CN113778047A - Complex spacecraft fault-tolerant control method considering measurement errors and comprehensive faults - Google Patents

Abstract

The invention relates to spacecraft fault diagnosis and fault-tolerant control, and aims to solve the problem of limited-time attitude fault-tolerant control of spacecraft under the influence of comprehensive faults. The present invention provides a complex spacecraft fault-tolerant control method considering measurement errors and comprehensive faults. First, considering the comprehensive influence of actuator multiplication faults, additive faults and attitude measurement errors, a dynamic model of spacecraft attitude tracking error is established, which is divided into Attitude angle subsystem and angular velocity subsystem; secondly, for the attitude angle and angular velocity subsystems, a finite-time adaptive multi-variable command filtering backstep fault-tolerant control strategy is proposed to realize finite-time filtering error compensation; intermediate variables are introduced to design the controller, and the An adaptive law is designed to achieve finite-time estimation and compensation of the upper bound of the fault, so as to solve the comprehensive fault impact. In addition, an adaptive law is designed for the unknown disturbance in the two subsystems, which is convenient for parameter adjustment. Mainly used in spacecraft fault diagnosis and fault-tolerant control occasions.

Description

A fault-tolerant control method for complex spacecraft considering measurement errors and comprehensive faults

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. Specifically, it involves a complex spacecraft fault-tolerant control method considering measurement errors and comprehensive faults.

Background technique

As one of the fastest-growing cutting-edge technologies in today's science and technology, aerospace technology is playing an increasingly important role in the military field, such as global surveillance and strike, military satellite communication services, space execution for reconnaissance and detection, and destruction of military satellite space base etc. After the satellite completes the network, it runs all day long. Due to the harsh and unknown space environment and the aging of the components on the satellite, it is inevitable that failure will occur. In the wartime state, it will lead to the loss of ground combat information, which will seriously affect the progress of the battlefield. The "TOPEX/Poseidon" ocean exploration satellite launched in 2005 by the United States and France ended its life due to the failure of the pitch reaction wheel used to maintain the orbital pointing on the satellite. The U.S. military once pointed out that the sky and the sea are the battlefields of the 20th century, and space will become the battlefield of the 21st century and the strategic commanding heights of modern warfare. In recent years, my country's aerospace industry has made brilliant achievements. The "Shenzhou" manned spacecraft, the "Chang'e-1" project, and the "Beidou" navigation system indicate that my country has made great achievements in space exploration. With the increasing complexity of space missions, higher requirements are placed on the reliability of spacecraft such as rockets and satellites. Therefore, to carry out research on spacecraft fault diagnosis and fault-tolerant control technology, to explore the feasibility of related methods in spacecraft fault diagnosis, to ensure the safe and reliable operation of spacecraft, to reduce the workload of ground staff and the cost of launch and operation, and to promote aerospace The healthy development of career has very important theoretical and practical significance.

However, due to the complex and unknown operating environment of the spacecraft, and with the increasing complexity of missions and star structures, the effects of model uncertainty are becoming more and more obvious. The spacecraft fault diagnosis and fault-tolerant control under the influence of interference and uncertainty It has always been the focus and difficult problem of aerospace research. At present, the observer-based fault diagnosis and fault-tolerant control method is the most widely used. By establishing the residual sequence, a fault detection mechanism is established to achieve the purpose of fault detection. However, the deficiencies in satellite fault diagnosis and fault-tolerant control design based on the existing theoretical methods are mainly reflected in the following aspects: (1) Most researchers mainly focus on multiplicative or additive faults, while in In practical engineering, these two kinds of faults will occur at the same time, and there are few studies on the finite-time fault-tolerant control of spacecraft under the influence of comprehensive faults; (2) In order to solve the problem of faults under the influence of interference, the existing methods mainly use complex coordinate transformation to Interference and fault decoupling, or the use of unknown input shapers, all require complex calculations, which are difficult to meet practical engineering problems with limited on-board computing resources, and cannot achieve limited time control; (3) Affected by complex external environment interference and Due to the limitation of Xingmin's own ability, it is difficult to achieve accurate measurement of attitude and angular velocity, and there will always be certain measurement errors, which will affect the control accuracy of the system. Therefore, how to comprehensively consider the influence of measurement error, multiplicative and additive faults, effectively deal with the fault under the influence of interference, and realize the limited-time fault-tolerant control of the spacecraft is a key problem that needs to be solved urgently. Critical theoretical significance and engineering value.

In view of the above limitations, in the research of the present invention, the influence of actuator multiplication and additive comprehensive faults on the safe flight of the spacecraft is comprehensively considered, and the fault-tolerant control strategy of the spacecraft is studied, and the split-loop control idea is adopted to divide the spacecraft system into attitude angles. The system and the angular velocity subsystem are designed with adaptive controllers respectively, and the finite-time estimation and compensation of the fault upper bound are realized through the adaptive law design, and the stability of the overall closed-loop system is proved to ensure the finite-time attitude tracking control of the spacecraft. And the effectiveness of the designed fault-tolerant control strategy is verified by simulation.

