CN113778047A - Complex spacecraft fault-tolerant control method considering measurement errors and comprehensive faults - Google Patents
Complex spacecraft fault-tolerant control method considering measurement errors and comprehensive faults Download PDFInfo
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Abstract
The invention relates to spacecraft fault diagnosis and fault-tolerant control, and aims to solve the problem of fault-tolerant control of finite-time attitude of a spacecraft under the influence of comprehensive faults. Firstly, considering the comprehensive influence of multiplicative faults, additive faults and attitude measurement errors of an actuator, establishing a spacecraft attitude tracking error dynamic model, and dividing the spacecraft attitude tracking error dynamic model into an attitude angle subsystem and an angular velocity subsystem; secondly, providing a finite time self-adaptive multivariable instruction filtering backstepping fault-tolerant control strategy aiming at the attitude angle subsystem and the angular velocity subsystem respectively, and realizing finite time filtering error compensation; intermediate variables are introduced to design a controller, and a self-adaptive law is designed to realize finite time estimation and compensation on the upper bound of the fault, so that the influence of the comprehensive fault is solved; in addition, aiming at unknown interference in the two subsystems, a self-adaptive law is designed, and parameter adjustment and parameter control are facilitated. The method is mainly applied to the occasions of spacecraft fault diagnosis and fault-tolerant control.
Description
Technical Field
The invention relates to the technical field of spacecraft fault diagnosis and fault-tolerant control, in particular to the field of complex spacecraft fault-tolerant control under the influence of comprehensive faults. In particular to a complex spacecraft fault-tolerant control method considering measurement errors and comprehensive faults.
Background
As one of the fastest growing sophisticated technologies in current science and technology, aerospace technology plays an increasingly important role in the military field, such as global surveillance and percussion, military satellite communication services, space-performing reconnaissance and detection, and destruction of military satellite space bases. The satellite runs all day after networking is completed, and due to the fact that the satellite runs in a harsh and unknown space environment, the aging of components on the satellite and the like, the fault is difficult to avoid, if the fault is not processed in time, the delay of the execution of space missions is possibly caused, and in a wartime state, the loss of ground combat information is caused, and the progress of a battlefield is seriously influenced. The 2005 united states co-launched "topees/bosch winter" (TOPEX/Poseidon) marine exploration satellite caused the end of life of the satellite due to failure of the on-board pitch reaction wheel used to maintain orbital pointing. The army pointed out that the sky and the ocean were the battlefield of the 20 th century, while the space became the battlefield of the 21 st century, becoming the strategic high point of modern war. In recent years, the aerospace industry of China has gained brilliant achievements. "Shenzhou" manned airship, "goddess Chang' e I" engineering, "big dipper" navigation system marks that china has obtained great achievement in the aspect of space exploration. With the increasing complexity of the space mission, higher requirements are put forward on the reliability of the spacecrafts such as rockets and satellites. Therefore, the method develops the research of spacecraft fault diagnosis and fault-tolerant control technology, discusses the feasibility of related methods in spacecraft fault diagnosis, and has very important theoretical and practical significance for ensuring safe and reliable operation of the spacecraft, reducing the workload and the launching and operating costs of ground workers and promoting the healthy development of the aerospace industry.
However, because the operating environment of the spacecraft is complex and unknown, and as the complexity of tasks and star structures is increased day by day, the influence of model uncertainty and the like is more and more obvious, the fault diagnosis and fault tolerance control of the spacecraft under the influence of interference and uncertainty are always the key and difficult problems of the research in the aerospace field. At present, the fault diagnosis and fault-tolerant control method based on the observer is most widely applied, and a fault detection mechanism is established by establishing a residual sequence so as to achieve the purpose of fault detection. However, when the existing theoretical method is used for satellite fault diagnosis and fault-tolerant control design, the defects are mainly reflected in the following aspects: (1) most researchers mainly and singly develop researches aiming at multiplicative or additive faults, in the practical engineering, the two faults can occur simultaneously, and the limited-time fault-tolerant control research aiming at the spacecraft under the influence of the comprehensive fault is less; (2) in order to solve the problem of faults under the influence of interference, the existing means mainly utilizes complex coordinate transformation to decouple the interference and the faults or utilizes an unknown input former, which both need more complex calculation, are difficult to meet the practical engineering problem of limited satellite calculation resources and can not realize limited time control; (3) due to the influence of the interference of a complex external environment and the capacity limitation of the satellite sensor, the accurate measurement of the attitude and the angular velocity is difficult to realize, a certain measurement error always exists, and the control precision of the system is influenced. Therefore, how to comprehensively consider the influence of measurement errors, multiplicative faults and additive faults and effectively process the fault problem under the influence of interference is a key problem to be solved urgently, and the method has vital theoretical significance and engineering value for ensuring the safe and stable flight of the spacecraft.
