CN117008460A - Saturated system autonomous reconstruction method based on normal and fault integrated design - Google Patents
Saturated system autonomous reconstruction method based on normal and fault integrated design Download PDFInfo
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- CN117008460A CN117008460A CN202310762776.6A CN202310762776A CN117008460A CN 117008460 A CN117008460 A CN 117008460A CN 202310762776 A CN202310762776 A CN 202310762776A CN 117008460 A CN117008460 A CN 117008460A
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- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
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Abstract
A saturation system autonomous reconstruction method based on normal and fault integrated design includes the steps of firstly, establishing a state space model of a spacecraft control system and designing a state feedback control law; then, linearizing the nonlinear effects of actuator saturation by placing the saturation feedback control law in a set of convex hulls that assist in the nonlinear control law; secondly, establishing a mapping relation between faults and fault system parameters, deducing a sufficient system reconfigurability condition and calculating the reconfigurability of the system in different modes; and then, optimizing the resource allocation parameters such as the number of system components, the installation configuration and the like and a control algorithm based on the integrated design of the normal mode and the fault mode to obtain a resource allocation scheme and a control scheme which can achieve both nominal performance and reconfigurability. The invention considers the saturation of the actuator in the reconfigurability research for the first time, gives out the reconfigurability judging conditions of the package and the system, and quantifies the reconfigurability.
Description
Technical Field
The invention relates to a saturated system autonomous reconstruction method based on normal and fault integrated design, and belongs to the technical field of overall design of spacecrafts.
Background
The space environment where the spacecraft is located is very severe, and solar activity, tiny meteorons, space garbage and the like can bring great potential safety hazards and even fatal injuries to the spacecraft. Because of the high manufacturing cost and heavy burden of the spacecraft, even minor faults of local links can bring about huge economic losses or disasters. Therefore, the system reconstruction capability, i.e. the reconfigurability, of the spacecraft under the fault must be improved, and the safe, reliable and autonomous operation of the spacecraft is realized.
In the development process of the existing spacecraft, normal mode and fault mode are generally performed by fracturing, namely, a nominal system is designed first, then a system reconstruction scheme under fault is injected into the designed system, the former focuses on the improvement of the nominal performance of the system (namely, the system performance under the condition of no fault), and the latter focuses on the improvement of the system reconfigurability. In the case of severely limited resources, this design approach may suffer from the problem of "losing each other" by either sacrificing too much of the reconfigurability of the system in order to increase its nominal performance, or unduly compromising its nominal performance in order to increase its reconfigurability, resulting in an overstocked design. Therefore, the integrated design of the normal mode and the fault mode of the spacecraft is needed, the nominal performance and the reconfigurability of the system are scientifically balanced, so that the distribution efficiency of the limited resources is improved, the comprehensive performance of the spacecraft in different working modes is effectively improved, and the problem that the limited resources are lost in consideration of each other in the development process of the spacecraft is solved.
The existing reconfigurability research does not consider the saturation influence of an actuator, but a spacecraft is limited by physical self in the actual control process and can only provide limited force, moment, voltage, current and the like, so that the phenomenon of the actuator saturation is frequently generated, the phenomenon is a strong nonlinear phenomenon, the complexity of system evaluation and design is greatly increased, the system can lose the regulation effect due to abnormal locking of control output, the dynamic performance of the system is reduced, and the stability of the system is influenced. Therefore, in the actual reconstruction process of the failed spacecraft, the problem of saturation of the control input of the actuator may greatly weaken the reconstruction performance of the system, so that the system which can reach global progressive stability originally can only be locally progressive stable, and under the condition of serious failure, the instability phenomenon may occur, so that the reconstruction task fails, and even serious safety accidents and disasters are caused. Although the saturation of the actuator can be avoided by reducing the control gain and the like so as not to cause the performance degradation or instability of the system, the processing mode often cannot fully utilize the control capacity of the system, and a series of problems such as the slow response, the reduced performance, the increased cost and the like of the system are further caused. Therefore, in designing the integration of the normal mode and the failure mode of the spacecraft, it is necessary to consider the effect of the saturation of the actuators.
