CN105843240A - Spacecraft attitude integral sliding mode fault tolerance control method taking consideration of performer fault - Google Patents

Abstract

The invention relates to a spacecraft attitude integral sliding mode fault tolerance control method taking consideration of a performer fault and provides a robustness attitude active fault tolerance control method based on an integral sliding mode surface for problems of the performer fault, external disturbance and control moment amplitude limits in a spacecraft attitude control process. The method comprises steps that firstly, a spacecraft attitude dynamics model taking consideration of the performer fault and containing external disturbance is established; secondly, on the condition that a performer is not in fault, a designed nominal controller can guarantee system stability, and input saturation amplitude limits can be easily satisfied through adjusting controller parameters; lastly, the fault information is introduced to design an integral sliding mode controller, robustness of external disturbance and the performer fault can be effectively improved, system stability is analyzed on the basis of an Lyapunov method. The method is advantaged in that stability of the attitude control system is guaranteed when a spacecraft operating on orbit generates the performer fault, and relatively strong fault tolerance capability and external disturbance robustness are realized.

Description

A kind of spacecraft attitude Integral Sliding Mode fault tolerant control method considering actuator failures

Technical field

The present invention relates to a kind of spacecraft attitude Integral Sliding Mode fault tolerant control method considering actuator failures, mainly apply Attitude control system during in spacecraft operation on orbit generation actuator failures and by external disturbance.

Background technology

The mankind promote greatly developing of aerospace industry, China " 13 " planning outline to constantly exploring of unknown universe Draft proposes, and survey of deep space and spacecraft is serviced in-orbit with maintenance system as six big " scientific and technical innovation 2030 weights One of large project ", and plan to build up space station before and after the year two thousand twenty.Attitude control system is as the most key one of spacecraft Subsystem, has structure complexity, work under bad environment, there is unknown disturbances and the feature of multiple uncertain factor, is that event occurs Hinder one of most subsystem.For spacecraft in-orbit, executor is broken down and is likely to cause within a very short time Space science experiment, economy and military affairs are caused and have a strong impact on by spacecraft rolling, attitude loss, and owing to holding on spacecraft The unrepairable of row device fault, therefore by effectively monitoring the running status of attitude control system, detects attitude in time Fault that control system is likely to occur also diagnoses, and fault is implemented effective active tolerant control, just can improve control The reliability of system.Additionally, spacecraft also suffers from the impact of disturbing moment in space from external environment condition, therefore, effectively Disturbance suppression, the robustness improving system is also the vital task of Spacecraft Attitude Control.

For spacecraft attitude faults-tolerant control problem, patent CN201210559209.2 first passes through rewriting flexible spacecraft Model, obtains a kind of form being more suitable for extended state observer, and then a kind of linear condition of design expansion observer, estimates system System state and general disturbance, general disturbance includes external disturbance, uncertainty in dynamics, and Spacecraft malfunction information here, And design a kind of Robust Fault-tolerant Controller with this, but, actuator failures is regarded as one in general disturbance by the method, and does not has Have and directly fault message is individually estimated, so the consideration to fault message is the most complete；Patent CN201510232385.9, based on a kind of three-axis force square effectiveness fault compression observer, utilizes fault compression estimated value to design Self-adaptation control method is so that spacecraft realizes maneuver autopilot under executor is broken down, but this method does not accounts for holding The saturated limited constraint of row device control ability, this problem will affect to a certain extent Spacecraft Attitude Control precision, even lead Cause whole attitude control system unstable.Additionally, general fault diagnosis algorithm is all the Failure Factor estimating executor, this Can only can use for the situation of executor's partial failure, but the fault that in reality, this actuator of flywheel occurs generally includes Idle running, stuck, stall, moment of friction increase and rotating speed continuous decrease, when polytype fault comprehensive is occurred, as What is directly diagnosed to be, and to there is the control moment part of fault be the major issue needing in faults-tolerant control to consider；Additionally, executor's event Barrier is not to start to occur as soon as from spacecraft task, can use nom inalcontroller, the most such as before fault occurs Where line reconfigurable controller, introduces the key problem that Fault Estimation information compensation control moment is also active tolerant control algorithm.

Summary of the invention

The technology of the present invention solves problem: for there is actuator failures, outer during Spacecraft Attitude Control simultaneously Portion's disturbance and the limited problem of control moment amplitude, propose a kind of robust attitude active tolerant control side based on Integral Sliding Mode face Method；Actuator failures is there is and by external disturbance and to there is control moment saturated limited when solving spacecraft operation on orbit Problem.