In order to overcome the limitations, in the research of the invention, the influence of multiplicative and additive comprehensive faults of an actuator on the safe flight of the spacecraft is comprehensively considered, the fault-tolerant control strategy of the spacecraft is researched, a ring-splitting control idea is adopted, the spacecraft system is divided into an attitude angle subsystem and an angular velocity subsystem, adaptive controller design is respectively carried out, the finite time estimation and compensation on the upper limit of the fault are realized through adaptive law design, the stability certification of the whole closed-loop system is carried out, the finite time attitude tracking control of the spacecraft is ensured, and the effectiveness of the designed fault-tolerant control strategy is verified through simulation.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention aims to provide a method for solving the problem of fault-tolerant control of finite-time attitude of a spacecraft under the influence of comprehensive faults. On the one hand, due to the complexity of the spacecraft mission itself and its non-linearity, the difficulty and complexity of fault diagnosis thereof are significantly increased. On the other hand, when the satellite runs in orbit, the satellite is subjected to various perturbation force actions of space environment and external interference in various aspects such as high temperature, low temperature, electromagnetic interference, space particle radiation and the like, and the complexity of satellite fault diagnosis is further increased. The traditional fault diagnosis method has the advantages that the influence of space disturbance torque and comprehensive faults is less comprehensively considered, and the finite-time fault-tolerant control of the spacecraft is difficult to realize. Based on the method, firstly, considering the comprehensive influence of multiplicative faults, additive faults and attitude measurement errors of an actuator, establishing a spacecraft attitude tracking error dynamic model, and dividing the spacecraft attitude tracking error dynamic model into an attitude angle subsystem and an angular velocity subsystem; secondly, providing a finite time self-adaptive multivariable instruction filtering backstepping fault-tolerant control strategy aiming at the attitude angle subsystem and the angular velocity subsystem respectively, and realizing finite time filtering error compensation; intermediate variables are introduced to design a controller, and a self-adaptive law is designed to realize finite time estimation and compensation on the upper bound of the fault, so that the influence of the comprehensive fault is solved; in addition, aiming at unknown interference in the two subsystems, a self-adaptive law is designed, and parameter adjustment and parameter control are facilitated.
MATLAB/Simulink simulation is adopted to verify the effectiveness of the invention.
The method comprises the following specific steps:
in the first part, the spacecraft orientation control model is established: analyzing the influence of multiplicative and additive comprehensive faults and measurement errors of a spacecraft actuating mechanism, and establishing a nonlinear tracking error kinematics and dynamics model of the complex spacecraft under the influence of external interference and comprehensive faults on the basis of a spacecraft kinematics and dynamics model;
and a second part, designing an attitude angle subsystem controller: aiming at the attitude angle subsystem, a novel auxiliary signal is designed to compensate the finite time compensation of the influence on the filtering signal of the virtual angular velocity control law; designing a virtual angular velocity control law based on the auxiliary signals and the attitude angle expected command to ensure the finite time stable tracking control of the attitude angle expected command;
and in the third part, the angular speed subsystem controller is designed as follows: aiming at an angular velocity subsystem, in order to solve multiplicative fault influence of an actuator, an intermediate variable is introduced to design a controller, an additive fault is processed through a self-adaptive law, the upper limit of the fault is estimated, multiplicative and additive fault influence is processed in a limited time, and a self-adaptive limited-time fault-tolerant controller is designed to ensure the limited-time fault-tolerant control of a spacecraft system after the fault occurs.
The detailed steps are as follows:
firstly, establishing a spacecraft orientation control model, describing a spacecraft attitude kinematics and dynamics model under the influence of flexible vibration and liquid shaking based on a spacecraft kinematics model described by improved Rockwell parameters (MRPs), and comprising the following steps of:
wherein p ═ p1 p2 p3]TFor MRPs vectors describing spacecraft attitude, G (p) e R3×3Is shown as
J is moment of inertia, ω ═ ω1 ω2 ω3]TIs the angular velocity of the spacecraft, d is unknown external interference, u is control moment, and x belongs to RN,η∈RMRespectively a flexible vibration mode and a liquid shaking mode, wherein N and M are modal orders. Ci,Ki(i ═ f, l) are respectively the compliance matrix and stiffness matrix of the vibration mode and the sway mode, and Cf＝diag(2ξjΛj,j＝1,2,…,N)，
Wherein ΛjIs the j th orderNatural frequency of flexible vibration mode, xijIs the j-th order damping coefficient. Mη＝diag(m1,m1,…,mM,mM) For shaking the mass matrix of the liquid fuel, miSloshing liquid mass, δ, for an ith order liquid sloshing modefIs a rigid-flexible coupling matrix, deltalIs a rigid-liquid coupling matrix, expressed as:
wherein, biIs the distance between the ith order liquid mode and the mass center
x×Is defined as:
the measurement errors of attitude angle and angular velocity brought by the influence of the external unknown environment and the measurement capability limitation of the star sensor and the gyroscope are considered and expressed as follows:
wherein,
as a measure of attitude angle and angular velocity, v1,v2The measurement errors of the attitude angle and the angular velocity are respectively.