SUMMARY OF THE INVENTION

In order to overcome the deficiencies of the prior art, the present invention aims to propose a method to solve the problem of limited-time attitude fault-tolerant control of spacecraft under the influence of comprehensive faults. On the one hand, due to the complexity of the spacecraft mission and its nonlinear characteristics, the difficulty and complexity of its fault diagnosis have increased significantly. On the other hand, satellites are affected by various perturbations of the space environment and various external disturbances such as high temperature, low temperature, electromagnetic interference, space particle radiation, etc., which increase the complexity of satellite fault diagnosis. The traditional fault diagnosis seldom comprehensively considers the influence of space disturbance torque and comprehensive faults, and it is difficult to realize the limited-time fault-tolerant control of spacecraft. Based on this, the present invention proposes a complex spacecraft fault-tolerant control method that considers measurement errors and comprehensive faults. First, considering the comprehensive effects of actuator multiplication faults, additive faults and attitude measurement errors, a dynamic model of spacecraft attitude tracking error is established. And it is divided into attitude angle subsystem and angular velocity subsystem; secondly, for the attitude angle and angular velocity subsystems, a finite-time adaptive multi-variable command filtering backstep fault-tolerant control strategy is proposed to realize the finite-time filtering error compensation; intermediate variables are introduced for the controller Design and design an adaptive law to achieve finite-time estimation and compensation of the fault upper bound to solve the comprehensive fault impact; in addition, an adaptive law is designed for unknown disturbances in the two subsystems to facilitate parameter adjustment.

The effectiveness of the present invention is verified by MATLAB/Simulink simulation.

Specific steps are as follows:

The first part, the establishment of spacecraft-oriented control model: analyze the influence of multiplicative and additive comprehensive faults and measurement errors of spacecraft actuators, and establish complex spacecraft under the influence of external interference and comprehensive faults based on spacecraft kinematics and dynamic models The nonlinear tracking error kinematics and dynamics model of ;

The second part, the design of the attitude angle subsystem controller: for the attitude angle subsystem, a new type of auxiliary signal is designed to compensate the limited time compensation for the influence of the virtual angular velocity control law filtering signal; based on the auxiliary signal and the attitude angle expectation command, the virtual angular velocity control is designed law to ensure a limited time stable tracking control for the desired command of the attitude angle;

The third part, the design of the angular velocity subsystem controller: for the angular velocity subsystem, in order to solve the influence of the multiplicative fault of the actuator, an intermediate variable is introduced to design the controller, and the additive fault is handled by the adaptive law, and the upper bound of the fault is estimated by , and deal with the multiplicative and additive fault effects in a limited time, and design an adaptive finite-time fault-tolerant controller to ensure the limited-time fault-tolerant control of the spacecraft system after a fault occurs.

The detailed steps are as follows:

The first step is to establish a spacecraft-oriented control model. Based on the spacecraft kinematics model described by the improved Rodrigue parameters (MRPs), the attitude kinematics and dynamic models of the spacecraft under the influence of flexible vibration and liquid sloshing are described as follows:

J为转动惯量，ω＝[ω₁ ω₂ ω₃]^T为航天器角速度，d为未知外界干扰，u为控制力矩，χ∈R^N,η∈R^M分别为柔性振动模态及液体晃动模态，N,M为模态阶数。C_i,K_i(i＝f,l)分别为振动模态及晃动模态的柔性矩阵及刚度矩阵，且 C_f＝diag(2ξ_jΛ_j,j＝1,2,…,N)，

其中Λ_j为第j阶柔性振动模态的自然频率，ξ_j为第j阶阻尼系数。M_η＝diag(m₁,m₁,…,m_M,m_M)为晃动液体燃料的质量矩阵， m_i为第i阶液体晃动模态的晃动液体质量，δ_f为刚柔耦合矩阵，δ_l为刚液耦合矩阵，表示为：Among them, p=[p ₁ p ₂ p ₃ ] ^T is the MRPs vector describing the attitude of the spacecraft, G(p)∈R ^3×3 , expressed as

J is the moment of inertia, ω=[ω ₁ ω ₂ ω ₃ ] ^T is the angular velocity of the spacecraft, d is the unknown external disturbance, u is the control torque, χ∈R ^N , η∈R ^M are the flexible vibration mode and liquid sloshing, respectively mode, where N and M are the modal order. C _i ,K _i (i=f,l) are the flexibility matrix and stiffness matrix of vibration mode and sway mode respectively, and C _f =diag(2ξ _j Λ _j ,j=1,2,...,N),

where Λ _j is the natural frequency of the j-th flexible vibration mode, and ξ _j is the j-th damping coefficient. M _η =diag(m ₁ ,m ₁ ,...,m _M ,m _M ) is the mass matrix of the sloshing liquid fuel, m _i is the sloshing liquid mass of the _i -th liquid sloshing mode, δf is the rigid-flexible coupling matrix, δ _l is the rigid-liquid coupling matrix, which is expressed as:

x^×定义为：where b _i is the distance between the i-th liquid mode and the centroid, and

x ^× is defined as:

Considering the influence of the unknown external environment and the measurement error of the attitude angle and angular velocity caused by the measurement capability limitation of the star sensor and the gyroscope itself, it is expressed as:

为姿态角及角速度的测量值，v₁,v₂分别为姿态角及角速度的测量误差。in,

are the measured values of attitude angle and angular velocity, v ₁ , v ₂ are the measurement errors of attitude angle and angular velocity, respectively.

