwork Opinion, uses s/ (| | s | |+τ) approximation to replace sign function s/ | | s | |, and wherein τ is a less positive number, is selected in 10^-3~ 10^-1Between；

Singularity problem: when each gyro output torque is coplanar, the normal direction of moment plane cannot output torque, now SGCMGs transverse matrix A_tNot full rank, formula (9) cannot solve, and therefore refers to the method that robust pseudoinverse solves and does formula (9) Go out to improve；

Therefore obtain improving control strategy and be:

$u=-A_t^T{\&lsqb;A_t{A}_t^T+\mathrm{\&lambda;}(I_{3\&times;3}+E_{3\&times;3})\&rsqb;}^{-1}\{{\mathrm{\&omega;}}_b^{\&times;}\&lsqb;{\mathrm{J\&omega;}}_b+h\&rsqb;-Jk\stackrel{\&CenterDot;}{x}+J\stackrel{\&CenterDot;}{F}\left(x\right)-\mathrm{\&gamma;}\left(t\right)\frac{s}{\left|\right|s\left|\right|+\mathrm{\&tau;}}-{\hat{M}}_d\frac{s}{\left|\right|s\left|\right|+\mathrm{\&tau;}}\}---\left(17\right)$

Wherein: λ is a little positive number, is taken at 10^-3～10^-1Between；I_3×3It is three rank unit matrixs, E_3×3For diagonal matrix, form For:

$E_{3\&times;3}=\left[\begin{array}{ccc}0& {\mathrm{\&epsiv;}}_3& {\mathrm{\&epsiv;}}_2\\ {\mathrm{\&epsiv;}}_3& 0& {\mathrm{\&epsiv;}}_1\\ {\mathrm{\&epsiv;}}_2& {\mathrm{\&epsiv;}}_1& 0\end{array}\right],$

In matrix, each element is: ε_j=0.01 (0.5 π t+ φ_j) (j=1,2,3), φ_j=π (j-1)/2.