The derivation of formula (5) and substitution of formula (1) can be obtained:
wherein,
defining a desired coordinate system FDRelative to the earth's inertial frame FILower spacecraft desired attitude angle pr＝[pr1pr2 pr3]TDesired angular velocity is ωr＝[ωr1 ωr2 ωr3]T. The expected attitude angle and the angular velocity satisfy:
to achieve efficient tracking of the desired attitude, the spacecraft desired coordinate system FDWith body coordinate system FBThe attitude angle error and the angular velocity error between the two are as follows:
wherein,
is FDTo FBThus, the spacecraft attitude angle and angular velocity tracking error is dynamically represented as:
wherein,
multiplicative faults and additive faults are mathematically represented as follows:
ui＝ρiτi+fi (10)
wherein, taui,i＝1,2,3For a desired control torque, uiControl moment, p, actually applied to the system by the actuatoriSatisfies rho of 0 & lt for the efficiency factor of the actuatoriLess than or equal to 1. Of note is ρ i1 represents that the actuator works normally, and 0 < rhoi< 1 indicates that the actuator partially failed, but is still functional. f. ofiTo implement drift failure, it is bounded.
Substituting the actuator fault model (10) into the spacecraft attitude tracking error dynamics (9) to obtain:
where ρ ═ diag (ρ)1,ρ2,ρ3),f＝[f1,f2,f3]T. Equation (11) is the established control-oriented model, and the controller design will be performed based on this model:
unknown uncertainty delta in a system (11)1,δ2Is bounded, but the upper bound is unknown, satisfying:
wherein λ1,λ2Is an unknown normal number, and defines an unknown variable λ ═ max (λ)1,λ2)；
The control targets are as follows: based on a spacecraft kinematics and dynamics model (11) under the influence of sensor measurement errors and actuator faults, a self-adaptive fault-tolerant controller tau is designed, the measurement errors and multiplicative and additive faults of the actuator are effectively processed, and the finite-time rapid and stable tracking control of expected attitude instructions is guaranteed;
and secondly, designing an attitude angle subsystem controller, aiming at the attitude angle subsystem:
by varying the angular velocity omegaeDesigning a virtual control input omega as a control quantitydRealizing the attitude angle tracking error peThe finite time of (c) converges. For ease of writing, new variables are defined:
wherein z is1In order to be an attitude angle tracking error,
inputting omega for virtual controldOutputting after filtering;
substituting the formula (13) into the attitude angle subsystem (12) to obtain
To compensate for command filtering errors
Designing the auxiliary signal xi as follows41：
Wherein k is1>0，l1>0，ξ2Defined by formula (22), the term G (p)e)ξ2For stability certification needs; for controller design, the following coordinate transformations are defined:
v1＝z1-ξ1,v2＝z2-ξ2 (16)
for v1Performing derivation and substituting the formula (14) to the formula (16)
Angular velocity virtual control input omegadThe design is as follows:
wherein,
a1＞0，
for handling unknown interference delta1、δ2Designing by using the adaptation shown in formula (26);
thirdly, designing an angular velocity subsystem controller, and inputting virtual control of the attitude angle subsystem
When the command is taken as an expected command of an angular velocity subsystem, the design of a self-adaptive controller is completed based on the attitude angular velocity, and an actual control moment tau is obtained;
for the angular velocity subsystem:
based on the angular velocity tracking error definition (13) and equation (19), the angular velocity tracking error dynamics is obtained as:
based on v2And an angular velocity tracking error dynamics (20) to obtain:
wherein,
as with the attitude angle subsystem, an auxiliary signal xi is designed2Comprises the following steps:
wherein k is2＞0,l2＞0。
Accounting for actuator multiplicative failure ρiAnd additive fault fi(i ═ 1,2,3) is bounded, and for subsequent processing of fault effects, the following new variables are defined:
wherein, θ and
are all unknown parameters, will subsequently utilize the adaptive law
And
carrying out estimation;
design of intermediate variables for controller design, solving multiplicative fault
Comprises the following steps:
wherein,
a2> 0 is a normal number.
And
designed by an adaptive law and respectively used for processing unknown interference deltaiAnd drift fault fi。
Adaptive parameters
And
the design is as follows:
wherein gamma is more than 0, r is more than 0, gamma is more than 0, sigma1,σ2,σ3＞0。
The true attitude controller τ is designed to:
based on the three steps, the whole fault-tolerant control process of the finite-time attitude of the spacecraft is completed.
The invention has the characteristics and beneficial effects that:
the designed step-by-step control algorithm can ensure the rapid convergence of the expected attitude angle, and has high convergence and control precision; the state of the auxiliary system can be changed continuously so as to compensate estimation errors brought by a filter in the design of the controller and ensure the control precision; and through adjusting a control algorithm, the flexible vibration and the liquid shaking are actively suppressed to zero.
Description of the drawings:
fig. 1 shows a spacecraft fault-tolerant control structure diagram under the influence of a comprehensive fault of an actuator.
FIG. 2 is a graph of attitude angle tracking error.
FIG. 3 is a graph of attitude angular velocity tracking error.
Fig. 4 is a graph of virtual angular velocity tracking.
Fig. 5 is a differentiator versus virtual angular velocity estimation diagram.
FIG. 6 is a graph of auxiliary system state changes.
Fig. 7 control input graph.
Fig. 8 is a graph of adaptive parameter variation.
FIG. 9 is a graph of liquid sloshing mode change.
FIG. 10 is a graph of a change in a mode of a flexural vibration.