Taking the derivative of equation (5) and substituting it into equation (1), we can get:

in,

Defining the desired attitude angle of the desired coordinate system ^FD relative to the earth inertial coordinate system _FI is _{pr =[pr1 pr2 pr3] T, and the desired angular velocity is ω r = [ ω r1 ω r2 ω r3} ] ^T . The desired attitude angle and angular velocity satisfy:

In order to achieve effective tracking of the desired attitude, the attitude angle error and angular velocity error between the desired coordinate system FD of the _spacecraft and the body coordinate system _FB are:

为F_D到F_B的旋转矩阵，因此，航天器姿态角及角速度跟踪误差动态表示为：in,

is the rotation matrix from F _D to F _B. Therefore, the spacecraft attitude angle and angular velocity tracking error are dynamically expressed as:

in,

Multiplicative faults and additive faults are mathematically expressed as follows:

u _i =ρ _i τ _i +f _i (10)

Among them, τ _i , i=1, 2, 3 is the desired control torque, _ui is the control torque that the actuator actually acts on the system, and ρ _i is the actuator efficiency factor, which satisfies 0<ρ _i ≤1. It is worth noting that ρ _i =1 indicates that the actuator works normally, and 0<ρ _i <1 indicates that the actuator partially fails, but it can still work. f _i is the actuator drift fault and is bounded.

Substituting the actuator fault model (10) into the spacecraft attitude tracking error dynamics (9), we can get:

Wherein, ρ=diag(ρ ₁ , ρ ₂ , ρ ₃ ), f=[f ₁ , f ₂ , f ₃ ] ^T . Equation (11) is the established control-oriented model, and the controller will be designed based on this model in the future:

其中λ₁,λ₂为未知正常数，并定义未知变量λ＝max(λ₁,λ₂)；The unknown and uncertain δ ₁ , δ ₂ in system (11) are bounded, but the upper bound is unknown, satisfying:

where λ ₁ , λ ₂ are unknown constants, and define the unknown variable λ=max(λ ₁ ,λ ₂ );

The control objective is to design an adaptive fault-tolerant controller τ based on the kinematics and dynamics model of the spacecraft under the influence of sensor measurement errors and actuator faults (11) to effectively handle measurement errors and actuator multiplicative and additive faults to ensure Limited time fast and stable tracking control for desired attitude commands;

The second step, the controller design of the attitude angle system, for the attitude angle system:

By taking the angular velocity ω _e as a control variable, a virtual control input ω _d is designed to achieve finite-time convergence of the attitude angle tracking error _pe . For writing convenience, define new variables:

为虚拟控制输入ω_d经过滤波后的输出；Among them, z ₁ is the attitude angle tracking error,

is the filtered output of the virtual control input ω _d ;

For the attitude angle system (12), substituting into equation (13) can be obtained

设计如下辅助信号ξ₄₁：To compensate for command filter error

The auxiliary signal ξ ₄₁ is designed as follows:

where k ₁ >0, l ₁ >0, ξ ₂ is defined by equation (22), and the term G( _pe )ξ ₂ is used for stability proof needs; for controller design, the following coordinate transformations are defined:

v ₁ =z ₁ -ξ ₁ , v ₂ =z ₂ -ξ ₂ (16)

Differentiate v ₁ and substitute it into equations (14)-(16) to get

The angular velocity virtual control input ω _d is designed as:

a₁＞0，

用来处理未知干扰δ₁、δ₂，利用式(26) 所示的自适应进行设计；in,

a ₁ > 0,

It is used to deal with the unknown interference δ ₁ , δ ₂ , and is designed using the self-adaptation shown in equation (26);

当作角速度子系统的期望指令，基于姿态角速度完成自适应控制器设计，获得实际的控制力矩τ；The third step, the design of the angular velocity subsystem controller, the virtual control input of the attitude angle subsystem

As the expected command of the angular velocity subsystem, the adaptive controller design is completed based on the attitude angular velocity, and the actual control torque τ 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 are:

Based on the definition of v ₂ (16) and the angular velocity tracking error dynamics (20), we get:

in,

Same as the attitude angle system, the design auxiliary signal ξ ₂ is:

Wherein, k ₂ >0, l ₂ >0.

Considering that the actuator multiplicative fault ρ _i and additive fault f _i (i=1, 2, 3) are bounded, in order to deal with the fault impact later, the following new variables are defined:

均为未知参数，将在后续利用自适应律

及

进行估计；where θ and

are unknown parameters, and the adaptive law will be used in the follow-up

and

make an estimate;

为：For controller design, to solve multiplicative faults, to design intermediate variables

for:

a₂＞0为正常数。

及

通过自适应律进行设计，分别用来处理未知干扰δ_i及漂移故障f_i。in,

a ₂ >0 is a positive number.

and

The adaptive law is designed to deal with unknown disturbance δ _i and drift fault f _i respectively.

及

设计为：adaptive parameters

and

Designed to:

Wherein, γ>0, r>0, Γ>0, σ ₁ , σ ₂ , σ ₃ >0.

The real attitude controller τ is designed as:

Based on the above three steps, the entire spacecraft's limited-time attitude fault-tolerant control process is completed.

The characteristics and beneficial effects of the present invention are:

The designed step-by-step control algorithm can ensure the rapid convergence of the desired attitude angle, and the convergence and control accuracy are high; the state of the auxiliary system will change continuously to compensate the estimation error caused by the filter in the controller design and ensure the control accuracy; Adjust the control algorithm to actively suppress the flexible vibration and liquid sloshing to zero.

Description of drawings:

Figure 1. The structure diagram of the spacecraft fault-tolerant control under the influence of the comprehensive fault of the actuator.

Fig. 2 Attitude angle tracking error curve.

Fig. 3 Attitude angular velocity tracking error curve diagram.

Figure 4 is a graph of virtual angular velocity tracking.

Figure 5. The differentiator estimates the virtual angular velocity.