Disclosure of Invention
The invention aims to solve the technical problems that: the method overcomes the defects of the prior art, and provides an autonomous reconstruction method of a saturated system based on normal and fault integrated design, which can give consideration to the nominal performance of the system without faults and the diagnosis reconstruction performance after the faults under the limited resources.
The invention aims at realizing the following technical scheme: a saturation system autonomous reconstruction method based on normal and fault integrated design comprises the following steps:
establishing a state space of a spacecraft control system by using spacecraft design parameters, and determining a constraint range of a system state x;
based on the obtained system state space, a state feedback control gain K is designed to obtain a control law u=Kx;
considering the saturation condition of the obtained control law, linearizing the nonlinear influence of the saturation of the actuator by placing the saturation feedback control law in a set of convex hulls of the auxiliary linear control law;
determining failure θ s Lower actuator selection matrix Σ s Build up of faults theta s And the mapping relation between system parameters after failure;
for failure theta s Performance evaluation J by the following System s Determining the target requirement of system reconstruction as J s η, wherein η is a specified performance threshold;
on the basis of estimating the performance boundary of the fault system by utilizing the linear control law convex hull, deducing the sufficient reconfigurability condition to judge that the system is in fault theta s Whether the target requirement of reconstruction is met or not, namely whether the target is reconfigurable or not;
based on the Schur's complement theorem, converting the reconfigurability sufficient condition into a linear matrix inequality form which is easy to solve;
calculating optimal performance boundaries of the system in different modes by using the reconfigurable conditions in the form of linear matrix inequality;
considering the reconfigurability constraint, namely carrying out the integrated design of a normal mode and a fault mode, and optimizing the number of system components, the installation configuration and other resource configuration parameters to obtain a resource configuration scheme capable of considering the nominal performance and the reconfigurability;
based on the optimized resource allocation scheme, updating system parameters, and further optimally designing a system control scheme to obtain a bottom-up expandable controller with both nominal performance and reconfigurability
The method for establishing a state space of a spacecraft control system by utilizing spacecraft design parameters and determining a constraint range of a system state x comprises the following steps:
establishing a state space (A, B, C, D, E) of a spacecraft control system by using spacecraft design parameters, determining a constraint range x epsilon omega (P, 1) of a system state x,
wherein,moment of inertia i=diag [ I ] x I y I z ]＝diag[86.24 85.07 113.59]kg·m 2 Track angular velocity omega o ＝0.001rad/s，For controlling the moment distribution matrix, the state constraint range parameter of the system is P=25I depending on the installation angle of the actuator 6×6 。
Considering the saturation of the resulting control law, linearizing the nonlinear effects of actuator saturation by placing the saturation feedback control law in a set of convex hulls that assist the linear control law, comprising:
for a system with M actuators, a diagonal matrix M with elements 0 or 1 is taken i ,i＝1,2,...,2 m And calculates identity matrices I and M i Is the difference of (2)Considering the saturation of the resulting control law, by placing the saturation feedback control law sat (u) in the convex hull +.>In linearizing the nonlinear effects of actuator saturation.
The determination of the fault theta s Lower actuator selection matrix Σ s Build up of faults theta s And a mapping relationship between system parameters after a failure, comprising:
determining failure θ s Lower actuator selection matrix Σ s The element related to the healthy actuator in the matrix is 1, the element related to the fault actuator is 0, and the fault theta is established s And mapping relation between system parameters after failure: θ s →(A,B s ,C,D s E), wherein B s ＝BΣ s ,D s ＝DΣ s 。
Based on estimating the performance boundary of the fault system by using the linear control law convex hull,deriving sufficient reconfigurability conditions to determine that the system is at fault θ s Whether the target requirements for reconstruction are met, namely whether the target requirements for reconstruction are met or not, comprising:
for failure θ s The following system, if matrix K, H, positive numbers are presentSum-plus-definite matrixSatisfy the following requirements
(a)
(b)
(c)
(d)
Wherein He [ X ]]＝X+X T ，Q＝C T C，The system is at fault theta s The lower is reconfigurable.