The technical solution of the present invention is: a kind of spacecraft attitude Integral Sliding Mode faults-tolerant control considering actuator failures Method, implementation step is as follows:

The first step, sets up and considers actuator failures and the spacecraft attitude dynamics model of external disturbance:

$J\stackrel{\·}{\mathrm{\ω}}=-S\left(\mathrm{\ω}\right)J\mathrm{\ω}+{\mathrm{Du}}_a+d$

$\stackrel{\·}{q}=\frac{1}{2}E\left(q\right)\mathrm{\ω}$

Wherein, ω=[ω₁,ω₂,ω₃]^TAttitude angle speed for spacecraft relative inertness coordinate system under body coordinate system Degree, ω₁,ω₂,ω₃It is respectively the angular velocity component in the x-axis, y-axis and z-axis of body series；Q=[q₀,q_v ^T]^T=[q₀,q₁, q₂,q₃]^TFor the attitude unit quaternion of spacecraft, whereinFor scalar, relevant with the angle around Eigenaxis rotation, θ Represent the angle turned over around Euler's axle, q_v=[q₁,q₂,q₃]^TFor the column vector containing three elements, with Euler's direction of principal axis It is relevant, e_x,e_y,e_zRepresent the rotary shaft on three directions of Euler's axle, and Meet q₀ ²+q_v ^Tq_v=1；J is the moment of inertia matrix of spacecraft, and is the symmetrical matrix of 3 × 3；u_a∈R^mFly for m retroaction The control moment of wheel reality output, wherein R^mRepresenting the m dimensional vector in real number space, m ＞ 3 represents the boat considering actuator failures The control moment that it device attitude control system is enough for ensureing offer, needs to use the redundancy strategy more than three executors, this In assume that the characteristic of each flywheel is identical, and need to meet amplitude saturated limited constraint | | u | |≤τ_max；D is the installation square of flywheel Battle array, and its order be rank (D)=3, d be real space environmental perturbation moment suffered by spacecraft, such as gravity gradient torque, aerodynamic force Square, solar radiation pressure moment and remanent magnetism moment, although the unknown still bounded of its value, upper dividing value is | | d | |≤d_max；S (ω) is oblique Symmetrical matrix, its form isFor in kinematical equation and appearance The matrix that state quaternary number is relevant, wherein

Second step, the spacecraft attitude dynamics model set up based on the first step, the design for the ease of controller needs First consider executor do not break down and not by external disturbance in the case of nominal control system, choose suitably with long-pending The sliding-mode surface of form-separating:

$\mathrm{\σ}=D\{\mathrm{\ω}\left(t\right)-\mathrm{\ω}\left(t_0\right)+{\∫}_{t_0}^t{J}^{-1}\[S\left(\mathrm{\ω}\right)J\mathrm{\ω}-u_{nom}\]d\mathrm{\ξ}\}$

Wherein, σ represents sliding-mode surface；t₀For the initial time of system, t is the current time that system is run；ω (t) and ω (t₀) it is respectively current and initial angular velocity；u_nomFor the nom inalcontroller described in power, for ease of theoretical proof, upper Line Integral is sliding Die face introduces D and J^-1Thus ensure DJ^-1Being nonsingular, D is the installation matrix of flywheel, J^-1Represent moment of inertia matrix Inverse；ξ express time；Here definition spacecraft dynamics nominal system is ignore the factor such as external disturbance and actuator failures one Class spacecraft dynamics system, it may be assumed that

$J\stackrel{\·}{\mathrm{\ω}}=-S\left(\mathrm{\ω}\right)J\mathrm{\ω}+u_{nom}$

Then the sliding-mode surface chosen is introduced nom inalcontroller u_nomDesign in, the logical of current aerospace engineering can be used By the method for method proportional-integral-differential, it is contemplated that control to input saturated limited constraint, the present invention is given to meet and satisfies With limited non-linear ratio-differential method, there is following form:

u_nom=-k_pq_v-k_dTanh(ω/α²(t))

Here k_p、k_dFor controller gain；α²T () is the acutance function of non-zero, its value determines u_nomAlong with angular velocity omega becomes The degree changed and change, and α²(t) bounded；Function Tanh (ω) ∈ R³, definition Tanh (ω)=[tanh (ω₁) tanh(ω₂) tanh(ω₃)]^THyperbolic tangent function for standard；

From controller u_nomForm it is found that by adjust controller parameter k_pWith k_dIt can be made to meet controller width It is worth limited constraint, it may be assumed that

$\left|u_{nom}^i\right|\≤\left|k_p{q}_{vi}\right|+\left|k_d\tanh ({\mathrm{\ω}}_i/{\mathrm{\α}}^2)\right|\≤k_p+k_d\≤{\mathrm{\τ}}_m$

HereU for nom inalcontroller_nomI-th component, τ_mFor the upper dividing value of controller amplitude, pass through to adjust simultaneously α²T () can also the impact on system of the pilot angle speed term；

3rd step, on the basis of second step, it is considered to spacecraft generation actuator failures and the situation by external disturbance, I.e. for the spacecraft attitude dynamics model set up in the first step, introduce wavelet neural network fault diagnosis algorithm and performed Device fault message, and it is as follows to design Integral Sliding Mode fault-tolerant controller process with this:

1) consider to exist the situation of actuator failures and external disturbance, at the nom inalcontroller u described in claim 1_nom's On the basis of, for realizing active tolerant control mechanism, it is ensured that the stability of system, executor should the actual control moment provided For:

$u_a=u_H+{\hat{u}}_F+{\mathrm{\Δu}}_F$

Wherein, u_HThe control moment provided for the executor of normal work,For actuator failures estimated information, Δ u_FFor Fault Estimation error；

Fault message is estimated by the method using state observer to combine wavelet neural network here, first, introduces State observer estimates spacecraft attitude observation informationAttitude observation error is calculated with thisAnd further To observing improvement factor, whenTime, represent attitude observation error quaternary numberNorm less than failure determination threshold value δ_f, then Fault is not now had to occur；WhenTime, attitude observation error quaternary numberNorm exceed failure determination threshold value δ_f, explanation Break down, therefore Fault Estimation valueIt is not zero, needs to calculate further；

