CN105843240B - A kind of spacecraft attitude Integral Sliding Mode fault tolerant control method considering actuator failures - Google Patents
A kind of spacecraft attitude Integral Sliding Mode fault tolerant control method considering actuator failures Download PDFInfo
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Abstract
The present invention relates to a kind of spacecraft Integral Sliding Mode fault tolerant control methods for considering actuator failures, exist simultaneously the limited problem of actuator failures, external disturbance and control moment amplitude in the process for Spacecraft Attitude Control, it is proposed a kind of robust posture Active Fault-tolerant Control Method based on Integral Sliding Mode face, it the steps include: to consider actuator failures and the spacecraft attitude dynamics model containing external disturbance firstly, establishing；Then, in the without failure situation of actuator, designed nom inalcontroller can guarantee system stabilization and be content with very little by adjusting controller parameter to input saturation amplitude limitation；Finally, introducing fault message designs integral sliding mode control device, the robustness to external disturbance and actuator failures, and the stability based on Lyapunov method analysis system are effectively improved；This method ensure that the stability of attitude control system when actuator failures occurs for spacecraft operation on orbit, have many advantages, such as stronger fault-tolerant ability and the robustness to external disturbance.
Description
Technical field
It is main to apply the present invention relates to a kind of spacecraft attitude Integral Sliding Mode fault tolerant control method for considering actuator failures
Actuator failures and attitude control system when by external disturbance occur in spacecraft operation on orbit.
Background technique
The mankind promote greatly developing for aerospace industry, China " 13 " planning outline to the continuous exploration in unknown universe
Draft proposes, using deep space exploration and spacecraft in-orbit service and 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 the characteristics that structure is complicated, working environment is severe, there are unknown disturbances and a variety of uncertain factors, is generation event
Hinder most one of subsystems.For in-orbit spacecraft, actuator failure is likely to cause within a very short time
Spacecraft rolling, attitude loss cause to seriously affect to space science experiment, economy and military affairs, and due to holding on spacecraft
The unrepairable of row device failure, therefore the operating status by effectively monitoring attitude control system, detect posture in time
Failure that control system is likely to occur simultaneously is diagnosed, and implements effective active tolerant control to failure, can improve control
The reliability of system.In addition, spacecraft also suffers from the influence of the disturbing moment in space from external environment, therefore, effectively
Disturbance suppression, the robustness for improving system is also the vital task of Spacecraft Attitude Control.
For spacecraft attitude faults-tolerant control problem, patent CN201210559209.2 passes through rewriting flexible spacecraft first
Model obtains a kind of form for being more suitable for extended state observer, then designs a kind of linear condition expansion observer, estimation system
System state and general disturbance, general disturbance includes external disturbance, uncertainty in dynamics and Spacecraft malfunction information here,
And a kind of Robust Fault-tolerant Controller is designed with this, however, actuator failures are regarded as one in general disturbance by the method, and do not have
Have and directly fault message is individually estimated, so to fault message the considerations of is not complete enough；Patent
CN201510232385.9 is based on a kind of three-axis force square validity fault compression observer, is designed using fault compression estimated value
Self-adaptation control method is so that spacecraft realizes maneuver autopilot under actuator failure, but this method does not account for holding
The limited constraint of the saturation of row device control ability, which will affect Spacecraft Attitude Control precision to a certain extent, or even lead
Cause entire attitude control system unstable.In addition, general fault diagnosis algorithm is all the Failure Factor for estimating actuator, this
The case where actuator partial failure can only be directed to, can be used, however the failure that this executing agency of flywheel occurs in practice generally includes
Idle running, stuck, stalling, moment of friction increases and revolving speed continues to decline, the case where appearance for a plurality of types of fault comprehensives, such as
It is the major issue for needing to consider in faults-tolerant control that, which is directly diagnosed to be there are the control moment part of failure,；In addition, actuator event
Barrier is not to occur as soon as since spacecraft task, nom inalcontroller can be used before failure generation, after failure such as
Where line reconfigurable controller, introduce Fault Estimation information compensation control moment be also active tolerant control algorithm key problem.