The method for converting the reconfigurability sufficient condition into a linear matrix inequality form which is easy to solve based on the Schur's supplementary rule comprises the following steps:
for failure θ s The following system, if there is a positive numberMatrix->Positive definite matrixAnd V s Satisfy the following requirements
(a)
(b)
(c)
(d1)
(d2)trace(V s )≤η
The system is at fault theta s The lower reconfigurable;
the control moment distribution matrix U is expressed as a function of the flywheel mounting angle:
using the reconfigurability condition in the form of a linear matrix inequality, an optimal performance boundary for the system in different modes is calculated, comprising:
obtaining optimal nominal performance of LMI tool box computing system under different modes based on optimal performance boundary of LMI tool box computing system by utilizing reconfigurable condition in form of linear matrix inequalityAnd the reconfigurable degree size in different faults +.>
(a)
(b)
(c)
Compared with the prior art, the invention has the following beneficial effects:
(1) The method provided by the invention provides an integrated design method of a normal mode and various fault modes of the system, realizes efficient overall allocation of limited resources in different modes, balances nominal performance in the normal mode and reconfigurability in the fault mode, and ensures that the system has good performance in different modes;
(2) According to the method, the saturation of the actuator is considered in the reconfigurable design for the first time, and the nonlinear influence of the saturation of the actuator is linearized by placing the saturation feedback control law in a convex hull of a group of auxiliary linear control laws; based on the above, a reconfigurability judgment condition in the form of a linear matrix inequality is deduced, and the reconfigurability of a fault system is quantified;
(3) The method of the invention provides the controller with the bottom-up expandability, under the action of the controller, the system configuration corresponding to the most serious fault and the upper layer expansion configuration thereof can be reconfigured, and the difficulty of the on-orbit reconfiguration of the spacecraft can be reduced.
Drawings
FIG. 1 is a flow chart of the method of the present invention.
Detailed Description
As shown in fig. 1, the process of the present invention is as follows:
(1) Establishing a state space (A, B, C, D, E) of a spacecraft control system by using spacecraft design parameters, determining a constraint range x epsilon omega (P, 1) of a system state x,
wherein,moment of inertia i=diag [ I ] x I y I z ]＝diag[86.24 85.07 113.59]kg·m 2 Track angular velocity omega o ＝0.001rad/s，For controlling the moment distribution matrix, the state constraint range parameter of the system is P=25I depending on the installation angle of the actuator 6×6 。
(2) Based on the system state space obtained in step (1), the state feedback control gain K is designed to obtain a control law u=kx.
(3) For a system with M actuators, a diagonal matrix M with elements 0 or 1 is taken i ,i＝1,2,...,2 m And calculates identity matrices I and M i Is the difference of (2)Considering the saturation condition of the control law obtained in the step (2), by placing the saturation feedback control law sat (u) in a set of convex hulls of the auxiliary linear control law Hx>In linearizing the nonlinear effects of actuator saturation.
(4) Determining failure θ s Lower actuator selection matrix Σ s The element related to the healthy actuator in the matrix is 1, the element related to the fault actuator is 0, and the fault theta is established s And mapping relation between system parameters after failure: θ s →(A,B s ,C,D s E), wherein B s ＝BΣ s ,D s ＝DΣ s 。
(5) For the fault theta in the step (4) s The following system performs performance evaluation by using the transfer function of the fault systemH of (2) 2 Norms as a function of the performance of the system, i.e.>Determining the target requirement of system reconstruction as J s And +.eta, wherein eta is a specified performance threshold.
(6) On the basis of estimating the performance boundary of the fault system by utilizing the linear control law convex hull in the step (3), deducing the following sufficient reconfigurability condition, and judging that the system is in fault theta s Whether the following meets the reconstruction target requirement in step (5), namely whether the reconstruction is possible:
for failure θ s The following system, if matrix K, H, positive numbers are presentSum-plus-definite matrixSatisfy the following requirements
(a)
(b)
(c)
(d)
Wherein He [ X ]]＝X+X T ，Q＝C T C,The system is at fault theta s The lower is reconfigurable.
(7) Based on Schur's complement theorem, the reconfigurability sufficiency condition in step (6) is converted into a linear matrix inequality form that is easy to solve:
for failure θ s The following system, if there is a positive numberMatrix->Positive definite matrixAnd V s Satisfy the following requirements
(a)
(b)
(c)
(d1)
(d2)trace(V s )≤η
The system is at fault theta s The lower is reconfigurable.
