CN111169666B - Method for determining reconfigurable envelope of limited system capable of recovering state domain - Google Patents

Method for determining reconfigurable envelope of limited system capable of recovering state domain Download PDF

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CN111169666B
CN111169666B CN202010059763.9A CN202010059763A CN111169666B CN 111169666 B CN111169666 B CN 111169666B CN 202010059763 A CN202010059763 A CN 202010059763A CN 111169666 B CN111169666 B CN 111169666B
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reconfigurable
envelope
spacecraft
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王大轶
屠园园
李文博
刘成瑞
张香燕
赵小宇
林海淼
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Beijing Institute of Spacecraft System Engineering
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Abstract

A method for determining a reconfigurable envelope of a limited system capable of recovering a state domain belongs to the technical field of space. According to the invention, through theoretical analysis and simulation verification, the maximum reconfigurable envelope of the spacecraft system can be given under the constraint conditions of time and energy, the quantitative analysis of reconfigurability of the limited system is realized, and the method can be used for optimizing the configuration and fault-tolerant control algorithm of the spacecraft system, realizing the on-orbit monitoring of the health state of the spacecraft system and the autonomous processing of faults, and improving the autonomous reconfiguration capability of the spacecraft system. Compared with the prior art, the method has the advantages of high precision, small calculated amount, easy realization and the like, and has enough flexibility and applicability in practical application.