Fig. 6 is a graph of state change of auxiliary system.

Figure 7 Control input graph.

Fig. 8 is a graph of adaptive parameter change.

Fig. 9 Variation curve diagram of liquid sloshing mode.

Figure 10. Curve diagram of flexible vibration mode change.

Detailed ways

The invention relates to the technical field of fault-tolerant control of spacecraft. Specifically, an adaptive finite-time fault-tolerant controller synthesis algorithm is firstly proposed, and then the effectiveness of the proposed algorithm is verified by MATLAB/Simulink simulation.

The purpose of the present invention is to propose a method to solve the problem of limited-time attitude fault-tolerant control of spacecraft under the influence of comprehensive faults. On the one hand, due to the complexity of the spacecraft mission and its nonlinear characteristics, the difficulty and complexity of its fault diagnosis have increased significantly. On the other hand, satellites are affected by various perturbations of the space environment and various external disturbances such as high temperature, low temperature, electromagnetic interference, space particle radiation, etc., which increase the complexity of satellite fault diagnosis. The traditional fault diagnosis seldom comprehensively considers the influence of space disturbance torque and comprehensive faults, and it is difficult to realize the limited-time fault-tolerant control of spacecraft. Based on this, the present invention proposes a finite-time fault-tolerant control method for spacecraft based on adaptive finite-time command filtering backstepping. The dynamic model of attitude tracking error of the controller is divided into attitude angle subsystem and angular velocity subsystem. Secondly, for the attitude angle and angular velocity subsystems, a finite-time adaptive multi-variable command filtering backstep fault-tolerant control strategy is proposed. Compared with backstepping control, this method can realize finite-time filtering error compensation through improved auxiliary signal design. The finite-time estimation and compensation of the bounded time limit can effectively solve the comprehensive fault impact; in addition, for the unknown interference in the two subsystems, different from the traditional estimation using two observers or adaptive laws respectively, the present invention only designs one adaptive law , which is convenient for parameter adjustment, and is more suitable for engineering practice. Finally, MATLAB/Simulink simulation is used to verify the effectiveness of the present invention. The adaptive finite-time command filtering backstep fault-tolerant control method proposed by the invention can effectively solve the combined effects of multiplicative faults and additive faults of the actuator, and the designed new auxiliary signal can compensate the filtering error in a limited time, and realize complex spacecraft. The limited time fault-tolerant control of attitude can effectively improve the reliability and safety of spacecraft operation.

The overall technical scheme of the spacecraft fault-tolerant control algorithm under the influence of the comprehensive fault of the actuator proposed by the present invention is shown in Figure 1. The whole system includes three parts: the establishment of the spacecraft-oriented control model, the design of the attitude angle subsystem controller, and the control design of the angular velocity subsystem. , the specific technical solutions are as follows:

The first part, the establishment of spacecraft-oriented control model: analyze the influence of multiplicative and additive comprehensive faults and measurement errors of spacecraft actuators, and establish complex spacecraft under the influence of external interference and comprehensive faults based on spacecraft kinematics and dynamic models The nonlinear tracking error kinematics and dynamics model.

The second part, the design of the attitude angle subsystem controller: for the attitude angle subsystem, a new type of auxiliary signal is designed to compensate the limited time compensation for the influence of the virtual angular velocity control law filtering signal; based on the auxiliary signal and the attitude angle expectation command, the virtual angular velocity control is designed law to ensure a limited time stable tracking control for the desired command of the attitude angle;

The third part, the design of the angular velocity subsystem controller: for the angular velocity subsystem, in order to solve the influence of the multiplicative fault of the actuator, intermediate variables are introduced to design the controller. Estimation, this method estimates the fault upper bound, deals with the multiplicative and additive fault effects in a limited time, and designs an adaptive finite-time fault-tolerant controller to ensure the finite-time fault-tolerant control of the spacecraft system after a fault occurs, which is different from the traditional method. In the present invention, two observers or adaptive laws are used to estimate the unknown interference in the two subsystems respectively. The present invention only designs one adaptive law, which is convenient for parameter adjustment and is more suitable for engineering practice.

Finally, in order to verify the validity of the algorithm proposed by the present invention, a MATLAB/Simulink simulation system for spacecraft attitude fault-tolerant control is built to verify the validity of the algorithm proposed by the present invention.

In order to verify the validity of the finite-time fault-tolerant control algorithm proposed by the present invention, the spacecraft attitude control system is firstly designed in Matlba/Simulink, and a simulation experiment is carried out. The main simulation process is as follows:

(1) Parameter setting

1) Spacecraft physical parameter setting: During the simulation process, the initial attitude value of the spacecraft is set to p(0)=[-0.2 0.20.4] ^T , and the initial angular velocity is set to ω(0)=[0 0 0] ^T rad/ s, the desired attitude value is set to p _r =[0.3sin(t/10)0.4sin(t/20)0.3cos(t/10)] ^T , the moment of inertia of the spacecraft is

Considering that the first few-order flexible vibration modes and liquid sloshing modes have the greatest impact on the spacecraft, with the increase of the order, the influence gradually decreases. Therefore, in the present invention, the first three-order vibration modes and the fourth-order sloshing are considered. modal. Among them, the rigid-flexible coupling matrix is

The natural frequencies of the vibration modes of each order are respectively set as: Λ ₁ =0.7681rad/s, Λ ₂ =1.1038rad/s, Λ ₃ =1.8733rad/s, the damping of each order is ξ ₁ =0.0056,ξ ₂ = 0.0086, ξ ₃ =0.013.