Detailed Description
The invention relates to the technical field of spacecraft fault-tolerant control. Specifically, an adaptive finite time fault-tolerant controller comprehensive algorithm is firstly proposed, and then the effectiveness of the algorithm proposed by the invention is verified through MATLAB/Simulink simulation.
The invention aims to provide a method for solving the problem of fault-tolerant control of finite-time attitude of a spacecraft under the influence of comprehensive faults. On the one hand, due to the complexity of the spacecraft mission itself and its non-linearity, the difficulty and complexity of fault diagnosis thereof are significantly increased. On the other hand, when the satellite runs in orbit, the satellite is subjected to various perturbation force actions of space environment and external interference in various aspects such as high temperature, low temperature, electromagnetic interference, space particle radiation and the like, and the complexity of satellite fault diagnosis is further increased. The traditional fault diagnosis method has the advantages that the influence of space disturbance torque and comprehensive faults is less comprehensively considered, and the finite-time fault-tolerant control of the spacecraft is difficult to realize. Based on the above, the invention provides a spacecraft finite time fault-tolerant control method based on self-adaptive finite time instruction filtering backstepping, which comprises the steps of firstly, considering the comprehensive influence of multiplicative faults, additive faults and attitude measurement errors of an actuator, establishing a complex spacecraft attitude tracking error dynamic model, and dividing the model into an attitude angle subsystem and an angular velocity subsystem; secondly, providing a finite time self-adaptive multivariable instruction filtering backstepping fault-tolerant control strategy aiming at the attitude angle subsystem and the angular velocity subsystem respectively, on one hand, compared with the traditional backstepping control, the method can realize finite time filtering error compensation through improved auxiliary signal design; on the other hand, in order to process multiplicative faults, an intermediate variable is introduced to design a controller, and an adaptive law is designed to realize finite time estimation and compensation on the upper bound of the faults, so that the influence of comprehensive faults is effectively solved; in addition, aiming at unknown interference in the two subsystems, the method is different from the traditional method of respectively estimating by adopting two observers or adaptive laws, only one adaptive law is designed, parameter adjustment is convenient, and the method is more suitable for engineering practice; and finally, verifying the effectiveness of the invention by adopting MATLAB/Simulink simulation. The adaptive finite time instruction filtering backstepping fault-tolerant control method provided by the invention can effectively solve the comprehensive influence of multiplicative faults and additive faults of the actuator, and the designed novel auxiliary signal can compensate filtering errors in finite time, thereby realizing the finite time fault-tolerant control of the complex spacecraft attitude and effectively improving the reliability and safety of the spacecraft operation.
The general technical scheme of the spacecraft fault-tolerant control algorithm under the influence of the comprehensive faults of the actuator is shown in figure 1, and the whole system comprises three parts: the method comprises the following steps of establishing a control-oriented model of the spacecraft, designing a controller of an attitude angle subsystem and controlling and designing an angular speed subsystem, wherein the specific technical scheme is as follows:
in the first part, the spacecraft orientation control model is established: analyzing the influence of multiplicative and additive comprehensive faults and measurement errors of a spacecraft actuating mechanism, and establishing a nonlinear tracking error kinematics and dynamics model of the complex spacecraft under the influence of external interference and comprehensive faults based on a spacecraft kinematics and dynamics model.
And a second part, designing an attitude angle subsystem controller: aiming at the attitude angle subsystem, a novel auxiliary signal is designed to compensate the finite time compensation of the influence on the filtering signal of the virtual angular velocity control law; designing a virtual angular velocity control law based on the auxiliary signals and the attitude angle expected command to ensure the finite time stable tracking control of the attitude angle expected command;
and in the third part, the angular speed subsystem controller is designed as follows: aiming at an angular velocity subsystem, in order to solve multiplicative fault influence of an actuator, an intermediate variable is introduced for designing a controller, additive faults are processed through an adaptive law, the estimation is different from the traditional estimation of the faults, the method estimates the upper bound of the faults, simultaneously processes multiplicative and additive fault influences in a limited time manner, designs an adaptive limited time fault-tolerant controller, ensures the limited time fault-tolerant control of a spacecraft system after the faults occur, and is different from the traditional method of respectively estimating unknown interference in two subsystems by adopting two observers or adaptive laws.
And finally, in order to verify the effectiveness of the algorithm provided by the invention, an MATLAB/Simulink simulation system for spacecraft attitude fault-tolerant control is set up, and the effectiveness of the algorithm provided by the invention is verified.