The present invention is based on wavelet transformation theory, structure input layer, wavelet layer and the Wavelet Neural Network of output layer three-decker Actuator failures estimated by network, inputs as observation improvement factor obtained above, and output is Fault Estimation valueIntermediate value Be 0 executor corresponding to element representation normally work, and executor corresponding to element representation that value is not 0 is broken down, because of Whether this can break down with each executor of real-time judge；

2) step 1 is introduced) the actuator failures information that obtainsIn claim 1 the 3rd step, the Integral Sliding Mode of design is held Wrong controller is:

$u=H\left(t\right)D_{pr}^T{\[D_{pr}H\left(t\right)D_{pr}^T\]}^{-1}\·(u_{nom}+u_1)$

Wherein, H (t) is to represent the m rank diagonal matrix that the most normally works of each executor, can be by step 1) described in therefore Barrier detection algorithm obtains, and the element value on its diagonal is 0 or 1, if to be 0 expression corresponding at this element of t for element value Executor is broken down, and normally works the executor that this element of t is corresponding if element value is 1 expression, therefore, and u_H=H T control moment that () u is provided by the executor of normal work；D_prFor by installing the transition matrix that matrix D decomposition obtains, it is assumed that There is the matrix D of a sequency spectrum_ps∈R^n×k, and every string of D can use D_psEach linear combination, be expressed as follows:

D=D_ps·D_pr

For D_prTransposed matrix, for realize sliding formwork control effect, and introduce step 1) in obtain actuator failures letter Breath realizes faults-tolerant control, designs switching control u₁, its form is:

$u_1=\left\{\begin{array}{cc}-\left(\mathrm{\ρ}\right(t)\·\frac{{\[D_{ps}{J}^{-1}\]}^T\mathrm{\σ}}{\left|\right|{\[D_{ps}{J}^{-1}\]}^T\mathrm{\σ}\left|\right|}+D_{pr}{\hat{u}}_F),& \mathrm{\σ}\≠0\\ 0,& \mathrm{\σ}=0\end{array}\right.$

Here the selection of parameter ρ (t) needs to meet ρ (t) ＞ δ_m+||J^-1[D_psJ^-1]^-1||·δ_u；Pass through controller compensation The general disturbance being subject to because of spacecraft after the moment of breakdown loss is:

$\begin{array}{c}{d}_g=d+{\mathrm{Du}}_F-D{\hat{u}}_F\\ =d+{\mathrm{D\Δu}}_F\end{array}$

General disturbance d_gCan be further separated into:

d_g=D_psd_m+d_u

Wherein, d_uOnly relevant with external disturbance, and d_mIncluding external disturbance and Fault Estimation error two, represent respectively such as Under:

$d_m=D_{ps}^{+}d+D_{pr}{\mathrm{\Δu}}_F$

$d_u=\[I_n-D_{ps}{D}_{ps}^{+}\]d$

Here,For D_psPlus sige inverse, its ensure matrix multiplication can rational arithmetic；Meanwhile, for the ease of Integral Sliding Mode The design of controller, assumes herein | | d_m||≤δ_m, | | d_u||≤δ_u, wherein δ_mAnd δ_uRespectively as d_mAnd d_uThe upper bound, and be all Positive constant；

The spacecraft attitude Integral Sliding Mode fault tolerant control method of the consideration actuator failures of present invention design and prior art The advantage compared is:

(1) a kind of of the present invention considers that the spacecraft attitude Integral Sliding Mode fault tolerant control method of actuator failures is at design mark Claim explicitly to introduce saturation function during controller, may be easy to meet the limited constraint of control moment by regulation controller parameter；

(2) additionally, based on state observer and combine wavelet neural network can with on-line checking and be diagnosed to be executor therefore Barrier information, including several different faults types, has preferable engineering practicability；

(3) relative to traditional sliding-mode surface design, the present invention is by introducing non-linear integral item Add the degree of freedom of system design, and be exactly based on and introduce this so that the controller of subsequent design is to constant value Interference has preferable robustness；By introducing-J ω (t₀) item so that system all states when initial motion meet to be slided In die face, i.e. it is a cancellation the arrival course movement process of sliding-mode surface, improves control speed, this Integral Sliding Mode face the most just Advantage place；The control method of design has robustness and spacecraft can be made to suppress the impact caused by fault external disturbance, And carry out attitude maneuver with certain precision.

Accompanying drawing explanation

Fig. 1 is the system frame of a kind of spacecraft attitude Integral Sliding Mode fault tolerant control method considering actuator failures of the present invention Figure；

Fig. 2 is the design stream of a kind of spacecraft attitude Integral Sliding Mode fault tolerant control method considering actuator failures of the present invention Cheng Tu；

Fig. 3 is the wavelet neural network structure chart that the present invention uses in fault diagnosis.

Detailed description of the invention

As it is shown in figure 1, a kind of spacecraft attitude Integral Sliding Mode fault-tolerant control system considering actuator failures includes integration Sliding formwork fault-tolerant controller, flywheel, spacecraft dynamics model, fault detection and diagnosis module, gyroscope, attitude sensor, boat It device kinematics model.