Description

Method for determining reconfigurable envelope of limited system capable of recovering state domain
Technical Field
The invention relates to a method for determining a reconfigurable envelope of a limited system capable of recovering a state domain, belonging to the technical field of space.
Background
The maximum reconstruction potential that a spacecraft has with limited resources is a matter of great concern to the engineer. In actual operation, the spacecraft is subject to multiple constraints, most typically energy and time constraints. Because the power generation capacity and the propellant carrying capacity of the solar sailboard are severely limited, the energy consumption constraint is a key factor influencing the reconfigurability of the spacecraft system. In addition, many specific tasks need to be completed within a specified time, and after a system failure, in order to continue to complete such a given task, system reconfiguration must be performed within a certain time window, and the smaller this window is, the smaller the time redundancy of the system is, the greater the corresponding reconfiguration difficulty is, so the system is subject to corresponding time constraints. Therefore, to describe the actual reconfiguration capability of a system, the practical constraint problems such as resource configuration, security time and the like need to be comprehensively considered.
At present, the most common reconfigurable envelope determination method based on the controllable gray matrix mainly has the following two defects: 1) the influence of energy constraint on system reconfigurability is only considered in the form of constant threshold, and other limit constraints such as time and the like are not considered comprehensively; 2) the Lyapunov equation needs to be solved in the calculation process of the reconfigurable envelope, the singularity problem exists, the calculation amount is large, and the on-track implementation is difficult. In view of this, the method has important practical engineering significance for researching the determination problem of the reconfigurable envelope on the basis of the recoverable state domain for typical limited systems such as spacecrafts.
Disclosure of Invention
The technical problem solved by the invention is as follows: the method for determining the reconfigurable envelope of the limited system with the recoverable state domain overcomes the defects of the prior art, can provide the maximum reconfigurable envelope of typical limited systems such as a spacecraft under the constraint of comprehensively considering time and energy, and meanwhile solves the reconfigurable envelope of the spacecraft system by using a fine integration algorithm, and has the advantages of high precision, small calculation amount, easiness in implementation and the like. The reconfigurable envelope of the spacecraft system determined by the invention can be directly used for optimizing the configuration and fault-tolerant control algorithm of the spacecraft system, realizing the on-orbit monitoring of the health state of the spacecraft system and the autonomous processing of faults, improving the autonomous reconfiguration capability of the spacecraft system, and being popularized and applied to other complex large-scale industrial systems such as industrial control, flight control, electric power equipment and the like.
The technical solution of the invention is as follows: a method for determining a reconfigurable envelope of a restricted system with a recoverable state field comprises the following steps:
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 tmisA 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.
Further, the state space model is
Figure BDA0002374069280000021
Figure BDA0002374069280000022
Figure BDA0002374069280000023
Cn＝I6×6(ii) a Wherein, Ix,Iy,IzIs the three-axis moment of inertia of the spacecraft system; x is formed by Rn、u∈RmAnd y ∈ RqRespectively 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, tfTime of occurrence of a failure, tmisA 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,...,θmIs the failure factor matrix of the hardware equipment in the system, thetai∈[0,1],i＝1,2,...,m；03×3、I3×3And I6×6Respectively a 3-order zero matrix, a 3-order identity matrix and a 6-order identity matrix; omegaoIs the orbital angular velocity of the spacecraft.
Further, the spacecraft recoverable minimum state envelope is (P)0,E0)＝{x∈Rn:xTP0x≤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.
Further, the system reconfigurability envelope obtained in S3 is (P (t)f),E*)＝{x∈Rn:xTP(tf)x≤E*}; wherein, P (t)f) For the moment of failure tfA weight coefficient matrix of the reconfigurable envelope of the time system; e*Representing the upper limit of available resources for the spacecraft system.
Further, the method for determining whether the system is reconfigurable is as follows:
if it is
Figure BDA0002374069280000031
Namely, it is
Figure BDA0002374069280000032
Positive determination, the system can be reconstructed; otherwise, it is not reconstructable.
Further, the reconfigurable degree is
Figure BDA0002374069280000033
Wherein the content of the first and second substances,
Figure BDA0002374069280000034
λmin＝min{λ1,λ2,...,λn}，λmax＝max{λ1,λ2,...,λn}，λi(i-1, …, n) is P (t)f) The ith characteristic value of (1).
Compared with the prior art, the invention has the advantages that:
(1) the invention provides a novel reconfigurable envelope determining method based on a recoverable state domain, aiming at the defects that the traditional reconfigurable envelope determining method cannot reflect the reasonability of the distribution of the reconfigurable potential, cannot directly compare different systems and the like, the reconfigurable envelope determining method can more pertinently, scientifically and reasonably guide the optimization of the reconfigurable envelope of the system by analyzing the recoverable state domain of the system in a certain time and energy, considering the distribution condition of the reconfigurable potential in each direction and the satisfaction degree of expected requirements and adding the maximum and minimum half-axis deviation terms of the recoverable state domain, coordinate identity and other technical means.
(2) Aiming at the defect that the traditional solving algorithm has singularities, the invention adopts the fine integral algorithm to carry out numerical solving on the reconfigurable envelope parameters of the system, can obtain the computer 'accurate solution' of the reconfigurable envelope, and has the advantages of small calculation amount, easy realization and the like.
(3) The invention can not only guide the optimization design of the system configuration from the perspective of improving the autonomous reconfiguration capability of the spacecraft system in the design stage, but also realize the online performance evaluation and the health state monitoring of the spacecraft system in the operation stage, thereby comprehensively and deeply excavating the autonomous fault processing potential of the system, further effectively improving the autonomous capability of the spacecraft system, and providing technical reserve for the deepening demonstration of subsequent deep space exploration tasks such as mars, asteroid and the like.
Detailed Description
The invention will be further explained and illustrated with reference to specific embodiments.
