CN111169666B - A Reconfigurability Envelope Determination Method for Restricted Systems in Recoverable State Domain - Google Patents

Abstract

A method for determining the reconfigurability envelope of a constrained system in a recoverable state domain belongs to the field of space technology. Through theoretical analysis and simulation verification, the invention can give the maximum reconfigurability envelope of the spacecraft system under the constraints of time and energy, realize quantitative analysis of the reconfigurability of the restricted system, and can be used for optimization The spacecraft system configuration and fault-tolerant control algorithm realize on-orbit monitoring of the spacecraft system health status and autonomous processing of faults, and improve the autonomous reconfiguration capability of the spacecraft system. Compared with the existing method, the patent of the present invention uses the fine integration algorithm to solve the reconfigurability envelope of the spacecraft system, which has the advantages of high precision, small calculation amount, easy implementation, etc., and has sufficient flexibility and practical application. applicability.

Description

A Recoverable State Domain Reconfigurable Envelope Determination Method for Restricted Systems

technical field

The invention relates to a method for determining the reconfigurability envelope of a constrained system in a recoverable state domain, and belongs to the field of space technology.

Background technique

The maximum reconfiguration potential of spacecraft with limited resources is a problem that engineers and technicians are very concerned about. In the actual operation process, the spacecraft is affected by multiple constraints, the most representative of which are energy and time constraints. Since the power generation capacity and propellant carrying capacity of solar panels are severely limited, energy consumption constraints are a key factor affecting the reconfigurability of spacecraft systems. In addition, many specific tasks need to be completed within a specified time. After a system failure, in order to continue to complete such established tasks, the system must be reconfigured within a certain time window. The smaller the window, the more time redundancy of the system. The smaller the value, the greater the corresponding reconstruction difficulty, so the system is subject to the corresponding time constraints. It can be seen that to describe the actual reconfiguration capability of a system, it is necessary to comprehensively consider practical constraints such as resource allocation and security time.

At present, the most common method for determining the reconfigurability envelope based on the controllable Gramma matrix has the following two deficiencies: 1) The influence of the energy constraint on the reconfigurability of the system is only considered in the form of a constant threshold, and there is no Other constraints such as time are fully considered; 2) The Lyapunov equation needs to be solved in the process of calculating the reconfigurability envelope, and there is a singularity problem, and the amount of calculation is large, which is difficult to implement on-orbit. In view of this, it is of great practical engineering significance to study the determination of the reconfigurability envelope for typical restricted systems such as spacecraft based on the recoverable state domain.

SUMMARY OF THE INVENTION

The technical problem solved by the invention is: to overcome the deficiencies of the prior art, a method for determining the reconfigurability envelope of a constrained system in a recoverable state domain is proposed, which can give a spacecraft under the constraints of time and energy comprehensively. The maximum reconfigurability envelope of this type of typical restricted system, and at the same time, the precise integration algorithm is used to solve the reconfigurability envelope of the spacecraft system, which has the advantages of high precision, small amount of calculation, and easy implementation. The reconfigurability envelope of the spacecraft system determined by the patent of the present invention can be directly used to optimize the spacecraft system configuration and fault-tolerant control algorithm, realize on-orbit monitoring of the spacecraft system health status and autonomous processing of faults, and improve the spacecraft system It can be applied to other complex industrial control, flight control, power equipment and other large-scale industrial systems.

The technical solution of the present invention is: a method for determining the reconfigurability envelope of a constrained system in a recoverable state domain, comprising the following steps:

S1, establish a state space model of the spacecraft system with limited energy and time under the failure of the spacecraft actuator;

S2, based on the state space model, mission requirements and safety requirements, set the minimum state envelope that the spacecraft can recover;

S3, based on the state space model, task requirements and safety requirements, by solving the differential Lyapunov equation, determine the reconfigurability envelope of the system under the given energy E ^* and time constraint t _mis ;

S4, by comparing the system reconfigurability envelope obtained in S3 with the minimum state envelope set by S2, to determine whether the system can be reconfigured; if the system cannot be reconfigured, end; if the system can be reconfigured, enter S5;

S5, based on the gain coefficient matrix in the system reconfigurability envelope obtained in S3, calculate the reconfigurability of the spacecraft system, optimize the spacecraft system configuration and fault-tolerant control algorithm according to the obtained reconfigurability, and realize the spacecraft system On-orbit monitoring of health status and autonomous handling of faults.