When spacecraft operation on orbit exists actuator failures and external disturbance, first in spacecraft attitude control system Gyroscope measurement obtains the angular velocity of spacecraft, and meanwhile, attitude sensor determines spacecraft attitude information, and attitude is introduced event Barrier detection calculates actuator failures information with diagnosis algorithm；Then, attitude, angular velocity and Fault Estimation information are collectively incorporated into Obtaining control signal in Integral Sliding Mode fault-tolerant controller designed by the present invention, finally, control signal is sent to flywheel, in order to The control moment providing actual acts on spacecraft, and now, spacecraft is also affected by external disturbance moment, spacecraft power And kinematics model represent the effective object of attitude control system, and kinetic model Output speed, kinematics model is defeated Going out attitude, both information is able to be recorded by gyroscope and attitude sensor.

As in figure 2 it is shown, the present invention implements step as follows (below with attitude maneuver process during spacecraft operation on orbit As a example by carry out implementing of illustration method):

The first step, sets up and considers actuator failures and the spacecraft attitude dynamics model of external disturbance

The angular velocity information setting spacecraft is set up in spacecraft body coordinate system, and its initial point o is defined on spacecraft At barycenter, and whole coordinate system is fixed on spacecraft；Wherein oz axle is also known as yaw axis, and oy axle is also known as pitch axis, and ox axle is also known as rolling Moving axis, three is parallel to each other with the inertial reference coordinate axes (gyroscope sensitive axes) being fixed on spacecraft respectively.Then consider to perform The spacecraft kinematics and dynamics modeling of device fault and external disturbance is:

$J\stackrel{\·}{\mathrm{\ω}}=-S\left(\mathrm{\ω}\right)J\mathrm{\ω}+{\mathrm{Du}}_a+d$

$\stackrel{\·}{q}=\frac{1}{2}E\left(q\right)\mathrm{\ω}$

Wherein, ω=[ω₁,ω₂,ω₃]^TAttitude angle speed for spacecraft relative inertness coordinate system under body coordinate system Degree, ω₁,ω₂,ω₃It is respectively the angular velocity component in the x-axis, y-axis and z-axis of body series；Q=[q₀,q_v ^T]^T=[q₀,q₁, q₂,q₃]^TFor the attitude unit quaternion of spacecraft, whereinFor scalar, relevant with the angle around Eigenaxis rotation, θ Represent the angle turned over around Euler's axle, q_v=[q₁,q₂,q₃]^TFor the column vector containing three elements, with Euler's direction of principal axis It is relevant, e_x,e_y,e_zRepresent the rotary shaft on three directions of Euler's axle, and Meet q₀ ²+q_v ^Tq_v=1；J is the moment of inertia matrix of spacecraft, and is the symmetrical matrix of 3 × 3, according to the design of real satellite Parameter, J can be taken as [1543.9-2.3-2.8； -2.3 471.6 -35； -2.8 -35 1713.3]；u_a∈R^mAnti-for m The control moment of the effect actual output of flywheel, wherein R^mRepresenting the m dimensional vector in real number space, m ＞ 3 represents that native system is guarantee Enough control moments are provided, need to use the redundancy strategy more than three executors, use three flywheels the most orthogonal here The four flywheel collocation methods that oblique axial with another flywheel is installed, it is assumed that the characteristic of each flywheel is identical, and needs to meet width It is worth saturated limited constraint | | u | |≤τ_max, herein according to the output torque scope of actual flywheel, set τ_max=1N m；D is for flying The installation matrix of wheel, and its order is rank (D)=3, provides a kind of mounting means to be hereExist The matrix D of one sequency spectrum_ps∈R^n×k, every string of D can use D_psEach linear combination, D=D can be expressed as_ps· D_pr, D_prBe order be the transition matrix of k；D is real space environmental perturbation moment suffered by spacecraft, such as gravity gradient torque, pneumatic Moment, solar radiation pressure moment and remanent magnetism moment, although the unknown still bounded of its value, upper dividing value is | | d | |≤d_max, here may be used It is taken asS (ω) is skew symmetric matrix, and its form isFor square relevant with attitude quaternion in kinematical equation Battle array, wherein

Second step, controller based on sliding-mode control design is broadly divided into two steps: be first the choosing of sliding-mode surface Take；Next to that the design of control law, and proof system state is sliding at any initial position finite time arrival sliding-mode surface and arrival Converge to equilibrium point after die face, thus ensure that spacecraft state is finally stable；Based on the spacecraft considering actuator failures The characteristic of kinetic model, chooses following Integral Sliding Mode face:

$\mathrm{\σ}=D\{\mathrm{\ω}\left(t\right)-\mathrm{\ω}\left(t_0\right)+{\∫}_{t_0}^t{J}^{-1}\[S\left(\mathrm{\ω}\right)J\mathrm{\ω}-u_{nom}\]d\mathrm{\ξ}\}$

Wherein, σ represents sliding-mode surface；t₀For the initial time of system, t is the current time that system is run；ω (t) and ω (t₀) it is respectively current and initial angular velocity, set ω (t₀)=[-0.01-0.005 0.003] rad/s；u_nomMove for spacecraft The control law of mechanics nominal system, above Integral Sliding Mode face introduces D and J^-1Thus ensure DJ^-1It is nonsingular, it is simple to theoretical Prove；ξ express time；Here definition spacecraft dynamics nominal system is to ignore the factor such as external disturbance and actuator failures One class spacecraft dynamics system, it may be assumed that