The control moment distribution matrix U is expressed as a function of the flywheel mounting angle:
analysis of the system at different installation angles using the above-described reconfigurability criteria may find: only when the elevation angle of the flywheel meets beta epsilon (23 degrees and 75 degrees), the system has reconfigurability under the fault of a heavy actuator; because of symmetry, azimuth has little effect on system reconfigurability.
(8) Obtaining the optimal nominal performance of the LMI toolbox computing system under different modes based on the optimal performance boundary of the LMI toolbox computing system by utilizing the reconfigurable condition in the form of the linear matrix inequality in the step (7)And the reconfigurable degree size in different faults +.>
(a)
(b)
(c)
(d1)
(d2)trace(V s )≤η
(9) The reconfigurability constraint is further considered on the basis of the method for calculating the optimal nominal performance in the step (8), namely the normal mode and the fault mode are integrally designed, and the system nominal performance J in the normal mode is calculated 0 As an optimization target, taking a system reconfigurability condition (7) under a fault mode set required to be processed as a constraint, optimizing the number of system components, the installation configuration and other resource configuration parameters can be found by optimizing the installation configuration of the flywheel: when the elevation angle beta of the flywheel * When the system is=56.8°, the nominal performance can be optimized on the basis of ensuring the fault reconfigurability of the single actuator of the system, so that a resource allocation scheme which can achieve both the nominal performance and the reconfigurability is obtained.
(10) Updating system parameters A, B, C, D and E based on the optimized resource allocation scheme in the step (9), and using the system nominal performance J in the normal mode 0 As an optimization target, taking a system reconfigurability condition (7) under a fault mode set required to be processed as a constraint, and optimally designing a system control scheme to obtain a bottom-up extensible controller capable of considering nominal performance and reconfigurability
In summary, through the above embodiment, the feasibility and effectiveness of the saturated system autonomous reconstruction method based on the normal and fault integrated design provided by the invention are verified.
The method provides an integrated design method of a normal mode and various fault modes of the system, realizes high-efficiency overall allocation of limited resources in different modes, balances nominal performance in the normal mode and reconfigurability in the fault mode, ensures that the system has good performance in different modes and is protected;
according to the method, the saturation of the actuator is considered in the reconfigurable design for the first time, and the nonlinear influence of the saturation of the actuator is linearized by placing the saturation feedback control law in a convex hull of a group of auxiliary linear control laws; based on the above, the reconfigurability judgment condition in the form of linear matrix inequality is deduced, and the reconfigurability of the fault system is quantified and protected;
the method of the invention provides a controller with bottom-up expandability, under the action of the controller, the system configuration corresponding to the most serious fault and the upper layer expansion configuration thereof can be reconfigured, thereby reducing the difficulty of the reconstruction of the spacecraft on the rail and protecting the spacecraft.
Claims (7)
1. The utility model provides a saturation system autonomous reconfiguration method based on normal and trouble integrated design which characterized in that includes:
establishing a state space of a spacecraft control system by using spacecraft design parameters, and determining a constraint range of a system state x;
based on the obtained system state space, a state feedback control gain K is designed to obtain a control law u=Kx;
considering the saturation condition of the obtained control law, linearizing the nonlinear influence of the saturation of the actuator by placing the saturation feedback control law in a set of convex hulls of the auxiliary linear control law;
determining failure θ s Lower actuator selection matrix Σ s Build up of faults theta s And the mapping relation between system parameters after failure;
for failure theta s Performance evaluation J by the following System s Determining the target requirement of system reconstruction as J s η, wherein η is a specified performance threshold;
on the basis of estimating the performance boundary of the fault system by utilizing the linear control law convex hull, deducing the sufficient reconfigurability condition to judge that the system is in fault theta s Whether the target requirement of reconstruction is met or not, namely whether the target is reconfigurable or not;
based on the Schur's complement theorem, converting the reconfigurability sufficient condition into a linear matrix inequality form which is easy to solve;
calculating optimal performance boundaries of the system in different modes by using the reconfigurable conditions in the form of linear matrix inequality;
considering the reconfigurability constraint, namely carrying out the integrated design of a normal mode and a fault mode, and optimizing the number of system components, the installation configuration and other resource configuration parameters to obtain a resource configuration scheme capable of considering the nominal performance and the reconfigurability;
based on the optimized resource allocation scheme, updating system parameters, and further optimally designing a system control scheme to obtain the bottom-up expandable controller with both nominal performance and reconfigurability.