Further, the state space model is

C_n＝I_6×6；其中，I_x,I_y,I_z为航天器系统的三轴转动惯量；x∈Rⁿ、u∈R^m和y∈R^q分别为系统的状态向量、输入向量以及输出向量，n、m、q为正整数，R表示实数域；t为时间，t_f为故障发生时刻，t_mis为实际任务的规定完成时间；α和β为系统中硬件设备的安装角度，Φ(α,β)为力矩分配矩阵，取决于硬件设备的安装构型；Λ＝diag{θ₁,θ₂,...,θ_m}为系统中硬件设备的失效因子矩阵，θ_i∈[0,1],i＝1,2,...,m；0_3×3、I_3×3和I_6×6分别为3阶零矩阵、3阶单位矩阵和6阶单位矩阵；ω_o为航天器的轨道角速度。

C _n =I _6×6 ; among them, I _x , I _y , I _z are the three-axis moment of inertia of the spacecraft system; ^x∈Rn , ^u∈Rm and ^y∈Rq are the state vector, input Vector and output vector, n, m, q are positive integers, R represents the real number domain; t is the time, t _f is the moment when the fault occurs, t _mis is the specified completion time of the actual task; α and β are the installation of hardware devices in the system Angle, Φ(α, β) is the torque distribution matrix, which depends on the installation configuration of the hardware equipment; Λ=diag{θ ₁ , θ ₂ ,...,θ _m } is the failure factor matrix of the hardware equipment in the system, θ _i ∈[0,1], i=1,2,...,m; 0 _3×3 , I _3×3 and I _6×6 are the third-order zero matrix, the third-order unit matrix and the sixth-order unit matrix, respectively ; ω _o is the orbital angular velocity of the spacecraft.

Further, the recoverable minimum state envelope of the spacecraft is ε(P ₀ , E ₀ )={x∈R ⁿ :x ^T P ₀ x≤E ₀ }; wherein, P ₀ is a positive definite symmetric matrix, representing At the initial moment, the system can restore the weight coefficient matrix of the minimum state envelope; E ₀ represents the set system energy threshold.

Further, the system reconfigurability envelope obtained by the S3 is ε(P(t _f ), E ^* )={x∈R ⁿ : xTP(t _f )x≤E ^* }; wherein, P(t _f ) is the weight coefficient matrix of the system reconfigurability envelope at the time of failure t _f ; E ^* represents the upper limit of the available resources of the spacecraft system.

Further, the method for determining whether the system is reconfigurable is:

即

正定，则系统可重构；否则，不可重构。like

which is

If it is positive definite, the system can be reconfigured; otherwise, it cannot be reconfigured.

其中，

λ_min＝min{λ₁,λ₂,...,λ_n}，λ_max＝max{λ₁,λ₂,...,λ_n}，λ_i(i＝1,…,n)为P(t_f)的第i个特征值。Further, the reconfigurability is

in,

λ _min =min{λ ₁ ,λ ₂ ,...,λ _n }, λ _max =max{λ ₁ ,λ ₂ ,...,λ _n }, λ _i (i=1,...,n) is The ith eigenvalue of P(t _f ).

The advantages of the present invention compared with the prior art are:

(1) The patent of the present invention proposes a novel reconfigurability envelope determination method based on the "recoverable state domain". For the traditional reconfigurability determination method, it cannot reflect the rationality of the reconfiguration potential distribution, and cannot The deficiencies in the direct comparison of different systems, etc., by analyzing the "recoverable state domain" of the system within a certain time and energy, considering the distribution of the reconstruction potential in all directions and the degree of satisfaction of the expected requirements, through the additional recoverable state domain. The technical means of restoring the maximum and minimum semi-axis deviation terms of the state domain and coordinate equivalence can guide the optimization of the reconfigurability envelope of the system more pertinently, scientifically and rationally.