$J\stackrel{\·}{\mathrm{\ω}}=-S\left(\mathrm{\ω}\right)J\mathrm{\ω}+u_{nom}$

For u_nomDesign, the method that the universal method proportional-integral-differential of current aerospace engineering can be used, but In view of controlling to input saturated limited constraint, the present invention is given and meets saturated limited non-linear ratio-differential method, has Following form:

u_nom=-k_pq_v-k_dTanh(ω/α²(t))

Here k_p、k_dFor controller gain, can be any real number more than zero in theory, but consider the limited constraint of amplitude, Repetition test also adjusts parameter and can choose k_p=0.65, k_d=0.35 to obtain preferable control performance；α²T () is the sharp of non-zero Degree function, can select the function of any appropriate, it is also possible to for constant, its value determines u_nomChange along with angular velocity omega change Degree, and α²(t) bounded；Function Tanh (ω) ∈ R³, definition Tanh (ω)=[tanh (ω₁) tanh(ω₂) tanh (ω₃)]^THyperbolic tangent function for standard；

From controller u_nomForm it is found that by adjust controller parameter k_pWith k_dIt can be made to meet amplitude limited Constraint, it may be assumed that

$\left|u_{nom}^i\right|\≤\left|k_p{q}_{vi}\right|+\left|k_d\tanh ({\mathrm{\ω}}_i/{\mathrm{\α}}^2)\right|\≤k_p+k_d\≤{\mathrm{\τ}}_m$

HereFor nom inalcontroller u_nomThe i-th component, τ_mFor inputting saturated upper dividing value, simultaneously by adjusting α² T () can also the impact on system of the pilot angle speed term；

3rd step, at nom inalcontroller u_nomOn the basis of, for realizing active tolerant control mechanism, it is considered to when fault occurs Time, for ensureing the stability of system, the control moment that executor should actual provide is:

U=u_H+u_F

Wherein, u_HThe control moment of the executor of the corresponding normal work of=H (t) u, H (t)=diag{H₁(t),...H_m (t)}·u,H_iT { 0,1} is m rank diagonal matrix to () ∈, may determine that fault occur by fault diagnosis algorithm in this paper Executor, H_iT ()=0 represents breaks down t i-th executor, H_iT ()=1 represents t i-th executor Normal work, H₁(t) and H_mT () represents whether the 1st break down in t with m-th executor, and H (t) has idempotent Property, i.e. H²(t)=H (t)；u_FThe control moment provided by the executor broken down, considers partial failure here and loses completely Imitating several failure condition, such as the 1st flywheel is after work 1s, and it thoroughly lost efficacy, and output torque is zero；2nd flywheel is in work After making 3s, there is partial failure, its control ability loss 20%；After work 10s, there is partial failure in the 3rd flywheel, its control Capacity loss 60% processed；4th flywheel, after work 2s, there is also partial failure, its control ability loss 80%, but these Fault message cannot directly record, and needs to use the fault diagnosis algorithm proposed in the present invention to estimate, fault message Can be expressed as:

$u_F={\hat{u}}_F+{\mathrm{\Δu}}_F$

Wherein,Represent the actuator failures information estimated, Δ u_FRepresent the Fault Estimation that unavoidably there will be by mistake Difference；Therefore, control moment is represented by:

$u_a=H\left(t\right)u+{\hat{u}}_F+{\mathrm{\Δu}}_F$

Accordingly, it is considered to the spacecraft attitude dynamics broken down can be written as:

$J\stackrel{\·}{\mathrm{\ω}}=-S\left(\mathrm{\ω}\right)J\mathrm{\ω}+D\[H\left(t\right)u+{\hat{u}}_F+{\mathrm{\Δu}}_F\]+d$

Actuator failures is taked following detection and diagnosis algorithm estimate fault message, first, introduces state observer For:

$\begin{array}{cc}\stackrel{\·}{\hat{q}}=\frac{1}{2}E\left(\hat{q}\right)\widehat{\mathrm{\ω}}+z_1& \hat{q}\left(0\right)=q\left(0\right)\end{array}$

$\begin{array}{cc}J\stackrel{\·}{\widehat{\mathrm{\ω}}}=-S\left(\widehat{\mathrm{\ω}}\right)J\widehat{\mathrm{\ω}}+Du+z_2& \widehat{\mathrm{\ω}}\left(0\right)=\mathrm{\ω}\left(0\right)\end{array}$

Here,WithBeing respectively spacecraft attitude and the estimated value of angular velocity, its initial value is true value, it is assumed here that Initial time is 0, and attitude quaternion initial value is q (0)=[0.8-0.64-0.32 0.18]^T；z₁And z₂For improvement factor, And be defined as follows:

With

Wherein,It is defined as Sgn () represents sign function,For the observation error quaternary number of attitude,Represent q respectively₀,q₁,q₂,q₃ Attitude estimation error；f(z₁) it is defined as f (z₁)=[| z₁₁|^1/2sgn(z₁₁)|z₁₂|^1/2sgn(z₁₂)|z₁₃|^1/2sgn(z₁₃)| z₁₄|^1/2sgn(z₁₄)]^T, z₁₁,z₁₂,z₁₃,z₁₄Represent z₁Several components；λ₁,λ₂,α₁,α₂It is all observer gain, and is positive Constant, and v₁,v₂For time-varying parameter, the most desirable λ₁=1, λ₂=1, α₁=0.5, α₂=0.5 is preferred value；