In order to verify the effectiveness of the finite time fault-tolerant control algorithm provided by the invention, firstly, a spacecraft attitude control system is integrated and designed in Matlba/Simulink, and a simulation experiment is carried out, wherein the main simulation process is as follows:
(1) parameter setting
1) Setting physical parameters of the spacecraft: in the simulation process, the initial attitude value of the spacecraft is set to p (0) [ -0.20.20.4 [ -]TThe initial angular velocity is set to ω (0) — 000]Trad/s, desired attitude value set to pr＝[0.3sin(t/10)0.4sin(t/20)0.3cos(t/10)]TThe moment of inertia of the spacecraft is
Considering that the first few orders of flexible vibration mode and liquid shaking mode have the largest influence on the spacecraft, and the influence is gradually reduced along with the increase of the orders, therefore, in the invention, the first three orders of vibration mode and the fourth order of shaking mode are considered. Wherein the rigid-flexible coupling matrix is
The natural frequencies of the vibration modes of the orders are respectively set as follows: lambda1＝0.7681rad/s,Λ2＝1.1038rad/s, Λ31.8733rad/s, each order modal damping is xi1＝0.0056,ξ2＝0.0086,ξ3＝0.013。
The damping matrix of the first four-order liquid shaking mode is ClBiag (3.334,3.334,0.237,0.237), stiffness matrix KlBiag (55.21,55.21,7.27,7.27) and the shaking liquid mass m1＝20kg,m2＝0.8kg， b1＝1.127m,b2＝0.994m。
The unknown interference is d ═ 0.01[ sin (t/10), cos (t/15), sin (t/20)]TNm。
Multiplicative time-varying fault values are sized as:
ρ41＝0.7+0.1sin(0.1t+π/3)+0.1sin(mod(t,30)-15)
ρ42＝0.6+0.1sin(0.1t+2π/3)+0.1sin(mod(t,40)-25)
ρ43＝0.7-0.1sin(0.1t+π)+0.1sin(mod(t,50)-25)
the additive time-varying fault value is sized to be:
f1＝0.005+0.02sin(0.2t),f2＝-0.02sin(0.2t+π/3),
f3＝-0.005+0.01sin(0.15t+π)
the adaptive and controller parameters are set to γ -5, r-10, k-0.001, Γ -2, σ -5, σ1＝10,σ2＝1，σ3＝0.2,k41＝1,k42＝0.02,c1＝0.2,c2＝0.02,a1＝1,a2＝1,m＝11/13。
2) The adaptive law and controller parameters are set as follows: γ is 5, r is 10, k is 0.001, Γ is 2, σ is 5, σ1＝10,σ2＝1，σ3＝0.2,k41＝1,k42＝0.02,c1＝0.2,c2＝0.02,a1＝1,a2＝1,m＝11/13。
(2) Analysis of results
To illustrate the effectiveness of the method, the following simulations are performed:
the simulation results are shown in fig. 2-10. Fig. 2 is a graph of an attitude angle tracking error. As can be seen from the simulation diagram, the designed step control algorithm can ensure the quick convergence of the expected attitude angle, even if the attitude angle is converged within 5s under the condition of the existence of attitude measurement error and actuator fault, and the tracking precision is 10 orders of magnitude-3. Fig. 3 is a graph showing a change in tracking error of the attitude angular velocity, and it can be seen from the simulation that the attitude angular velocity can converge in about 5s, but the convergence accuracy is not as high as the attitude angular convergence accuracy because the controller first acts on the attitude angular velocity system, and then acts on the attitude angular velocity system to ensure the convergence of the attitude angle, and the control amount of the attitude angular system is smoother, so the convergence accuracy is higher. Fig. 4 is a graph of a virtual angular velocity tracking. As can be seen from the simulation diagram, the actual angular velocity can be basically realized
Estimation of virtual reference commands
To estimate the value
And the virtual reference instruction omega can be realized by a finite time differentiatordAs shown in fig. 5, it can be seen that,
can realize the pair omega within 2sdIs estimated.
Further, to compensate for errors introduced by the differentiator estimate, the auxiliary system state ξ1iFunction, as shown in FIG. 6, to more clearly observe ξ1iIn fig. 6, only the change map within 5s is placed. Since the virtual reference command ω is implemented within 2s in fig. 5dSo it can be seen from the simulation of fig. 6 that ω is estimateddBefore, the auxiliary system state may notAnd changing continuously to compensate estimation errors brought by the filter in the design of the controller, so that the control precision is ensured. When realizing the pair omegadAfter estimation of (c), the auxiliary system state xi1iWill no longer function and will converge for a limited time, of the order of 10-5So as to reduce the influence on the control precision of the system.
Fig. 7 is a control input change curve diagram, which is initially a graph ensuring fast convergence of a state, and a control input value is large but satisfies a constraint condition, and it can be seen from the graph that some fluctuation exists in the control input due to high-frequency fluctuation effects such as measurement error and shaking vibration. FIG. 8 is a diagram of adaptive parameters
The curve diagram is changed, and self-adaptive parameters continuously fluctuate to ensure the control performance of the system as can be seen from the simulation diagram. Fig. 9 and 10 are graphs showing the variation of the liquid shaking mode and the flexible vibration mode, respectively, and it can be seen from the graphs that both the flexible vibration and the liquid shaking strength are attenuated continuously, and the influence thereof is handled by the adaptive law, but it can be seen that the flexible vibration and the liquid shaking are not completely suppressed, and still have a certain influence on the control performance, and the flexible vibration and the liquid shaking are actively suppressed to zero by adjusting the control algorithm, and it will be a working focus in the future to improve the control accuracy.
The invention provides a spacecraft attitude fault-tolerant control algorithm under the influence of comprehensive faults by taking a finite time instruction filtering backstepping design theory as a main research means, and the specific implementation process is as follows.