A method for determining a reconfigurable envelope of a restricted system with a recoverable state field comprises the following steps:
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 tmisA 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.
The method comprises the following specific steps:
firstly, establishing a spacecraft system state space model with limited energy and time under the condition of spacecraft actuating mechanism failure fault:
Figure BDA0002374069280000051
Figure BDA0002374069280000052
Figure BDA0002374069280000053
Cn＝I6×6；
wherein, Ix,Iy,IzIs the three-axis moment of inertia of the spacecraft system; x is formed by Rn、u∈RmAnd y ∈ RqRespectively 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, tfTime of occurrence of a failure, tmisA 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,...,θmIs the failure factor matrix of the hardware equipment in the system, thetai∈[0,1],i＝1,2,...,m；03×3、I3×3And I6×6Respectively a 3-order zero matrix, a 3-order identity matrix and a 6-order identity matrix; omegaoIs the orbital angular velocity of the spacecraft.
E(tf,tmis) For spacecraft systems throughout the fault phase tf～tmisControlling energy consumption:
Figure BDA0002374069280000054
wherein R is a positive definite symmetric matrix.
Setting a recoverable minimum state envelope of the spacecraft based on a state space model, task requirements and safety requirements:
the recoverable minimum state envelope of the spacecraft is in the following specific form:
Figure BDA0002374069280000055
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; e0Representing the set original system energy threshold.
Determining given energy E by solving a differential Lyapunov equation based on a state space model, task requirements and safety requirements*With time constraint tmisThe reconfigurable envelope of the following system:
according to the system parameters and the fault parameters, solving the following matrix differential equation:
Figure BDA0002374069280000061
P(tmis)＝∞
wherein, Bf＝BuΛ。
Specifically, the matrix differential equation can be solved by using a fine integration algorithm, and the method specifically comprises the following steps:
given A, D ═ PBfR-1Bf TP and step τ, taking N as 20 and τ/2N；
② calculating G (), F' (), and storing Gc,Fc'：
G()＝g1+g2 2+g3 3+g4 4，F'()＝f1+f2 2+f3 3+f4 4
Wherein:
g1＝D,f1＝-AT,g2＝(f1 Tg1+g1f1)/2,f2＝f1 2/2,
g3＝(f2 Tg1+g1f2+f1 Tg1f1)/3,f3＝f1f2/3,
g4＝(f3 Tg1+g1f3+f1 Tg1f2+f2 Tg1f1)/4,f4＝f1f3/4
③ calculating G (tau), F (tau) and transmitting G1,G2,F1,F2：
{For i＝1:N，G1＝G2＝Gc,F1'＝F2'＝Fc'，Gc＝G1+(I+F1')TG2(I+F1')，Fc'＝F1'+F2'+F2'F1'}，Fc＝(I+Fc') to obtain G (tau) ═ Gc,F(τ)＝Fc；
Calculating P (t)
{For k＝tmis/τ：1,Gc＝G1+F1 TG2F1，Fc＝F2F1For k station, save current Gc,FcG (t), F (t), calculating P-1(t)＝G(t)+FT(t)P-1(tmis) F (t), (t ═ k τ), in k stations, G2＝Gc,F2＝Fc,G1,F1Remain unchanged }.
In calculating P (t)f) Then, the system is determined to be in the specified energy consumption E*At the next specified time tmisThe reconfigurable envelope in the following specific form:
(P(tf),E*)＝{x∈Rn:xTP(tf)x≤E*}
wherein, P (t)f) To failTime tfA weight coefficient matrix of the reconfigurable envelope of the time system; e*Representing the upper limit of available resources for the spacecraft system.
Fourthly, judging whether the system is reconfigurable or not by comparing the system reconfigurable envelope obtained in the third step with the minimum state envelope set in the second step; if the system can not be reconstructed, ending; if the system is reconfigurable, entering the step five:
the conditions for determining the reconfigurability of the system are as follows:
if it is
Figure BDA0002374069280000071
Namely, it is
Figure BDA0002374069280000072
If the timing is not positive, the system can not be reconstructed, and the operation is finished;
if it is
Figure BDA0002374069280000073
Namely, it is
Figure BDA0002374069280000074
When the time is positive, the system can be reconstructed, in this case, the size of the system reconfigurability is further quantized, and the step five is entered.
Fifthly, calculating the reconfigurable degree of the spacecraft system based on the gain coefficient matrix in the system reconfigurable envelope obtained in the step three:
firstly, calculating the radii of an inscribed circle and an circumscribed circle of the reconfigurable envelope of the spacecraft system:
Figure BDA0002374069280000075
wherein λ ismin＝min{λ1,λ2,...,λn}，λmax＝max{λ1,λ2,...,λn}，λi(i-1, …, n) is P (t)f) The ith characteristic value of (1).
On the basis, a specific calculation formula of the reconfigurable degree of the spacecraft system is as follows:
Figure BDA0002374069280000076
wherein the content of the first and second substances,
Figure BDA0002374069280000077
the invention discloses a reconfigurable envelope (reconfigurable degree) of a restricted system obtained based on a recoverable state field, which can be used as a quantization target and directly used for optimizing spacecraft system configuration and fault-tolerant control algorithm, thereby realizing on-orbit monitoring of the health state of a spacecraft system and autonomous processing of faults.
In order to verify the effectiveness of the reconfigurable envelope determination method provided by the patent of the invention, a spacecraft control system with a four-oblique momentum wheel configuration is taken as an example below, and compared with the traditional reconfigurable envelope determination method based on the energy control gray matrix.
The parameters of the relevant spacecraft control system are shown in table 1.
TABLE 1 spacecraft control System and orbital parameters thereof
Figure BDA0002374069280000081
Setting the reconfigurable envelope of the system to (P)01); wherein, P0100 diag (111111); through the steps, the reconfigurable degree of the system can be obtained as follows: DOR 0.05778.
In conclusion, the feasibility and the effectiveness of the limited system reconfigurable envelope determining method based on the recoverable state domain provided by the invention are verified through simulation analysis.
Those skilled in the art will appreciate that those matters not described in detail in the present specification are well known 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 tmisA 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
Figure FDA0002374069270000011
Figure FDA0002374069270000012
Figure FDA0002374069270000013
Cn＝I6×6(ii) a Wherein, Ix,Iy,IzIs the three-axis moment of inertia of the spacecraft system; x is formed by Rn、u∈RmAnd y ∈ RqRespectively 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, tfFor the occurrence of a faultTime of day tmisA 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,...,θmIs the failure factor matrix of the hardware equipment in the system, thetai∈[0,1],i＝1,2,...,m；03×3、I3×3And I6×6Respectively a 3-order zero matrix, a 3-order identity matrix and a 6-order identity matrix; omegaoIs 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:xTP0x≤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:xTP(tf)x≤E*}; wherein, P (t)f) For the moment of failure tfA 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
Figure FDA0002374069270000021
Namely, it is
Figure FDA0002374069270000022
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
Figure FDA0002374069270000023
Wherein the content of the first and second substances,
Figure FDA0002374069270000024
λmin＝min{λ1,λ2,...,λn}，λmax＝max{λ1,λ2,...,λn}，λi(i-1, …, n) is P (t)f) The ith characteristic value of (1).
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