WhenTime, represent attitude observation error quaternary numberNorm less than failure determination threshold value δ_f, the most now do not have Fault occurs, and this threshold value can be chosen less to ensure the robustness of system as far as possible, chooses 10^-3Preferable control can be obtained Effect processed, Fault Estimation valueIt is set to zero；WhenTime, attitude observation error quaternary numberNorm exceed fault detect threshold Value δ_f, explanation breaks down, therefore Fault Estimation valueIt is not zero, needs to calculate further；

The present invention, based on wavelet transformation theory, constructs three layers of wavelet neural network and estimates actuator failures, including input Layer, wavelet layer and output layer；Relation between input layer and each node of wavelet layer can be expressed as:

${\mathrm{net}}_i^1={\mathrm{ni}}_i,{\mathrm{no}}_i^1=f_i^1\left({\mathrm{net}}_i^1\right)={\mathrm{net}}_i^1,i=1,2$

Here ni_iIt is the input of wavelet neural network, wherein ni₁=z₁And Represent input layer joint Point,Represent the output of input layer；In wavelet layer, carry out changing and amplifying setting up little wave system about mother wavelet function, The present invention chooses Gaussian function ψ (x)=-xexp (-x²/ 2) as mother wavelet function, exp () represents natural Exponents letter Number；f_i ¹Represent the function being input to output in input layer；For the node in wavelet layer, there is a following relation:

${\mathrm{net}}_{ij}^2=\frac{{\mathrm{no}}_i^1-c_{ij}}{{\mathrm{\σ}}_{ij}}$

$\begin{array}{c}{\mathrm{no}}_{ij}^2={\mathrm{\φ}}_{ij}\left({\mathrm{net}}_{ij}^2\right)\\ =-{\mathrm{net}}_{ij}^2\exp (-{\left({\mathrm{net}}_{ij}^2\right)}^2/2),j=1,...,p\end{array}$

Here,Representing the node of wavelet layer, p represents the node number in wavelet layer about each input node, here Can arrange p=6, then in wavelet neural network, wavelet layer comprises 12 nodes altogether；c_ijAnd σ_ijRepresent wavelet layer respectively I-th inputsConversion factor and amplification factor to pth node；Represent the output of wavelet layer；

At output layer, output node needs to add up all input signals, thus obtains whole wavelet neural network Output, calculate process as follows:

${\mathrm{net}}_o^3=\underset{ij}{\Σ}{W}_{ijo}^3{\mathrm{no}}_{ij}^2$

${\mathrm{no}}_o^3=f_o^3\left({\mathrm{net}}_o^3\right)={\mathrm{net}}_o^3,o=1$

Here, ∑ represents summation symbol,For output layer node, o represents output layer node number, only considers here One output node；Represent that in wavelet layer, each node is to the connection weight of output layer node；Represent in output layer It is input to the function of output；For the output of whole wavelet neural network, meanwhile, byExecutor's event can be obtained Barrier information Intermediate value be 0 executor corresponding to element representation normally work, and value is not corresponding the holding of element representation of 0 Whether row device breaks down, therefore can break down with each executor of real-time judge and obtain matrix H (t)；

On the basis of nom inalcontroller, introducing failure diagnosis information, design spacecraft attitude active tolerant control device is:

$u=H\left(t\right)D_{pr}^T{\[D_{pr}H\left(t\right)D_{pr}^T\]}^{-1}\·(u_{nom}+u_1)$

Wherein,For D_prTransposed matrix, u₁For switching control, its form is:

$u_1=\left\{\begin{array}{cc}-\left(\mathrm{\ρ}\right(t)\·\frac{{\[D_{ps}{J}^{-1}\]}^T\mathrm{\σ}}{\left|\right|{\[D_{ps}{J}^{-1}\]}^T\mathrm{\σ}\left|\right|}+D_{pr}{\hat{u}}_F),& \mathrm{\σ}\≠0\\ 0,& \mathrm{\σ}=0\end{array}\right.$

Here the selection of parameter ρ (t) needs to meet ρ (t) ＞ δ_m+||J^-1[D_psJ^-1]^-1||·δ_u；Owing to fault diagnosis is calculated Method is it is estimated that fault message thus design controller compensate the control moment of loss, and after being so compensated, outside is disturbed The disturbance that dynamic and both actuator failures produce jointly is:

$\begin{array}{c}{d}_g=d+{\mathrm{Du}}_F-D{\hat{u}}_F\\ =d+{\mathrm{D\Δu}}_F\end{array}$

d_gFor compensating because of the general disturbance after the moment of breakdown loss, and it can be further separated into:

d_g=D_psd_m+d_u

Wherein, d_uOnly relevant with external disturbance, and d_mIncluding external disturbance and Fault Estimation error two, represent respectively such as Under:

$d_m=D_{ps}^{+}d+D_{pr}{\mathrm{\Δu}}_F$

$d_u=\[I_n-D_{ps}{D}_{ps}^{+}\]d$

Here,For D_psPlus sige inverse, it is ensured that matrix multiplication can rational arithmetic；Meanwhile, for the ease of Integral Sliding Mode control The design of device processed, it is assumed that | | d_m||≤δ_m, | | d_u||≤δ_u, wherein δ_mAnd δ_uRespectively as d_mAnd d_uThe upper bound, and be all positive normal Number；

It can be seen that u₁Need to use failure diagnosis information to compensate the impact that actuator failures causes, and work as system State deviation sliding-mode surface time u₁Being activated, under the effect of the integral sliding mode control device u of present invention design, system can reach Consistent asymptotic stability.