The damping matrix of the first four-order liquid sloshing mode is C _l =diag(3.334,3.334,0.237,0.237), the stiffness matrix is K _l =diag(55.21,55.21,7.27,7.27), and the sloshing liquid mass is m ₁ =20kg , m ₂ =0.8kg, b ₁ =1.127m, b ₂ =0.994m.

The unknown disturbance is d=0.01[sin(t/10), cos(t/15), sin(t/20)] ^T Nm.

The magnitude of the multiplicative time-varying fault value is set as:

ρ ₄₁ =0.7+0.1sin(0.1t+π/3)+0.1sin(mod(t,30)-15)

ρ ₄₂ =0.6+0.1sin(0.1t+2π/3)+0.1sin(mod(t,40)-25)

ρ ₄₃ =0.7-0.1sin(0.1t+π)+0.1sin(mod(t,50)-25)

The additive time-varying fault value size is set as:

f ₁ =0.005+0.02sin(0.2t),f ₂ =-0.02sin(0.2t+π/3),

f ₃ =-0.005+0.01sin(0.15t+π)

The adaptive and controller parameters are set as γ=5, r=10, κ=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: γ=5, r=10, κ=0.001, Γ=2, σ=5, σ ₁ =10, σ ₂ =1, σ ₃ =0.2, k ₄₁ = 1, _k42 =0.02, c1 ₌ 0.2, c2=0.02, a1= ₁ , a2= ₁ , m= ₁₁ /13.

(2) Analysis of results

In order to illustrate the effectiveness of this method, relevant simulations will be carried out as follows:

对虚拟参考指令的估计值

的有效跟踪，而估计值

又可以通过有限时间微分器实现对虚拟参考指令ω_d的有效估计，如图5所示，可以看出，

可以在2s之内实现对ω_d的估计。The simulation results are shown in Figure 2-Figure 10. Among them, Figure 2 is an attitude angle tracking error curve. It can be seen from the simulation diagram that the designed step-by-step control algorithm can ensure the rapid convergence of the desired attitude angle. Even in the presence of attitude measurement errors and actuator faults, the attitude angle can be converged within about 5s, and the tracking The precision is on the order of 10 ^-3 . Figure 3 shows the change curve of the attitude angular velocity tracking error. It can also be seen from the simulation diagram that the attitude angular velocity can achieve convergence in about 5s, but the convergence accuracy is not as high as that of the attitude angle, because the controller first acts on the attitude The angular velocity system is then acted on by the attitude angular velocity to ensure the convergence of the attitude angle. The control amount of the attitude angle system is smoother than that of the attitude angle system, so the convergence accuracy is higher. FIG. 4 is a graph of virtual angular velocity tracking. It can be seen from the simulation diagram that the actual angular velocity can basically be achieved

Estimated value of virtual reference command

effective tracking of , while the estimated value

The effective estimation of the virtual reference instruction ω _d can also be realized by the finite-time differentiator, as shown in Figure 5, it can be seen that,

The estimation of ω _d can be achieved within 2s.

Further, in order to compensate the error brought by the differentiator estimation, the auxiliary system state ξ _1i plays a role, as shown in Fig. 6, in order to observe the change of ξ _1i more clearly, only the change graph within 5s is placed in Fig. 6. Since the estimation of the virtual reference command ω _d is realized within 2s in Fig. 5, it can be seen from the simulation Fig. 6 that the state of the auxiliary system will change continuously before estimating ω _d to compensate the filtering in the controller design The estimation error brought by the controller ensures the control accuracy. When the estimation of ω _d is realized, the auxiliary system state ξ _1i will no longer play a role, and will converge in a finite time with an order of magnitude of 10 ^-5 , so as to reduce the impact on the system control accuracy.

变化曲线图，从仿真图中可以看出，自适应参数不断波动，以保证系统的控制性能。图9及图10分别为液体晃动模态及柔性振动模态变化曲线图，从图中可以看出，柔性振动及液体晃动强度均会不断衰减，其产生的影响通过自适应律进行处理，但可以看出柔性振动及液体晃动并未完全抑制，仍然会对控制性能产生一定影响，而通过调整控制算法，将柔性振动及液体晃动主动抑制到零，提高控制精度也将是将来的工作重点。Figure 7 is a graph of the control input change. Initially, to ensure the rapid convergence of the state, the control input value is large, but it satisfies the constraints. Due to the influence of high-frequency fluctuations such as measurement error and swaying vibration, it can be seen from the figure that the control input exists. some volatility. Figure 8 shows the adaptive parameters

It can be seen from the simulation diagram that the adaptive parameters fluctuate constantly to ensure the control performance of the system. Figure 9 and Figure 10 are the change curves of the liquid sloshing mode and the flexible vibration mode, respectively. It can be seen from the figures that the flexible vibration and the liquid sloshing intensity will be attenuated continuously. It can be seen that the flexible vibration and liquid sloshing are not completely suppressed, and will still have a certain impact on the control performance. By adjusting the control algorithm, the flexible vibration and liquid sloshing are actively suppressed to zero, and the improvement of control accuracy will also be the focus of future work.

The invention takes the finite-time instruction filtering backstepping design theory as the main research method, and proposes a spacecraft attitude fault-tolerant control algorithm under the influence of comprehensive faults. The specific implementation process is as follows.