Summary of the invention
Technology of the invention solves the problems, such as: for existing simultaneously actuator failures, outer during Spacecraft Attitude Control
The problem that portion's disturbance and control moment amplitude are limited, proposes a kind of robust posture active tolerant control side based on Integral Sliding Mode face
Method；Actuator failures occur when solving spacecraft operation on orbit and limited by external disturbance and there are control moment saturation
Problem.
A kind of technical solution of the invention are as follows: spacecraft attitude Integral Sliding Mode faults-tolerant control for considering actuator failures
Method, implementation step are as follows:
The first step establishes the spacecraft attitude dynamics model for considering actuator failures and external disturbance:
Wherein, ω=[ω1,ω2,ω3]TFor the attitude angle speed of spacecraft relative inertness coordinate system under body coordinate system
Degree, ω1,ω2,ω3Angular velocity component respectively in the x-axis, y-axis and z-axis of this system；Q=[q0,qv T]T=[q0,q1,
q2,q3]TFor the posture unit quaternion of spacecraft, whereinIt is related with the angle around Eigenaxis rotation for scalar, θ
Indicate the angle turned over around Euler's axis, qv=[q1,q2,q3]TFor containing there are three the column vectors of element, with Euler's axis direction
It is related, ex,ey,ezThe rotary shaft on three directions of Euler's axis is represented, and
Meet q0 2+qv Tqv=1；J is the moment of inertia matrix of spacecraft, and is 3 × 3 symmetrical matrix；ua∈RmFly for m reaction
The control moment of reality output is taken turns, wherein RmIndicate that the m dimensional vector in real number space, m > 3 indicate to consider the boat of actuator failures
Its device attitude control system provides enough control moments for guarantee, needs using the redundancy strategy greater than three actuators, this
In assume that the characteristic of each flywheel is identical, and need to meet the limited constraint of amplitude saturation | | u | |≤τmax；D is the installation square of flywheel
Battle array, and it is real space environmental perturbation torque suffered by spacecraft that its order, which is rank (D)=3, d, such as gravity gradient torque, aerodynamic force
Square, solar radiation pressure torque and remanent magnetism torque, although its unknown bounded of value, upper dividing value are | | d | |≤dmax；S (ω) is oblique
Symmetrical matrix, form areFor in kinematical equation and appearance
The related matrix of state quaternary number, wherein
Second step is needed based on the spacecraft attitude dynamics model that the first step is established for the ease of the design of controller
Consider to choose suitably with product in the case that actuator is without failure and nominal control system not by external disturbance first
The sliding-mode surface of form-separating:
Wherein, σ indicates sliding-mode surface；t0For the initial time of system, t is the current time of system operation；ω (t) and ω
(t0) it is respectively current and initial angular velocity；unomTo weigh the nom inalcontroller, for convenient for theoretical proof, upper Line Integral is sliding
D and J is introduced in die face-1To guarantee DJ-1It is nonsingular, installation matrix of the D for flywheel, J-1Indicate moment of inertia matrix
It is inverse；ξ indicates the time；Here defining spacecraft dynamics nominal system is ignore the factors such as external disturbance and actuator failures one
Class spacecraft dynamics system, it may be assumed that
Then the sliding-mode surface of selection is introduced into nom inalcontroller unomDesign in, can be using the logical of current aerospace engineering
With the method for method proportional-integral-differential, it is contemplated that the constraint that control input saturation is limited, it is full that the present invention provides satisfaction
With limited non-linear ratio-differential method, there is following form:
unom=-kpqv-kdTanh(ω/α2(t))
Here kp、kdFor controller gain；α2It (t) is the acutance function of non-zero, value determines unomAs angular velocity omega becomes
The degree changed and changed, and α2(t) bounded；Function Tanh (ω) ∈ R3, define Tanh (ω)=[tanh (ω1) tanh(ω2)
tanh(ω3)]TFor the hyperbolic tangent function of standard；
From controller unomForm it can be found that by adjusting controller parameter kpWith kdIt can be made to meet controller width
The limited constraint of value, it may be assumed that
HereFor the u of nom inalcontrollernomI-th of component, τmFor the upper dividing value of controller amplitude, while by adjusting
α2(t) it also can control influence of the angular speed item to system；
Third step, on the basis of second step, consider spacecraft there is a situation where actuator failures and by external disturbance,
I.e. for the spacecraft attitude dynamics model established in the first step, introduces wavelet neural network fault diagnosis algorithm and executed
Device fault message, and it is as follows with this to design Integral Sliding Mode fault-tolerant controller process:
1) the case where considering that there are actuator failures and external disturbances, nom inalcontroller u described in claim 1nom's
On the basis of, to realize active tolerant control mechanism, guarantee the stability of system, the control moment that actuator should be provided actually
Are as follows:
Wherein, uHFor the control moment that the actuator of normal work provides,For actuator failures estimated information, Δ uFFor
Fault Estimation error；
Here the method for adoption status observer combination wavelet neural network estimates fault message, firstly, introducing
State observer estimates spacecraft attitude observation informationPosture observation error is calculated with thisAnd further
To observation improvement factor, whenWhen, indicate posture observation error quaternary numberNorm be less than failure determination threshold value δf, then
There is no failure at this time；WhenWhen, posture observation error quaternary numberNorm be more than failure determination threshold value δf, explanation
It breaks down, therefore Fault Estimation valueIt is not zero, needs to further calculate；
The present invention is based on wavelet transformation theories, construct the Wavelet Neural Network of input layer, wavelet layer and output layer three-decker
Network estimates actuator failures, inputs as observation improvement factor obtained above, output is Fault Estimation valueIntermediate value
It is worked normally for the 0 corresponding actuator of element representation, and is worth and does not break down for the 0 corresponding actuator of element representation, because
Whether this can be broken down with each actuator of real-time judge；
2) the actuator failures information that step 1) obtains is introducedThe Integral Sliding Mode designed in claim 1 third step is held
Wrong controller are as follows:
Wherein, H (t) is the m rank diagonal matrix for indicating each actuator and whether working normally, can be as the event described in step 1)
Barrier detection algorithm obtains, and the element value on diagonal line is 0 or 1, if element value is that in t moment, this element is corresponding for 0 expression
Actuator breaks down, if element value is 1 to indicate to work normally in the corresponding actuator of t moment this element, therefore, uH=H
(t) u is control moment provided by the actuator of normal work；DprFor the transition matrix decomposed by installation matrix D, it is assumed that
There are the matrix Ds of a sequency spectrumps∈Rn×k, and each column of D can use DpsEach linear combination, be expressed as follows:
D=Dps·Dpr
For DprTransposed matrix, for realize sliding formwork control effect, and introduce step 1) obtained in actuator failures
Information realization faults-tolerant control designs switching control u1, form are as follows:
Here the selection of parameter ρ (t) needs to meet ρ (t) > δm+||J-1[DpsJ-1]-1||·δu；Pass through controller compensation
Because of the general disturbance that spacecraft is subject to after the torque of breakdown loss are as follows:
General disturbance dgIt can be further separated into:
dg=Dpsdm+du
Wherein, duIt is only related with external disturbance, and dmIncluding external disturbance and Fault Estimation error two, respectively indicate as
Under:
Here,For DpsPlus sige it is inverse, guarantee matrix multiplication being capable of rational arithmetic；Meanwhile for the ease of Integral Sliding Mode
The design of controller is assumed herein | | dm||≤δm, | | du||≤δu, wherein δmAnd δuRespectively as dmAnd duThe upper bound, and be all
Positive constant；
The spacecraft attitude Integral Sliding Mode fault tolerant control method and the prior art of the considerations of present invention designs actuator failures
Compared to the advantages of be:
(1) a kind of spacecraft attitude Integral Sliding Mode fault tolerant control method of consideration actuator failures of the invention is marked in design
Claim explicitly to introduce saturation function when controller, may be easy to meet the limited constraint of control moment by adjusting controller parameter；
(2) in addition, based on state observer and combine wavelet neural network can with on-line checking and be diagnosed to be actuator therefore
Hinder information, including several different faults types, there is preferable engineering practicability；
(3) it is designed relative to traditional sliding-mode surface, the present invention is by introducing non-linear integral item
The freedom degree of system design is increased, and is exactly based on and introduces this, so that the controller of subsequent design is to constant value
Interference has preferable robustness；Pass through introducing-J ω (t0) item, so that the stateful satisfaction of system institute in initial motion is in cunning
In die face, that is, it is a cancellation the arrival course movement process of sliding-mode surface, improves control speed, this is also exactly Integral Sliding Mode face
Where advantage；The control method of design has robustness external disturbance and spacecraft can be made to inhibit the influence as caused by failure,
And attitude maneuver is carried out with certain precision.