The content not being described in detail in description of the invention belongs to prior art known to professional and technical personnel in the field.

Claims (5)

1. the spacecraft attitude Integral Sliding Mode fault tolerant control method considering actuator failures, it is characterised in that realize step such as Under:

(1) consideration actuator failures and the spacecraft attitude dynamics model containing external disturbance, wherein actuator failures are set up Increasing and rotating speed continuous decrease including idle running, stuck, stall, moment of friction, external disturbance includes gravity gradient torque, aerodynamic force Square, solar radiation pressure moment and remanent magnetism moment；

(2) the spacecraft attitude dynamics model set up based on the first step, the design for the ease of controller needs first to consider Executor do not break down and not by external disturbance in the case of nominal control system, choose the sliding formwork with integrated form Face；Then being introduced by the sliding-mode surface chosen in the design of controller, at this moment designed controller is referred to as nom inalcontroller, nominal Controller makes spacecraft attitude nominal control system state arrive sliding-mode surface at any initial position finite time and arrive sliding Converge to equilibrium point after die face, thus ensure that spacecraft state is finally stable, and be prone to full by adjusting controller parameter Foot inputs saturated amplitude and limits；

(3) on the basis of second step, it is considered to spacecraft generation actuator failures and the situation by external disturbance, i.e. for The spacecraft attitude dynamics model set up in one step, introduces wavelet neural network fault diagnosis algorithm and obtains actuator failures letter Breath, and design Integral Sliding Mode fault-tolerant controller with this, it is effectively improved the robustness to actuator failures and external disturbance, and base Stability in Lyapunov methods analyst system.

The spacecraft attitude Integral Sliding Mode fault tolerant control method of consideration actuator failures the most according to claim 1, it is special Levy and be: in the described first step, it is considered to actuator failures and the spacecraft attitude dynamics model containing external disturbance are as follows:

$J\stackrel{\·}{\mathrm{\ω}}=-S\left(\mathrm{\ω}\right)J\mathrm{\ω}+{\mathrm{Du}}_a+d$

$\stackrel{\·}{q}=\frac{1}{2}E\left(q\right)\mathrm{\ω}$

Wherein, ω=[ω₁,ω₂,ω₃]^TFor spacecraft attitude angular velocity of relative inertness coordinate system under body coordinate system, ω₁,ω₂,ω₃It is respectively the angular velocity component in the x-axis, y-axis and z-axis of body series；Q=[q₀,q_v ^T]^T=[q₀,q₁,q₂,q₃ ]^TFor the attitude unit quaternion of spacecraft, whereinFor scalar, relevant with the angle around Eigenaxis rotation, θ represents The angle turned over around Euler's axle, q_v=[q₁,q₂,q₃]^TFor the column vector containing three elements, have with Euler's direction of principal axis Close, e_x,e_y,e_zRepresent the rotary shaft on three directions of Euler's axle, and full Foot q₀ ²+q_v ^Tq_v=1；J is the moment of inertia matrix of spacecraft, and is the symmetrical matrix of 3 × 3；u_a∈R^mFor m counteraction flyback The control moment of actual output, wherein R^mRepresenting that m ties up real number vector space, m > 3 is expressed as ensureing the control moment that offer is enough, Need to use more than the redundancy strategy of three executors, it is assumed that the characteristic of each flywheel is identical, and need to meet that amplitude is saturated to be subject to Limit constraint | | u_a||≤τ_max；D is the installation matrix of flywheel, and its order be rank (D)=3, d be real space suffered by spacecraft Environmental perturbation moment, upper dividing value is | | d | |≤d_max；S (ω) is skew symmetric matrix, and its form is For square relevant with attitude quaternion in kinematical equation Battle array, wherein

The spacecraft attitude Integral Sliding Mode fault tolerant control method of consideration actuator failures the most according to claim 1, it is special Levying and be: in described second step, choosing of sliding-mode surface is as follows:

$\mathrm{\σ}=D\{\mathrm{\ω}\left(t\right)-\mathrm{\ω}\left(t_0\right)+{\∫}_{t_0}^t{J}^{-1}\[S\left(\mathrm{\ω}\right)J\mathrm{\ω}-u_{nom}\]d\mathrm{\ξ}\}$

Wherein, σ represents sliding-mode surface；t₀For the initial time of system, t is the current time that system is run；ω (t) and ω (t₀) point Wei not currently and initial angular velocity；u_nomFor nom inalcontroller, for ease of theoretical proof, above Integral Sliding Mode face introduces D and J^-1 Thus ensure DJ^-1It is nonsingular, J^-1Represent the inverse of moment of inertia matrix, ξ express time.