In the first step, the spacecraft-oriented control model is established. Based on the spacecraft kinematics model described by improved Rodrigue parameters (MRPs), the attitude kinematics and dynamic models of the spacecraft under the influence of flexible vibration and liquid sloshing are described as follows:

J为转动惯量，ω＝[ω₁ ω₂ ω₃]^T为航天器角速度，d为未知外界干扰，u为控制力矩，χ∈R^N,η∈R^M分别为柔性振动模态及液体晃动模态，N,M为模态阶数。C_i,K_i(i＝f,l)分别为振动模态及晃动模态的柔性矩阵及刚度矩阵，且 C_f＝diag(2ξ_jΛ_j,j＝1,2,…,N)，

其中Λ_j为第j阶柔性振动模态的自然频率，ξ_j为第j阶阻尼系数。M_η＝diag(m₁,m₁,…,m_M,m_M)为晃动液体燃料的质量矩阵， m_i为第i阶液体晃动模态的晃动液体质量。δ_f为刚柔耦合矩阵，δ_l为刚液耦合矩阵，表示为：Among them, p=[p ₁ p ₂ p ₃ ] ^T is the MRPs vector describing the attitude of the spacecraft, G(p)∈R ^3×3 , expressed as

J is the moment of inertia, ω=[ω ₁ ω ₂ ω ₃ ] ^T is the angular velocity of the spacecraft, d is the unknown external disturbance, u is the control torque, χ∈R ^N , η∈R ^M are the flexible vibration mode and liquid sloshing, respectively mode, where N and M are the modal order. C _i ,K _i (i=f,l) are the flexibility matrix and stiffness matrix of vibration mode and sway mode respectively, and C _f =diag(2ξ _j Λ _j ,j=1,2,...,N),

where Λ _j is the natural frequency of the j-th flexible vibration mode, and ξ _j is the j-th damping coefficient. M _η =diag(m ₁ ,m ₁ ,...,m _M ,m _M ) is the mass matrix of the sloshing liquid fuel, and mi is the sloshing liquid mass of the _i -th liquid sloshing mode. _δf is the rigid-flexible coupling matrix, and _δl is the rigid-liquid coupling matrix, expressed as:

x^×定义为：where b _i is the distance between the i-th liquid mode and the centroid. right

x ^× is defined as:

Considering the influence of the unknown external environment and the measurement error of the attitude angle and angular velocity caused by the measurement capability limitation of the star sensor and the gyroscope itself, it is expressed as:

为姿态角及角速度的测量值，v₁,v₂分别为姿态角及角速度的测量误差。in,

are the measured values of attitude angle and angular velocity, v ₁ , v ₂ are the measurement errors of attitude angle and angular velocity, respectively.

Taking the derivative of equation (5) and substituting it into equation (1), we can get:

in,

Defining the desired attitude angle of the desired coordinate system ^FD relative to the earth inertial coordinate system _FI is _{pr =[pr1 pr2 pr3] T, and the desired angular velocity is ω r = [ ω r1 ω r2 ω r3} ] ^T . The desired attitude angle and angular velocity satisfy:

In order to achieve effective tracking of the desired attitude, the attitude angle error and angular velocity error between the desired coordinate system FD of the _spacecraft and the body coordinate system _FB are:

为F_D到F_B的旋转矩阵。in,

is the rotation matrix from F _D to F _B.

Therefore, the spacecraft attitude angle and angular velocity tracking error are dynamically expressed as:

in,

Further, during the maneuvering process of the spacecraft, due to the influence of the space environment and the aging of the spacecraft components, actuator failures, including multiplicative failures and additive failures, are prone to occur. The mathematical expression is as follows:

u _i =ρ _i τ _i +f _i (10)

Among them, τ _i , i=1, 2, 3 is the desired control torque, _ui is the control torque that the actuator actually acts on the system, and ρ _i is the actuator efficiency factor, which satisfies 0<ρ _i ≤1. It is worth noting that ρ _i =1 indicates that the actuator works normally, and 0<ρ _i <1 indicates that the actuator partially fails, but it can still work. f _i is the actuator drift fault and is bounded.

Substituting the actuator fault model (10) into the spacecraft attitude tracking error dynamics (9), we can get:

Wherein, ρ=diag(ρ ₁ , ρ ₂ , ρ ₃ ), f=[f ₁ , f ₂ , f ₃ ] ^T . Equation (11) is the established control-oriented model, and the controller will be designed based on this model in the future.

其中λ₁,λ₂为未知正常数，并定义未知变量λ＝max(λ₁,λ₂)。Assumption 1: The unknown and uncertain δ ₁ and δ ₂ in the system (11) are bounded, but the upper bound is unknown, satisfying:

Among them, λ ₁ , λ ₂ are unknown constants, and the unknown variable λ=max(λ ₁ , λ ₂ ) is defined.

The control objective of the present invention is to design an adaptive fault-tolerant controller τ based on the kinematics and dynamics model (11) of the spacecraft under the influence of sensor measurement errors and actuator faults, so as to effectively deal with measurement errors and actuator multiplicative and additive properties faults to ensure fast and stable tracking control with limited time for the desired attitude command.

The second step is to design the controller of the attitude angle system. For the attitude angle system:

By taking the angular velocity ω _e as a control variable, a virtual control input ω _d is designed to achieve finite-time convergence of the attitude angle tracking error _pe . For writing convenience, define new variables:

为虚拟控制输入ω_d经过滤波后的输出。Among them, z ₁ is the attitude angle tracking error,

is the filtered output of the virtual control input ω _d .