Detailed description of the invention
Fig. 1 is a kind of system frame for the spacecraft attitude Integral Sliding Mode fault tolerant control method for considering actuator failures of the present invention
Figure；
Fig. 2 is a kind of design stream for the spacecraft attitude Integral Sliding Mode fault tolerant control method for 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.
Specific embodiment
As shown in Figure 1, a kind of spacecraft attitude Integral Sliding Mode fault-tolerant control system for considering actuator failures includes integral
Sliding formwork fault-tolerant controller, flywheel, spacecraft dynamics model, fault detection and diagnosis module, gyroscope, attitude sensor, boat
Its device kinematics model.
When spacecraft operation on orbit is there are when actuator failures and external disturbance, first in spacecraft attitude control system
Gyroscope measurement obtains the angular speed of spacecraft, meanwhile, attitude sensor determines spacecraft attitude information, and posture is introduced event
Barrier detection calculates actuator failures information with diagnosis algorithm；Then, posture, angular speed and Fault Estimation information are collectively incorporated into
Control signal is obtained in Integral Sliding Mode fault-tolerant controller designed by the present invention, finally, control signal is sent to flywheel, to
Actual control moment is provided and acts on spacecraft, at this point, spacecraft is also influenced by external disturbance torque, spacecraft power
It learns and kinematics model represents the effective object of attitude control system, kinetic model output angular velocity, kinematics model is defeated
Posture out, both information are able to be measured by gyroscope and attitude sensor.
As shown in Fig. 2, the present invention the specific implementation steps are as follows (attitude maneuver process when below with spacecraft operation on orbit
For carry out the specific implementation of illustration method):
The first step establishes the spacecraft attitude dynamics model for considering actuator failures and external disturbance
The angular velocity information for setting spacecraft is established in spacecraft body coordinate system, and origin o is defined on spacecraft
At mass center, and whole coordinate system is fixed on spacecraft；Wherein oz axis is also known as yaw axis, and oy axis is also known as pitch axis, and ox axis also known as rolls
Moving axis, three are parallel to each other with the inertial reference reference axis (gyroscope sensitive axes) that is fixed on spacecraft respectively.Then consider to execute
The spacecraft kinematics and dynamics modeling of device failure and external disturbance are as follows:
Wherein, ω=[ω1,ω2,ω3]TFor the attitude angle speed of spacecraft relative inertness coordinate system under body coordinate system
Degree, ω1,ω2,ω3Angular velocity component respectively in the x-axis, y-axis and z-axis of this system；Q=[q0,qv T]T=[q0,q1,
q2,q3]TFor the posture unit quaternion of spacecraft, whereinIt is related with the angle around Eigenaxis rotation for scalar, θ
Indicate the angle turned over around Euler's axis, qv=[q1,q2,q3]TFor containing there are three the column vectors of element, with Euler's axis direction
It is related, ex,ey,ezThe rotary shaft on three directions of Euler's axis is represented, and
Meet q0 2+qv Tqv=1；J is the moment of inertia matrix of spacecraft, and is 3 × 3 symmetrical matrix, 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]；ua∈RmIt is anti-for m
The control moment of flywheel reality output is acted on, wherein RmIndicate that the m dimensional vector in real number space, m > 3 indicate that this system is to guarantee
Enough control moments are provided, are needed using the redundancy strategy greater than three actuators, it is axially orthogonal using three flywheels here
With four flywheel configuration methods of another flywheel axial direction oblique installation, it is assumed that the characteristic of each flywheel is identical, and needs to meet width
The limited constraint of value saturation | | u | |≤τmax, herein according to the output torque range of practical flywheel, set τmax=1Nm；D is winged
The installation matrix of wheel, and its order is rank (D)=3, providing a kind of mounting means here isIn the presence of
The matrix D of one sequency spectrumps∈Rn×k, each column of D can use DpsEach linear combination, D=D can be expressed asps·
Dpr, DprIt is the transition matrix that order is k；D is real space environmental perturbation torque suffered by spacecraft, such as gravity gradient torque, pneumatically