Firstly, a spacecraft orientation control model is established. A spacecraft kinematics model described based on improved Reed-Solomon parameters (MRPs) is described as follows by considering spacecraft attitude kinematics and dynamics models under the influence of flexible vibration and liquid sloshing:
wherein p ═ p1 p2 p3]TFor MRPs vectors describing spacecraft attitude, G (p) e R3×3Is shown as
J is moment of inertia, ω ═ ω1 ω2 ω3]TIs the angular velocity of the spacecraft, d is unknown external interference, u is control moment, and x belongs to RN,η∈RMRespectively a flexible vibration mode and a liquid shaking mode, wherein N and M are modal orders. Ci,Ki(i ═ f, l) are respectively the compliance matrix and stiffness matrix of the vibration mode and the sway mode, and Cf＝diag(2ξjΛj,j＝1,2,…,N)，
Wherein ΛjIs the natural frequency, xi, of the j-th order flexible vibration modejIs the j-th order damping coefficient. Mη＝diag(m1,m1,…,mM,mM) For shaking the mass matrix of the liquid fuel, miA rocking liquid mass being an ith order liquid rocking mode. DeltafIs a rigid-flexible coupling matrix, deltalIs a rigid-liquid coupling matrix, expressed as:
wherein, biIs the distance between the ith order liquid mode and the centroid. To pair
x×Is defined as:
the measurement errors of attitude angle and angular velocity brought by the influence of the external unknown environment and the measurement capability limitation of the star sensor and the gyroscope are considered and expressed as follows:
wherein,
as a measure of attitude angle and angular velocity, v1,v2The measurement errors of the attitude angle and the angular velocity are respectively.
The derivation of formula (5) and substitution of formula (1) can be obtained:
wherein,
defining a desired coordinate system FDRelative to the earth's inertial frame FILower spacecraft desired attitude angle pr＝[pr1pr2 pr3]TDesired angular velocity is ωr＝[ωr1 ωr2 ωr3]T. The expected attitude angle and the angular velocity satisfy:
to achieve efficient tracking of the desired attitude, the spacecraft desired coordinate system FDBook and notebookBody coordinate system FBThe attitude angle error and the angular velocity error between the two are as follows:
wherein,
is FDTo FBThe rotation matrix of (2).
Therefore, the spacecraft attitude angle and angular velocity tracking error is dynamically expressed as:
wherein,
further, in the maneuvering process of the spacecraft, actuator faults, including multiplicative faults and additive faults, are very easy to occur due to the influence of space environment and the aging of components of the spacecraft, and the mathematical expression is as follows:
ui＝ρiτi+fi (10)
wherein, tauiI is 1,2,3 is the desired control torque, uiControl moment, p, actually applied to the system by the actuatoriSatisfies rho of 0 & lt for the efficiency factor of the actuatoriLess than or equal to 1. Of note is ρ i1 represents that the actuator works normally, and 0 < rhoi< 1 indicates that the actuator partially failed, but is still functional. f. ofiTo implement drift failure, it is bounded.
Substituting the actuator fault model (10) into the spacecraft attitude tracking error dynamics (9) to obtain:
where ρ ═ diag (ρ)1,ρ2,ρ3),f＝[f1,f2,f3]T. Equation (11) is the established control-oriented model, and controller design is subsequently performed based on the model.
Assume that 1: unknown uncertainty delta in a system (11)1,δ2Is bounded, but the upper bound is unknown, satisfying:
wherein λ1,λ2Is an unknown normal number, and defines an unknown variable λ ═ max (λ)1,λ2)。
The control targets of the invention are: based on a spacecraft kinematics and dynamics model (11) under the influence of sensor measurement errors and actuator faults, a self-adaptive fault-tolerant controller tau is designed, the measurement errors and multiplicative and additive faults of the actuator are effectively processed, and the fast and stable tracking control of the finite time of an expected attitude command is ensured.
And secondly, designing an attitude angle subsystem controller. For the attitude angle subsystem:
by varying the angular velocity omegaeDesigning a virtual control input omega as a control quantitydRealizing the attitude angle tracking error peThe finite time of (c) converges. For ease of writing, new variables are defined:
wherein z is1In order to be an attitude angle tracking error,
for virtual controlInput omegadAnd outputting after filtering.
Substituting the formula (13) into the attitude angle subsystem (12) to obtain
To compensate for command filtering errors
Designing the auxiliary signal xi as follows41：
Wherein k is1>0，l1>0，ξ2Defined by formula (22), the term G (p)e)ξ2For stability proving requirements.
For controller design, the following coordinate transformations are defined:
v1＝z1-ξ1,v2＝z2-ξ2 (16)
for v1The derivative is obtained by substituting the formula (14) to the formula (16)
Angular velocity virtual control input omegadThe design is as follows:
wherein,
a1＞0，
for handling unknown interference delta1、δ2The design is performed by using the adaptation shown in equation (26).
And thirdly, designing an angular speed subsystem controller. Inputting virtual control of attitude angle subsystem
And when the expected command of the angular velocity subsystem is used, the design of the self-adaptive controller is completed based on the attitude angular velocity, and the actual control moment tau is obtained.