For the attitude angle system (12), substituting into equation (13) can be obtained

设计如下辅助信号ξ₄₁：To compensate for command filter error

The auxiliary signal ξ ₄₁ is designed as follows:

where k ₁ >0, l ₁ >0, ξ ₂ is defined by equation (22), and the term G( _pe )ξ ₂ is required for stability proof.

For controller design, define the following coordinate transformations:

v ₁ =z ₁ -ξ ₁ , v ₂ =z ₂ -ξ ₂ (16)

Differentiate v ₁ and substitute it into equation (14)-(16) to get

The angular velocity virtual control input ω _d is designed as:

a₁＞0，

用来处理未知干扰δ₁、δ₂，利用式(26) 所示的自适应进行设计。in,

a ₁ > 0,

It is used to deal with unknown interference δ ₁ , δ ₂ , and is designed using the adaptation shown in equation (26).

当作角速度子系统的期望指令，基于姿态角速度完成自适应控制器设计，获得实际的控制力矩τ。The third step is to design the angular velocity subsystem controller. Input the virtual control of the pose angle system

As the expected command of the angular velocity subsystem, the adaptive controller design is completed based on the attitude angular velocity, and the actual control torque τ is obtained.

For the angular velocity subsystem:

Based on the angular velocity tracking error definition (13) and equation (19), the dynamic angular velocity tracking error can be obtained as:

Based on the definition of v ₂ (16) and the angular velocity tracking error dynamics (20), we can get

in,

Same as the attitude angle system, the design auxiliary signal ξ ₂ is:

Wherein, k ₂ >0, l ₂ >0.

Considering that the actuator multiplicative fault ρ _i and additive fault f _i (i=1, 2, 3) are bounded, in order to deal with the fault impact later, the following new variables are defined:

均为未知参数，将在后续利用自适应律

及

进行估计。where θ and

are unknown parameters, and the adaptive law will be used in the follow-up

and

make an estimate.

为：For controller design, to solve multiplicative faults, to design intermediate variables

for:

a₂＞0为正常数。

及

通过自适应律进行设计，分别用来处理未知干扰δ_i及漂移故障f_i。in,

a ₂ >0 is a positive number.

and

The adaptive law is designed to deal with unknown disturbance δ _i and drift fault f _i respectively.

及

设计为：adaptive parameters

and

Designed to:

Wherein, γ>0, r>0, Γ>0, σ ₁ , σ ₂ , σ ₃ >0.

The real attitude controller τ is designed as:

Based on the above three steps, the entire spacecraft's limited-time attitude fault-tolerant control process is completed.

The above are only preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention shall be included in the protection of the present invention. within the range.

Claims (3)

1. A complex spacecraft fault-tolerant control method considering measurement errors and comprehensive faults, characterized in that, firstly, considering the combined effects of actuator multiplication faults, additive faults and attitude measurement errors, establish spacecraft attitude tracking error dynamics The model is divided into attitude angle subsystem and angular velocity subsystem; secondly, for the attitude angle and angular velocity subsystems, a finite-time adaptive multi-variable command filtering backstep fault-tolerant control strategy is proposed to realize the finite-time filtering error compensation; The controller is designed, and an adaptive law is designed to realize the finite-time estimation and compensation of the upper bound of the fault, so as to solve the comprehensive fault impact; in addition, an adaptive law is designed for the unknown disturbance in the two subsystems to facilitate parameter adjustment. 2. the complex spacecraft fault-tolerant control method considering measurement error and comprehensive fault as claimed in claim 1, is characterized in that, concrete steps are as follows: The first part, the establishment of spacecraft-oriented control model: analyze the influence of multiplicative and additive comprehensive faults and measurement errors of spacecraft actuators, and establish complex spacecraft under the influence of external interference and comprehensive faults based on spacecraft kinematics and dynamic models The nonlinear tracking error kinematics and dynamics model of ; The second part, the design of the attitude angle subsystem controller: for the attitude angle subsystem, a new type of auxiliary signal is designed to compensate the limited time compensation for the influence of the virtual angular velocity control law filtering signal; based on the auxiliary signal and the attitude angle expectation command, the virtual angular velocity control is designed law to ensure a limited time stable tracking control for the desired command of the attitude angle; The third part, the design of the angular velocity subsystem controller: for the angular velocity subsystem, in order to solve the influence of the multiplicative fault of the actuator, an intermediate variable is introduced to design the controller, and the additive fault is handled by the adaptive law, and the upper bound of the fault is estimated by , and deal with the multiplicative and additive fault effects in a limited time, and design an adaptive finite-time fault-tolerant controller to ensure the limited-time fault-tolerant control of the spacecraft system after a fault occurs. 3. the complex spacecraft fault-tolerant control method considering measurement error and comprehensive fault as claimed in claim 1, is characterized in that, detailed steps are as follows: The first step is to establish a spacecraft-oriented control model. Based on the spacecraft kinematics model described by the improved Rodrigue parameters (MRPs), the attitude kinematics and dynamic models of the spacecraft under the influence of flexible vibration and liquid sloshing are described as follows:

Among them, p=[p ₁ p ₂ p ₃ ] ^T is the MRPs vector describing the attitude of the spacecraft, G(p)∈R ^3×3 , expressed as