Torque, solar radiation pressure torque and remanent magnetism torque, although its unknown bounded of value, upper dividing value are | | d | |≤dmax, here may be used
It is taken asS (ω) is skew symmetric matrix, and form isFor square related with attitude quaternion in kinematical equation
Battle array, wherein
Second step, the controller based on sliding-mode control design are broadly divided into two steps: being the choosing of sliding-mode surface first
It takes；The followed by design of control law, and proof system state reaches sliding-mode surface and reaches and slides in any initial position finite time
Equalization point is converged to after die face, to ensure that spacecraft state is finally stablized；Based on the spacecraft for considering actuator failures
The characteristic of kinetic model chooses following Integral Sliding Mode face:
Wherein, σ indicates sliding-mode surface；t0For the initial time of system, t is the current time of system operation；ω (t) and ω
(t0) it is respectively current and initial angular velocity, set ω (t0)=[- 0.01-0.005 0.003] rad/s；unomIt is dynamic for spacecraft
The control law of mechanics nominal system, above D and J is introduced in Integral Sliding Mode face-1To guarantee DJ-1Be it is nonsingular, convenient for theory
It proves；ξ indicates the time；Here defining spacecraft dynamics nominal system is to ignore the factors such as external disturbance and actuator failures
A kind of spacecraft dynamics system, it may be assumed that
For unomDesign, can using current aerospace engineering universal method proportional-integral-differential method, still
In view of the limited constraint of control input saturation, the present invention, which provides, meets the limited non-linear ratio-differential method of saturation, has
Following form:
unom=-kpqv-kdTanh(ω/α2(t))
Here kp、kdIt can be theoretically any real number greater than zero for controller gain, but consider the limited constraint of amplitude,
Simultaneously adjusting parameter can choose k to repetition testp=0.65, kd=0.35 to obtain preferable control performance；α2It (t) is the sharp of non-zero
Function is spent, can choose any appropriate function, or constant, value determine unomChange as angular velocity omega changes
Degree, and α2(t) bounded；Function Tanh (ω) ∈ R3, define Tanh (ω)=[tanh (ω1) tanh(ω2) tanh
(ω3)]TFor the hyperbolic tangent function of standard；
From controller unomForm it can be found that by adjusting controller parameter kpWith kdIt can be made to meet amplitude limited
Constraint, it may be assumed that
HereFor nom inalcontroller unomThe i-th component, τmTo input the upper dividing value being saturated, while by adjusting α2
(t) it also can control influence of the angular speed item to system；
Third step, in nom inalcontroller unomOn the basis of, to realize active tolerant control mechanism, failure is worked as in consideration
When, for the stability for guaranteeing system, the control moment that actuator should be provided actually are as follows:
U=uH+uF
Wherein, uHThe control moment of the corresponding actuator worked normally of=H (t) u, H (t)=diag { H1(t),...Hm
(t)}·u,Hi(t) ∈ { 0,1 } is m rank diagonal matrix, may determine that failure occur by fault diagnosis algorithm proposed in this paper
Actuator, Hi(t)=0 it indicates to break down in i-th of actuator of t moment, Hi(t)=1 it indicates in i-th of actuator of t moment
It works normally, H1(t) and Hm(t) whether expression the 1st and m-th of actuator break down in t moment, and H (t) has idempotent
Property, i.e. H2(t)=H (t)；uFControl moment provided by actuator for failure considers partial failure here and loses completely
Several fault conditions are imitated, such as the 1st flywheel thoroughly fails after the 1s that works, output torque zero；2nd flywheel is in work
After making 3s, there are partial failure, control ability losses 20%；3rd flywheel is after the 10s that works, and there are partial failure, controls
Capacity loss 60% processed；4th flywheel is after the 2s that works, there is also partial failure, control ability loss 80%, but these
Fault message can not be measured directly, need to estimate using the fault diagnosis algorithm proposed in the present invention, fault message
It can indicate are as follows:
Wherein,Indicate the actuator failures information estimated, Δ uFIndicate that the Fault Estimation that unavoidably will appear is missed
Difference；Therefore, control moment may be expressed as:
Accordingly, it is considered to which the spacecraft attitude dynamics to break down can be written as:
Following detection and diagnosis algorithm is taken to estimate fault message actuator failures, firstly, introducing state observer
Are as follows:
Here,WithRespectively the estimated value of spacecraft attitude and angular speed, initial value are 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 it is defined as follows:
With
Wherein,It is defined as
Sgn () indicates sign function,For the observation error quaternary number of posture,Respectively indicate q0,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,z14Indicate z1Several components；λ1,λ2,α1,α2It is all observer gain, and be positive
Constant, and v1,v2For time-varying parameter, λ can use here1=1, λ2=1, α1=0.5, α2=0.5 is preferred value；
WhenWhen, indicate posture observation error quaternary numberNorm be less than failure determination threshold value δf, then do not have at this time
Failure occurs, this threshold value can choose to obtain the smaller robustness to guarantee system as far as possible, chooses 10-3Preferable control can be obtained
Effect processed, Fault Estimation valueIt is set as zero；WhenWhen, posture observation error quaternary numberNorm be more than fault detection threshold
Value δf, illustrate to break down, therefore Fault Estimation valueIt is not zero, needs to further calculate；
The present invention is based on wavelet transformation theory, three layers of wavelet neural network are constructed to estimate actuator failures, including input
Layer, wavelet layer and output layer；Relationship between input layer and each node of wavelet layer can indicate are as follows:
Here niiIt is the input of wavelet neural network, wherein ni1=z1And Indicate input layer section
Point,Indicate the output of input layer；In wavelet layer, conversion is carried out about mother wavelet function and amplification can establish small wave system,
The present invention chooses Gaussian function ψ (x)=- xexp (- x2/ 2) it is used as mother wavelet function, exp () indicates natural Exponents letter
Number；fi 1Indicate the function that output is input in input layer；For the node in wavelet layer, there is following relationship:
Here,Indicate that the node of wavelet layer, p indicate the node number in wavelet layer about each input node, this
In p=6 can be set, then wavelet layer includes 12 nodes in total in wavelet neural network；cijAnd σijRespectively indicate wavelet layer
I-th inputTo the conversion factor and amplification factor of p-th of node；Indicate the output of wavelet layer；
In output layer, output node needs to add up all input signals, to obtain entire wavelet neural network
Output, calculating process is as follows:
Here, ∑ indicates summation symbol,To export node layer, o indicates output layer node number, considers only have here
One output node；Connection weight of each node to output node layer in expression wavelet layer；It indicates in output layer
It is input to the function of output；For the output of entire wavelet neural network, meanwhile, byAvailable actuator event
Hinder information The corresponding actuator of element representation that intermediate value is 0 works normally, and the element representation that value is not 0 corresponding is held
Whether row device breaks down, therefore can be broken down with each actuator of real-time judge and obtain matrix H (t)；
On the basis of nom inalcontroller, failure diagnosis information is introduced, designs spacecraft attitude active tolerant control device are as follows:
Wherein,For DprTransposed matrix, u1For switching control, form are as follows:
Here the selection of parameter ρ (t) needs to meet ρ (t) > δm+||J-1[DpsJ-1]-1||·δu；Since fault diagnosis is calculated
Method is estimated that fault message and designs controller thus to compensate the control moment of loss, and outside is disturbed after being compensated in this way
The disturbance that both dynamic and actuator failures generate jointly are as follows:
dgTo compensate because of the general disturbance after the torque of breakdown loss, and it can be further separated into:
dg=Dpsdm+du
Wherein, duIt is only related with external disturbance, and dmIncluding external disturbance and Fault Estimation error two, respectively indicate as
Under:
Here,For DpsPlus sige it is inverse, guarantee matrix multiplication being capable of rational arithmetic；Meanwhile for the ease of Integral Sliding Mode control
The design of device processed, it is assumed that | | dm||≤δm, | | du||≤δu, wherein δmAnd δuRespectively as dmAnd duThe upper bound, and be all positive normal
Number；
It can be seen that u1It needs to use failure diagnosis information to compensate influence caused by actuator failures, and works as system
State deviate sliding-mode surface when u1It is activated, under the action of the integral sliding mode control device u that the present invention designs, system be can achieve
Consistent asymptotic stability.