(2) In view of the shortcomings of the singularity of the traditional solution algorithm, the patent of the present invention uses the fine integration algorithm to numerically solve the reconfigurability envelope parameters of the system, and the computer "exact solution" of the reconfigurability envelope can be obtained. , and has the advantages of small computational complexity and easy implementation.

(3) The patent of the present invention can not only guide the optimal design of the system configuration configuration from the perspective of improving the autonomous reconfiguration capability of the spacecraft system in the design stage, but also realize the on-line performance evaluation and health status monitoring of the spacecraft system in the operation stage, In this way, the autonomous fault handling potential of the system can be fully and deeply explored, thereby effectively improving the autonomous capability of the spacecraft system, and providing technical reserves for the in-depth demonstration of subsequent deep space exploration missions such as Mars and asteroids.

Detailed ways

The present invention will be further explained and illustrated below in conjunction with specific embodiments.

A method for determining the reconfigurability envelope of a constrained system in a recoverable state domain, comprising the following steps:

S1, establish a state space model of the spacecraft system with limited energy and time under the failure of the spacecraft actuator;

S2, based on the state space model, mission requirements and safety requirements, set the minimum state envelope that the spacecraft can recover;

S3, based on the state space model, task requirements and safety requirements, by solving the differential Lyapunov equation, determine the reconfigurability envelope of the system under the given energy E ^* and time constraint t _mis ;

S4, by comparing the system reconfigurability envelope obtained in S3 with the minimum state envelope set by S2, to determine whether the system can be reconfigured; if the system cannot be reconfigured, end; if the system can be reconfigured, enter S5;

S5, based on the gain coefficient matrix in the system reconfigurability envelope obtained in S3, calculate the reconfigurability of the spacecraft system, optimize the spacecraft system configuration and fault-tolerant control algorithm according to the obtained reconfigurability, and realize the spacecraft system On-orbit monitoring of health status and autonomous handling of faults.

details as follows:

1. Establish a state space model of the spacecraft system with limited energy and time in the event of a spacecraft actuator failure:

C_n＝I_6×6；

C _n =I _6×6 ;

Among them, I _x , I _y , I _z are the three-axis moment of inertia of the spacecraft system; x∈R ⁿ , u∈R ^m and y∈R ^q are the state vector, input vector and output vector of the system, respectively, n, m , q is a positive integer, R represents the real number field; t is the time, t _f is the moment when the fault occurs, t _mis is the specified completion time of the actual task; α and β are the installation angles of the hardware devices in the system, Φ(α, β) is the torque distribution matrix, which depends on the installation configuration of the hardware equipment; Λ=diag{θ ₁ ,θ ₂ ,...,θ _m } is the failure factor matrix of the hardware equipment in the system, θ _i ∈[0,1], i=1,2,...,m; 0 _3×3 , I _3×3 and I _6×6 are the third-order zero matrix, the third-order unit matrix and the sixth-order unit matrix, respectively; ω _o is the orbit of the spacecraft angular velocity.

E(t _f , t _mis ) is the control energy consumption of the spacecraft system in the whole failure stage t _f ~ t _mis :

where R is a positive definite symmetric matrix.

2. Based on the state space model, mission requirements and safety requirements, set the minimum state envelope that the spacecraft can recover:

The minimum state envelope that the spacecraft can recover, the specific form is as follows:

Among them, P ₀ is a positive definite symmetric matrix, which represents the weight coefficient matrix of the minimum state envelope that the system can restore at the initial moment; E ₀ represents the set original system energy threshold.

3. Based on the state space model, task requirements and safety requirements, by solving the differential Lyapunov equation, determine the reconfigurability envelope of the system under the given energy E ^* and time constraint t _mis :

According to the system parameters and fault parameters, the following matrix differential equations are solved:

P(t _mis )=∞

Wherein, B _f =B _u Λ.