The spacecraft attitude Integral Sliding Mode fault tolerant control method of consideration actuator failures the most according to claim 1, it is special Levying and be: in described second step, the design of described nom inalcontroller is as follows:

Ignore the spacecraft dynamics nominal system of external disturbance and actuator failures, it may be assumed that

$J\stackrel{\·}{\mathrm{\ω}}=-S\left(\mathrm{\ω}\right)J\mathrm{\ω}+u_{nom}$

Wherein u_nomFor nom inalcontroller, for u_nomDesign, uses and meets saturated limited non-linear ratio-differential method, tool There is a following form:

u_nom=-k_pq_v-k_dTanh(ω/α²(t))

Wherein k_p、k_dFor controller gain；α²T () is the acutance function of non-zero, its value determines u_nomAlong with angular velocity omega change The degree of change, and α²(t) bounded；Function Tanh (ω) ∈ R³, definition Tanh (ω)=[tanh (ω₁) tanh(ω₂) tanh(ω₃)]^THyperbolic tangent function for standard；

By adjusting controller parameter k_pWith k_dMeet the constraint that amplitude is limited, it may be assumed that

$\left|u_{nom}^i\right|\≤\left|k_p{q}_{vi}\right|+\left|k_d\tanh ({\mathrm{\ω}}_i/{\mathrm{\α}}^2)\right|\≤k_p+k_d\≤{\mathrm{\τ}}_m$

For nom inalcontroller u_nomI-th component, τ_mFor inputting saturated upper dividing value, simultaneously by adjusting α²T () can also The impact on system of the pilot angle speed term.

The spacecraft attitude Integral Sliding Mode fault tolerant control method of consideration actuator failures the most according to claim 1, it is special Levying and be: in described 3rd step, introducing state observer combines wavelet neural network fault diagnosis algorithm and obtains actuator failures Information, and design Integral Sliding Mode fault-tolerant controller with this and be implemented as:

(31) first, introduce state observer and estimate spacecraft attitude observation informationAttitude observation error is calculated with thisAnd obtain further observing improvement factor, whenTime, represent attitude observation error quaternary numberNorm little In failure determination threshold value δ_f, the most now do not have fault to occur；WhenTime, attitude observation error quaternary numberNorm exceed Failure determination threshold value δ_f, explanation breaks down, therefore Fault Estimation valueIt is not zero, needs to enter (32) and calculate further；

(32) based on wavelet transformation theory, the wavelet neural network of structure input layer, wavelet layer and output layer three-decker is estimated Meter actuator failures, the input of wavelet neural network is observation improvement factor obtained above, and output is the execution estimated Device fault messageMeanwhile, definition H (t) is to represent the m rank diagonal matrix that each executor the most normally works, based on execution The value of device fault message,Middle i-th element value is not that 0 expression is broken down t i-th executor, and i represents executor Label, then on H (t) diagonal, i-th element value takes 0；And work asMiddle i-th element value is that 0 expression is held in t i-th Row device normally works, and on H (t) diagonal, the value of i-th element takes 1；

(33) the actuator failures information obtained based on fault diagnosis algorithm in step (31) and (32), then executor is actual provides Control moment be:

$u_a=H\left(t\right)u+{\hat{u}}_F+{\mathrm{\Δu}}_F$

Here, Δ u_FThe estimation difference inevitably produced during for obtaining actuator failures information；Now, the integration of design is sliding Mould fault-tolerant controller is:

$u=H\left(t\right)D_{pr}^T{\[D_{pr}H\left(t\right)D_{pr}^T\]}^{-1}\·(u_{nom}+u_1)$

D_prFor by installing the transition matrix that matrix D decomposition obtains, it is assumed that there are the matrix D of a sequency spectrum_ps∈R^n×k, and D Every string all uses D_psEach linear combination, be expressed as follows:

D=D_ps·D_pr

For D_prTransposed matrix, for realize sliding formwork control effect, be simultaneously introduced the actuator failures information that (32) obtain, if Meter switching control u₁, its form is:

$u_1=\left\{\begin{array}{cc}-\left(\mathrm{\ρ}\right(t)\·\frac{{\[D_{ps}{J}^{-1}\]}^T\mathrm{\σ}}{\left|\right|{\[D_{ps}{J}^{-1}\]}^T\mathrm{\σ}\left|\right|}+D_{pr}{\hat{u}}_F),& \mathrm{\σ}\≠0\\ 0,& \mathrm{\σ}=0\end{array}\right.$

The selection of parameter ρ (t) needs to meet ρ (t) > δ_m+||J^-1[D_psJ^-1]^-1||·δ_u；By controller compensation because of breakdown loss Moment after the general disturbance that is subject to of spacecraft be:

$\begin{array}{c}{d}_g=d+{\mathrm{Du}}_F-D{\hat{u}}_F\\ =d+{\mathrm{D\Δu}}_F\end{array}$

General disturbance d_gIt is further separated into:

d_g=D_psd_m+d_u

Wherein, d_uOnly relevant with external disturbance, and d_mIncluding external disturbance and Fault Estimation error two, it is expressed as follows respectively:

$d_m=D_{ps}^{+}d+D_{pr}{\mathrm{\Δu}}_F$

$d_u=\[I_n-D_{ps}{D}_{ps}^{+}\]d$

For D_psPlus sige inverse, it is ensured that matrix multiplication can rational arithmetic；Meanwhile, setting for the ease of integral sliding mode control device Meter, it is assumed that | | d_m||≤δ_m, | | d_u||≤δ_u, wherein δ_mAnd δ_uRespectively as d_mAnd d_uThe upper bound, and be all positive constant.