For the angular velocity subsystem:
based on the angular velocity tracking error definition (13) and equation (19), the angular velocity tracking error dynamics can be obtained as:
based on v2The definition (16) and the angular velocity tracking error dynamics (20) of (2) are obtained
Wherein,
as with the attitude angle subsystem, an auxiliary signal xi is designed2Comprises the following steps:
wherein k is2＞0,l2＞0。
Accounting for actuator multiplicative failure ρiAnd additive fault fi(i＝1,2,3)Is bounded, for subsequent processing of fault effects, the following new variables are defined:
wherein, θ and
are all unknown parameters, will subsequently utilize the adaptive law
And
and (6) estimating.
Design of intermediate variables for controller design, solving multiplicative fault
Comprises the following steps:
wherein,
a2> 0 is a normal number.
And
designed by an adaptive law and respectively used for processing unknown interference deltaiAnd drift fault fi。
Adaptive parameters
And
the design is as follows:
wherein gamma is more than 0, r is more than 0, gamma is more than 0, sigma1,σ2,σ3＞0。
The true attitude controller τ is designed to:
based on the three steps, the whole fault-tolerant control process of the finite-time attitude of the spacecraft is completed.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.
Claims (3)
1. A complex spacecraft fault-tolerant control method considering measurement errors and comprehensive faults is characterized in that firstly, comprehensive influences of multiplicative faults, additive faults and attitude measurement errors of an actuator are considered, a spacecraft attitude tracking error dynamic model is established and is divided into an attitude angle subsystem and an angular velocity subsystem; secondly, providing a finite time self-adaptive multivariable instruction filtering backstepping fault-tolerant control strategy aiming at the attitude angle subsystem and the angular velocity subsystem respectively, and realizing finite time filtering error compensation; intermediate variables are introduced to design a controller, and a self-adaptive law is designed to realize finite time estimation and compensation on the upper bound of the fault, so that the influence of the comprehensive fault is solved; in addition, aiming at unknown interference in the two subsystems, a self-adaptive law is designed, and parameter adjustment and parameter control are facilitated.
2. The method for fault-tolerant control of a complex spacecraft taking into account measurement errors and synthetic faults as claimed in claim 1, characterized by comprising the following steps:
in the first part, the spacecraft orientation control model is established: analyzing the influence of multiplicative and additive comprehensive faults and measurement errors of a spacecraft actuating mechanism, and establishing a nonlinear tracking error kinematics and dynamics model of the complex spacecraft under the influence of external interference and comprehensive faults on the basis of a spacecraft kinematics and dynamics model;
and a second part, designing an attitude angle subsystem controller: aiming at the attitude angle subsystem, a novel auxiliary signal is designed to compensate the finite time compensation of the influence on the filtering signal of the virtual angular velocity control law; designing a virtual angular velocity control law based on the auxiliary signals and the attitude angle expected command to ensure the finite time stable tracking control of the attitude angle expected command;
and in the third part, the angular speed subsystem controller is designed as follows: aiming at an angular velocity subsystem, in order to solve multiplicative fault influence of an actuator, an intermediate variable is introduced to design a controller, an additive fault is processed through a self-adaptive law, the upper limit of the fault is estimated, multiplicative and additive fault influence is processed in a limited time, and a self-adaptive limited-time fault-tolerant controller is designed to ensure the limited-time fault-tolerant control of a spacecraft system after the fault occurs.
3. The method for fault-tolerant control of a complex spacecraft taking into account measurement errors and synthetic faults as claimed in claim 1, characterized by the detailed steps of:
firstly, establishing a spacecraft orientation control model, describing a spacecraft attitude kinematics and dynamics model under the influence of flexible vibration and liquid shaking based on a spacecraft kinematics model described by improved Rockwell parameters (MRPs), and comprising the following steps of:
wherein p ═ p1 p2 p3]TFor MRPs vectors describing spacecraft attitude, G (p) e R3×3Is shown as
J is moment of inertia, ω ═ ω1 ω2 ω3]TIs the angular velocity of the spacecraft, d is unknown external interference, u is control moment, and x belongs to RN,η∈RMRespectively a flexible vibration mode and a liquid shaking mode, wherein N and M are modal orders. Ci,Ki(i ═ f, l) are respectively the compliance matrix and stiffness matrix of the vibration mode and the sway mode, and Cf＝diag(2ξjΛj,j＝1,2,…,N)，
Wherein ΛjIs the natural frequency, xi, of the j-th order flexible vibration modejIs the j-th order damping coefficient. Mη＝diag(m1,m1,…,mM,mM) For shaking the mass matrix of the liquid fuel, miSloshing liquid mass, δ, for an ith order liquid sloshing modefIs a rigid-flexible coupling matrix, deltalIs a rigid-liquid coupling matrix, expressed as:
wherein, biIs the distance between the ith order liquid mode and the mass center
x×Is defined as:
the measurement errors of attitude angle and angular velocity brought by the influence of the external unknown environment and the measurement capability limitation of the star sensor and the gyroscope are considered and expressed as follows:
wherein,
as a measure of attitude angle and angular velocity, v1,v2The measurement errors of the attitude angle and the angular velocity are respectively.