Specifically, the precise integration algorithm can be used to solve the above matrix differential equation, and the specific steps are as follows:

① Given A, D=PB _f R ^-1 B _f ^T P and step size τ, take N=20, ε=τ/2 ^N ;

②Calculate G(ε), F'(ε), and save G _c , F _c ':

G(ε)=g ₁ ε+g ₂ ε ² +g ₃ ε ³ +g ₄ ε ⁴ , F'(ε)=f ₁ ε+f ₂ ε ² +f ₃ ε ³ +f ₄ ε ⁴

in:

g ₁ =D,f ₁ =-A ^T ,g ₂ =(f ₁ ^T g ₁ +g ₁ f ₁ )/2,f ₂ =f ₁ ² /2,

g ₃ =(f ₂ ^T g ₁ +g ₁ f ₂ +f ₁ ^T g ₁ f ₁ )/3, f ₃ =f ₁ f ₂ /3,

g ₄ =(f ₃ ^T g ₁ +g ₁ f ₃ +f ₁ ^T g ₁ f ₂ +f ₂ ^T g ₁ f ₁ )/4,f ₄ =f ₁ f ₃ /4

③ Calculate G(τ), F(τ), and save G ₁ , G ₂ , F ₁ , F ₂ :

{For i=1:N, G ₁ =G ₂ =G _c ,F ₁ '=F ₂ '=F _c ',G _c =G ₁ +(I+F ₁ ') ^T G ₂ (I+F ₁ '), F _c '=F ₁ '+F ₂ '+F ₂ 'F ₁ '}, F _c =(I+F _c '), thus G(τ)=G _c , F(τ)= F _c ;

④Calculate P(t)

{For k=t _mis /τ: 1, G _c =G ₁ +F ₁ ^T G ₂ F ₁ , F _c =F ₂ F ₁ , save the current G _c ,F _c for k station, denoted as G(t) ,F(t), calculate P ^-1 (t)=G(t)+FT (t)P ^-1 (t _mis )F( ^t ),(t=kτ), stored in k station, G ₂ = G _c , F ₂ =F _c , G ₁ , F ₁ remain unchanged}.

After calculating P(t _f ), determine the reconfigurability envelope of the system under the specified energy consumption E ^* and within the specified time t _mis . The specific form is as follows:

ε(P(t _f ),E ^* )={x∈R ⁿ :x ^T P(t _f )x≤E ^* }

Among them, P(t _f ) is the weight coefficient matrix of the system reconfigurability envelope at the time of failure t _f ; E ^* represents the upper limit of the available resources of the spacecraft system.

4. Determine whether the system can be reconfigured by comparing the system reconfigurability envelope obtained in step 3 with the minimum state envelope set in step 2; if the system cannot be reconfigured, end; if the system can be reconfigured, enter Step 5:

The criterion for system reconfigurability is:

即

非正定时，则系统不可重构，结束；like

which is

If the timing is not positive, the system cannot be reconfigured and ends;

即

正定时，则系统可重构，在这种情况下，进一步量化系统可重构性的大小，进入步骤五。like

which is

If the timing is positive, the system can be reconfigured. In this case, further quantify the reconfigurability of the system, and go to step five.

5. Calculate the reconfigurability of the spacecraft system based on the gain coefficient matrix in the system reconfigurability envelope obtained in step 3:

First, calculate the radii of the inscribed and circumscribed circles of the spacecraft system reconfigurability envelope:

where λ _min =min{λ ₁ ,λ ₂ ,...,λ _n },λ _max =max{λ ₁ ,λ ₂ ,...,λ _n },λ _i (i=1,...,n ) is the ith eigenvalue of P(t _f ).

On this basis, the specific calculation formula of the reconfigurability of the spacecraft system is given as:

in,

The patent of the present invention is based on the reconfigurability envelope (reconfigurability) of a class of constrained systems obtained from the recoverable state domain, which can be used as a quantitative target to directly optimize the spacecraft system configuration and fault-tolerant control algorithm. On-orbit monitoring of spacecraft system health and autonomous handling of faults.

In order to verify the effectiveness of the reconfigurability envelope determination method proposed in the patent of the present invention, the following takes the spacecraft control system of the four inclined momentum wheel configuration as an example, and the Comparison of envelope determination methods.

The parameters of the relevant spacecraft control system are shown in Table 1.