The content that description in the present invention is not described in detail belongs to the prior art well known to professional and technical personnel in the field.
Claims (4)
1. a kind of spacecraft attitude Integral Sliding Mode fault tolerant control method for considering actuator failures, it is characterised in that realize step such as
Under:
(1) it establishes and considers actuator failures and the spacecraft attitude dynamics model containing external disturbance, wherein actuator failures
Increase including idle running, stuck, stalling, moment of friction and revolving speed continues to decline, external disturbance includes gravity gradient torque, aerodynamic force
Square, solar radiation pressure torque and remanent magnetism torque；
(2) the spacecraft attitude dynamics model established based on the first step, needs to consider first for the ease of the design of controller
In the case that actuator is without failure and nominal control system not by external disturbance, the sliding formwork for having integrated form is chosen
Face；Then the sliding-mode surface of selection is introduced into the design of controller, at this moment designed controller is known as nom inalcontroller, nominally
Controller makes the nominal control system state of spacecraft attitude reach sliding-mode surface in any initial position finite time and reaches cunning
Equalization point is converged to after die face, to ensure that spacecraft state is finally stablized, and is easy to full by adjusting controller parameter
Foot input saturation amplitude limitation；
(3) on the basis of second step, spacecraft is considered there is a situation where actuator failures and by external disturbance, i.e., for the
The spacecraft attitude dynamics model established in one step introduces wavelet neural network fault diagnosis algorithm and obtains actuator failures letter
Breath, and Integral Sliding Mode fault-tolerant controller is designed with this, effectively improve the robustness to actuator failures and external disturbance, and base
In the stability of Lyapunov method analysis system；
In the first step, consider that actuator failures and spacecraft attitude dynamics model containing external disturbance are as follows:
Wherein, ω=[ω1,ω2,ω3]TFor the attitude angular velocity of spacecraft relative inertness coordinate system under body coordinate system,
ω1,ω2,ω3Angular velocity component respectively in the x-axis, y-axis and z-axis of this system；Q=[q0,qv T]T=[q0,q1,q2,q3
]TFor the posture unit quaternion of spacecraft, whereinRelated with the angle around Eigenaxis rotation for scalar, θ is indicated
The angle turned over around Euler's axis, qv=[q1,q2,q3]TTo have with Euler's axis direction containing there are three the column vectors of element
It closes, ex,ey,ezThe rotary shaft on three directions of Euler's axis is represented, and full
Sufficient q0 2+qv Tqv=1；J is the moment of inertia matrix of spacecraft, and is 3 × 3 symmetrical matrix；ua∈RmFor m counteraction flyback
The control moment of reality output, wherein RmIndicating that m ties up real vector space, m > 3 are expressed as guaranteeing to provide enough control moments,
Need using greater than three actuators redundancy strategy, it is assumed that the characteristic of each flywheel is identical, and need to meet amplitude saturation by
Limit constraint | | ua||≤τmax；D is the installation matrix of flywheel, and it is real space suffered by spacecraft that its order, which is rank (D)=3, d,
Environmental perturbation torque, upper dividing value be | | d | |≤dmax；S (ω) is skew symmetric matrix, and form is For square related with attitude quaternion in kinematical equation
Battle array, wherein
2. the spacecraft attitude Integral Sliding Mode fault tolerant control method according to claim 1 for considering actuator failures, special
Sign is: in the second step, the selection of sliding-mode surface is as follows:
Wherein, σ indicates sliding-mode surface；t0For the initial time of system, t is the current time of system operation；ω (t) and ω (t0) point
It Wei not current and initial angular velocity；unomFor nom inalcontroller, for convenient for theoretical proof, above introduce D and J in Integral Sliding Mode face
-1To guarantee DJ-1It is nonsingular, J-1Indicate that the inverse of moment of inertia matrix, ξ indicate the time.