2. The method for autonomous reconfiguration of a saturation system based on integrated design of normal and fault as claimed in claim 1, wherein the establishing a state space of a spacecraft control system using spacecraft design parameters, determining a constraint range of a system state x, includes:
establishing a state space (A, B, C, D, E) of a spacecraft control system by using spacecraft design parameters, determining a constraint range x epsilon omega (P, 1) of a system state x,
C＝[I 6×6 0] T ,
wherein,moment of inertia i=diag [ I ] x I y I z ]＝diag[86.24 85.07 113.59]kg·m 2 Track angular velocity omega o ＝0.001rad/s，For controlling the moment distribution matrix, the state constraint range parameter of the system is P=25I depending on the installation angle of the actuator 6×6 。
3. The method for autonomous reconfiguration of a saturation system based on an integrated design of normal and fault according to claim 2, wherein linearizing the nonlinear effects of actuator saturation by placing a saturation feedback control law in a convex hull of a set of auxiliary linear control laws, taking into account the saturation conditions of the resulting control laws, comprises:
for a system with M actuators, a diagonal matrix M with elements 0 or 1 is taken i ,i＝1,2,...,2 m And calculates identity matrices I and M i Is the difference of (2)Considering the saturation of the resulting control law, by placing the saturation feedback control law sat (u) in the convex hull +.>In linearizing the nonlinear effects of actuator saturation.
4. A saturated system autonomous reconstruction method based on a normal and fault integrated design as recited in claim 3, wherein said determining a fault θ s Lower actuator selection matrix Σ s Build up of faults theta s And a mapping relationship between system parameters after a failure, comprising:
determining failure θ s Lower actuator selection matrix Σ s The moment ofThe element related to the healthy actuator in the array is 1, the element related to the fault actuator is 0, and a fault theta is established s And mapping relation between system parameters after failure: θ s →(A,B s ,C,D s E), wherein B s ＝BΣ s ,D s ＝DΣ s 。
5. The method for autonomous reconfiguration of a saturated system based on an integrated design with both normal and fault as claimed in claim 4, wherein the reconfigurability sufficiency condition is derived based on estimating the performance boundary of the faulty system using the linear control law convex hull to determine that the system is at fault θ s Whether the target requirements for reconstruction are met, namely whether the target requirements for reconstruction are met or not, comprising:
for failure θ s The following system, if matrix K, H, positive numbers are presentSum-plus-definite matrixSatisfy the following requirements
(a)
(b)
(c)
(d)
Wherein He [ X ]]＝X+X T ，Q＝C T C,The system is at fault theta s The lower is reconfigurable.
6. The method for autonomous reconfiguration of a saturated system based on an integrated design of normal and fault according to claim 5, wherein the transformation of the reconfigurability sufficiency condition into a form of a linear matrix inequality that is easy to solve based on Schur's complement theorem includes:
for failure θ s The following system, if there is a positive numberMatrix->Positive definite matrix +.>And V s Satisfy the following requirements
(a)
(b)
(c)
(d1)
(d2)trace(V s )≤η
The system is malfunctioningθ s The lower reconfigurable;
the control moment distribution matrix U is expressed as a function of the flywheel mounting angle:
7. the method for autonomous reconfiguration of a saturated system based on an integrated design of normal and fault of claim 6, wherein calculating the optimal performance boundaries for the system in different modes using the reconfigurability condition in the form of a linear matrix inequality includes:
obtaining optimal nominal performance of LMI tool box computing system under different modes based on optimal performance boundary of LMI tool box computing system by utilizing reconfigurable condition in form of linear matrix inequalityAnd the reconfigurable degree size in different faults +.>
(a)
(b)
(c)
(d1)
(d2)trace(V s )≤η。
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