The derivation of formula (5) and substitution of formula (1) can be obtained:
wherein,
defining a desired coordinate system FDRelative to the earth's inertial frame FILower spacecraft desired attitude angle pr＝[pr1 pr2pr3]TDesired angular velocity is ωr＝[ωr1 ωr2 ωr3]T. The expected attitude angle and the angular velocity satisfy:
to achieve efficient tracking of the desired attitude, the spacecraft desired coordinate system FDWith body coordinate system FBThe attitude angle error and the angular velocity error between the two are as follows:
wherein,
is FDTo FBThus, the spacecraft attitude angle and angular velocity tracking error is dynamically represented as:
wherein,
multiplicative faults and additive faults are mathematically represented as follows:
ui＝ρiτi+fi (10)
wherein, tauiI is 1,2,3 is the desired control torque, uiControl moment, p, actually applied to the system by the actuatoriSatisfies rho of 0 & lt for the efficiency factor of the actuatoriLess than or equal to 1. Of note is ρi1 represents that the actuator works normally, and 0 < rhoi< 1 indicates that the actuator partially failed, but is still functional. f. ofiTo implement drift failure, it is bounded.
Substituting the actuator fault model (10) into the spacecraft attitude tracking error dynamics (9) to obtain:
where ρ ═ diag (ρ)1,ρ2,ρ3),f＝[f1,f2,f3]T. Equation (11) is the established control-oriented model, and the controller design will be performed based on this model:
unknown uncertainty delta in a system (11)1,δ2Is bounded, but the upper bound is unknown, satisfying:
wherein λ1,λ2Is an unknown normal number, and defines an unknown variable λ ═ max (λ)1,λ2)；
The control targets are as follows: based on a spacecraft kinematics and dynamics model (11) under the influence of sensor measurement errors and actuator faults, a self-adaptive fault-tolerant controller tau is designed, the measurement errors and multiplicative and additive faults of the actuator are effectively processed, and the finite-time rapid and stable tracking control of expected attitude instructions is guaranteed;
and secondly, designing an attitude angle subsystem controller, aiming at the attitude angle subsystem:
by varying the angular velocity omegaeDesigning a virtual control input omega as a control quantitydRealizing the attitude angle tracking error peThe finite time of (c) converges. For ease of writing, new variables are defined:
wherein z is1In order to be an attitude angle tracking error,
inputting omega for virtual controldOutputting after filtering;
substituting the formula (13) into the attitude angle subsystem (12) to obtain
To compensate for command filtering errors
Designing the auxiliary signal xi as follows41：
Wherein k is1>0，l1>0，ξ2Defined by formula (22), the term G (p)e)ξ2For stability certification needs; for controller design, the following coordinate transformations are defined:
v1＝z1-ξ1,v2＝z2-ξ2 (16)
for v1Performing derivation and substituting the formula (14) to the formula (16)
Angular velocity virtual control input omegadThe design is as follows:
wherein, c1＞0,0＜m＜1,
a1＞0，
For handling unknown interference delta1、δ2Designing by using the adaptation shown in formula (26);
thirdly, designing an angular velocity subsystem controller, and inputting virtual control of the attitude angle subsystem
When the command is taken as an expected command of an angular velocity subsystem, the design of a self-adaptive controller is completed based on the attitude angular velocity, and an actual control moment tau is obtained;
for the angular velocity subsystem:
based on the angular velocity tracking error definition (13) and equation (19), the angular velocity tracking error dynamics is obtained as:
based on v2And an angular velocity tracking error dynamics (20) to obtain:
wherein,
as with the attitude angle subsystem, an auxiliary signal xi is designed2Comprises the following steps:
wherein k is2＞0,l2＞0。
Accounting for actuator multiplicative failure ρiAnd additive fault fi(i ═ 1,2,3) is bounded, and for subsequent processing of fault effects, the following new variables are defined:
wherein,
and
are all unknown parameters, will subsequently utilize the adaptive law
And
carrying out estimation;
design of intermediate variables for controller design, solving multiplicative fault
Comprises the following steps:
wherein k is2＞0,c2＞0,κ＞0,
a2> 0 is a normal number.
And
designed by an adaptive law and respectively used for processing unknown interference deltaiAnd drift fault fi。
Adaptive parameters
And
the design is as follows:
wherein gamma is more than 0, r is more than 0, gamma is more than 0, sigma1,σ2,σ3＞0。
The true attitude controller τ is designed to:
based on the three steps, the whole fault-tolerant control process of the finite-time attitude of the spacecraft is completed.
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| CN116382084A (en) * | 2023-04-04 | 2023-07-04 | 天津大学 | Helicopter intelligent vibration reduction method based on self-adaptive dynamic programming |
| CN116923730A (en) * | 2023-07-24 | 2023-10-24 | 哈尔滨工业大学 | Spacecraft attitude active fault-tolerant control method with self-adjusting preset performance constraint |
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN116382084A (en) * | 2023-04-04 | 2023-07-04 | 天津大学 | Helicopter intelligent vibration reduction method based on self-adaptive dynamic programming |
| CN116382084B (en) * | 2023-04-04 | 2023-12-05 | 天津大学 | Helicopter intelligent vibration reduction method based on self-adaptive dynamic programming |
| CN116923730A (en) * | 2023-07-24 | 2023-10-24 | 哈尔滨工业大学 | Spacecraft attitude active fault-tolerant control method with self-adjusting preset performance constraint |
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