Table 1 Spacecraft control system and its orbital parameters

Set the reconfigurability envelope of the system as ε(P ₀ ,1); where P ₀ =100·diag(111111); through the above steps, the reconfigurability of the system can be obtained as: DOR=0.05778 .

To sum up, through simulation analysis, the feasibility and effectiveness of a method for determining the reconfigurability envelope of a constrained system based on the recoverable state domain proposed by the present invention is verified.

The content not described in detail in the specification of the present invention belongs to the well-known technology of those skilled in the art.

Claims (6)

1. A method for determining a reconfigurable envelope of a restricted system with a recoverable state domain, comprising the steps of:

s1, establishing a spacecraft system state space model with limited energy and time under the condition of failure and fault of a spacecraft actuating mechanism;

s2, setting a recoverable minimum state envelope of the spacecraft based on the state space model, the task requirements and the safety requirements;

s3, determining given energy E by solving a differential Lyapunov equation based on the state space model, the task demand and the safety requirement^*With time constraint t_misA reconfigurable envelope of the lower system;

s4, judging whether the system is reconfigurable or not by comparing the system reconfigurable envelope obtained in S3 with the minimum state envelope set in S2; if the system can not be reconstructed, ending; if the system is reconfigurable, go to S5;

and S5, calculating the reconfigurable degree of the spacecraft system based on the gain coefficient matrix in the system reconfigurable envelope obtained in S3, optimizing the configuration of the spacecraft system and a fault-tolerant control algorithm according to the obtained reconfigurable degree, and realizing on-orbit monitoring of the health state of the spacecraft system and autonomous processing of faults.

2. The method of claim 1, wherein the state space model is a recoverable state domain constrained system reconfigurable envelope determination method

C_n＝I_6×6(ii) a Wherein, I_x,I_y,I_zIs the three-axis moment of inertia of the spacecraft system; x is formed by Rⁿ、u∈R^mAnd y ∈ R^qRespectively a state vector, an input vector and an output vector of the system, wherein n, m and q are positive integers, and R represents a real number domain; t is time, t_fFor the occurrence of a faultTime of day t_misA specified completion time for the actual task; alpha and beta are installation angles of hardware equipment in the system, and phi (alpha, beta) is a moment distribution matrix and depends on the installation configuration of the hardware equipment; Λ ═ diag { theta ═₁,θ₂,...,θ_mIs the failure factor matrix of the hardware equipment in the system, theta_i∈[0,1],i＝1,2,...,m；0_3×3、I_3×3And I_6×6Respectively a 3-order zero matrix, a 3-order identity matrix and a 6-order identity matrix; omega_oIs the orbital angular velocity of the spacecraft.

3. The method of claim 2, wherein the minimum state envelope recoverable by the spacecraft is (P) and₀,E₀)＝{x∈Rⁿ:x^TP₀x≤E₀}; wherein, P₀The weight coefficient matrix is a positive definite symmetric matrix and represents the recoverable minimum state envelope of the system at the initial moment; e₀Indicating a set system energy threshold.

4. The method for determining the reconfigurable envelope of the limited system with recoverable state domain according to claim 2, wherein the reconfigurable envelope of the system obtained at S3 is (P (t)_f),E^*)＝{x∈Rⁿ:x^TP(t_f)x≤E^*}; wherein, P (t)_f) For the moment of failure t_fA weight coefficient matrix of the reconfigurable envelope of the time system; e^*Representing the upper limit of available resources for the spacecraft system.

5. The method for determining the reconfigurable envelope of the limited system with recoverable state domains as claimed in claim 2, wherein the method for determining whether the system is reconfigurable is as follows:

if it is

Namely, it is

Positive determination, the system can be reconstructed; otherwise, it is not reconstructable.

6. The method of claim 2, wherein the reconfigurability of the constrained system is determined according to a reconfiguration degree of

Wherein,

λ_min＝min{λ₁,λ₂,...,λ_n}，λ_max＝max{λ₁,λ₂,...,λ_n}，λ_i(i-1, …, n) is P (t)_f) The ith characteristic value of (1).