J is the moment of inertia, ω=[ω ₁ ω ₂ ω ₃ ] ^T is the angular velocity of the spacecraft, d is the unknown external disturbance, u is the control torque, χ∈R ^N , η∈R ^M are the flexible vibration mode and liquid sloshing, respectively mode, where N and M are the modal order. C _i ,K _i (i=f,l) are the flexibility matrix and stiffness matrix of vibration mode and sway mode respectively, and C _f =diag(2ξ _j Λ _j ,j=1,2,...,N),

where Λ _j is the natural frequency of the j-th flexible vibration mode, and ξ _j is the j-th damping coefficient. M _η =diag(m ₁ ,m ₁ ,...,m _M ,m _M ) is the mass matrix of the sloshing liquid fuel, m _i is the sloshing liquid mass of the _i -th liquid sloshing mode, δf is the rigid-flexible coupling matrix, δ _l is the rigid-liquid coupling matrix, which is expressed as:

where b _i is the distance between the i-th liquid mode and the centroid, and

x ^× is defined as:

Considering the influence of the unknown external environment and the measurement error of the attitude angle and angular velocity caused by the measurement capability limitation of the star sensor and the gyroscope itself, it is expressed as:

in,

are the measured values of attitude angle and angular velocity, v ₁ , v ₂ are the measurement errors of attitude angle and angular velocity, respectively. Taking the derivative of equation (5) and substituting it into equation (1), we can get:

in,

Define the desired attitude angle of the desired coordinate system FD relative to the Earth's inertial coordinate system _FI as _{pr =[pr r1 pr r2 pr r3 ] T , and the desired angular velocity as ω r = [} ^ω _{r1 ω r2 ω r3 ]} ^T . The desired attitude angle and angular velocity satisfy:

In order to achieve effective tracking of the desired attitude, the attitude angle error and angular velocity error between the desired coordinate system FD of the _spacecraft and the body coordinate system _FB are:

in,

is the rotation matrix from F _D to F _B. Therefore, the spacecraft attitude angle and angular velocity tracking error are dynamically expressed as:

in,

Multiplicative faults and additive faults are mathematically expressed as follows: u _i =ρ _i τ _i +f _i (10) Among them, τ _i , i=1, 2, 3 is the desired control torque, _ui is the control torque that the actuator actually acts on the system, and ρ _i is the actuator efficiency factor, which satisfies 0<ρ _i ≤1. It is worth noting that ρ _i =1 indicates that the actuator works normally, and 0<ρ _i <1 indicates that the actuator partially fails, but it can still work. f _i is the actuator drift fault and is bounded. Substituting the actuator fault model (10) into the spacecraft attitude tracking error dynamics (9), we can get:

Wherein, ρ=diag(ρ ₁ , ρ ₂ , ρ ₃ ), f=[f ₁ , f ₂ , f ₃ ] ^T . Equation (11) is the established control-oriented model, and the controller will be designed based on this model in the future: The unknown and uncertain δ ₁ , δ ₂ in system (11) are bounded, but the upper bound is unknown, satisfying:

where λ ₁ , λ ₂ are unknown constants, and define the unknown variable λ=max(λ ₁ ,λ ₂ ); The control objective is to design an adaptive fault-tolerant controller τ based on the kinematics and dynamics model of the spacecraft under the influence of sensor measurement errors and actuator faults (11) to effectively handle measurement errors and actuator multiplicative and additive faults to ensure Limited time fast and stable tracking control for desired attitude commands; The second step, the controller design of the attitude angle system, for the attitude angle system:

By taking the angular velocity ω _e as a control variable, a virtual control input ω _d is designed to achieve finite-time convergence of the attitude angle tracking error _pe . For writing convenience, define new variables:

Among them, z ₁ is the attitude angle tracking error,

is the filtered output of the virtual control input ω _d ; For the attitude angle system (12), substituting into equation (13) can be obtained

To compensate for command filter error

The auxiliary signal ξ ₄₁ is designed as follows:

where k ₁ >0, l ₁ >0, ξ ₂ is defined by equation (22), the term G( _pe )ξ ₂ is used for stability proof needs; for controller design, the following coordinate transformations are defined: v ₁ =z ₁ -ξ ₁ , v ₂ =z ₂ -ξ ₂ (16) Differentiate v ₁ and substitute it into equations (14)-(16) to get

The angular velocity virtual control input ω _d is designed as:

Among them, c ₁ >0, 0<m<1,

a ₁ > 0,

It is used to deal with unknown interference δ ₁ , δ ₂ , and is designed using the self-adaptation shown in formula (26); The third step, the design of the angular velocity subsystem controller, the virtual control input of the attitude angle subsystem

As the expected command of the angular velocity subsystem, the adaptive controller design is completed based on the attitude angular velocity, and the actual control torque τ 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 are:

Based on the definition of v ₂ (16) and the angular velocity tracking error dynamics (20), we get:

in,

Same as the attitude angle system, the design auxiliary signal ξ ₂ is:

Wherein, k ₂ >0, l ₂ >0. Considering that the actuator multiplicative fault ρ _i and additive fault f _i (i=1, 2, 3) are bounded, in order to deal with the fault effects later, the following new variables are defined:

in,

and

are unknown parameters, and the adaptive law will be used in the follow-up

and

make an estimate; For controller design, to solve multiplicative faults, to design intermediate variables

for:

Among them, k ₂ >0, c ₂ >0, κ >0,

a ₂ >0 is a positive number.

and

The adaptive law is designed to deal with unknown disturbance δ _i and drift fault f _i respectively. adaptive parameters

and

Designed to:

Wherein, γ>0, r>0, Γ>0, σ ₁ , σ ₂ , σ ₃ >0. The real attitude controller τ is designed as:

Based on the above three steps, the entire spacecraft's limited-time attitude fault-tolerant control process is completed.

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