3. the spacecraft attitude Integral Sliding Mode fault tolerant control method according to claim 1 for considering actuator failures, special
Sign is: in the second step, the nom inalcontroller design is as follows:
Ignore the spacecraft dynamics nominal system of external disturbance and actuator failures, it may be assumed that
Wherein unomFor nom inalcontroller, for unomDesign is had using the limited non-linear ratio-differential method of saturation is met
There is following form:
unom=-kpqv-kdTanh(ω/α2(t))
Wherein kp、kdFor controller gain；α2It (t) is the acutance function of non-zero, value determines unomWith angular velocity omega variation
The degree of variation, and α2(t) bounded；Function Tanh (ω) ∈ R3, define Tanh (ω)=[tanh (ω1) tanh(ω2)
tanh(ω3)]TFor the hyperbolic tangent function of standard；
By adjusting controller parameter kpWith kdMeet the limited constraint of amplitude, it may be assumed that
For nom inalcontroller unomI-th of component, τmTo input the upper dividing value being saturated, while by adjusting α2(t) may be used
Influence with pilot angle speed term to system.
4. the spacecraft attitude Integral Sliding Mode fault tolerant control method according to claim 1 for considering actuator failures, special
Sign is: in the third step, introducing state observer combination wavelet neural network fault diagnosis algorithm and obtains actuator failures
Information, and the specific implementation of Integral Sliding Mode fault-tolerant controller is designed with this are as follows:
(31) firstly, introducing state observer estimates spacecraft attitude observation informationPosture observation error is calculated with thisAnd observation improvement factor is further obtained, whenWhen, indicate posture observation error quaternary numberNorm it is small
In failure determination threshold value δf, then there is no failure at this time；WhenWhen, posture observation error quaternary numberNorm be more than
Failure determination threshold value δf, illustrate to break down, therefore Fault Estimation valueIt is not zero, needs to enter (32) and further calculate；
(32) it is based on wavelet transformation theory, constructs the wavelet neural network of input layer, wavelet layer and output layer three-decker to estimate
Actuator failures are counted, the input of wavelet neural network is observation improvement factor obtained above, and output is the execution estimated
Device fault messageMeanwhile defining H (t) is the m rank diagonal matrix for indicating each actuator and whether working normally, based on execution
The value of device fault message,In i-th of element value not to be 0 expression break down in i-th of actuator of t moment, i indicates actuator
Label, then i-th of element value takes 0 on H (t) diagonal line；And work asIn i-th element value be 0 to indicate to hold at i-th of t moment
Row device works normally, and the value of i-th of element takes 1 on H (t) diagonal line；
(33) the actuator failures information obtained based on fault diagnosis algorithm in step (31) and (32), then actuator is practical provides
Control moment are as follows:
Here, △ uFFor the evaluated error inevitably generated when obtaining actuator failures information；At this point, the integral of design is sliding
Mould fault-tolerant controller are as follows:
DprFor the transition matrix decomposed by installation matrix D, it is assumed that there are the matrix D of a sequency spectrumps∈Rn×k, and D
Each column all use DpsEach linear combination, be expressed as follows:
D=Dps·Dpr
For DprTransposed matrix while introducing the actuator failures information that (32) obtain to realize sliding formwork control effect, if
Count switching control u1, form are as follows:
The selection of parameter ρ (t) needs to meet ρ (t) > δm+||J-1[DpsJ-1]-1||·δu；By controller compensation because of breakdown loss
Torque after the general disturbance that is subject to of spacecraft are as follows:
General disturbance dgIt is further separated into:
dg=Dpsdm+du
Wherein, duIt is only related with external disturbance, and dmIncluding external disturbance and Fault Estimation error two, respectively indicate as follows:
For DpsPlus sige it is inverse, guarantee matrix multiplication being capable of rational arithmetic；Meanwhile setting for the ease of integral sliding mode control device
Meter, it is assumed that | | dm||≤δm, | | du||≤δu, wherein δmAnd δuRespectively as dmAnd duThe upper bound, and be all positive constant.
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