CN111381581A - Integrated method and system for fault diagnosis and fault-tolerant control of execution mechanism - Google Patents

Integrated method and system for fault diagnosis and fault-tolerant control of execution mechanism Download PDF

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CN111381581A
CN111381581A CN202010153200.6A CN202010153200A CN111381581A CN 111381581 A CN111381581 A CN 111381581A CN 202010153200 A CN202010153200 A CN 202010153200A CN 111381581 A CN111381581 A CN 111381581A
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CN111381581B (en
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王淑一
李文博
刘细军
刘文静
武云丽
郭建新
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Beijing Institute of Control Engineering
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    • G05B23/0259—Electric testing or monitoring by means of a monitoring system capable of detecting and responding to faults characterized by the response to fault detection
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Abstract

An integrated method for diagnosing the failure of executing mechanism and controlling the fault tolerance of executing mechanism includes such steps as integrating the effective factor gamma (n) describing the failure mode of executing mechanism with the gain parameter K (n) of controller, and integrating the comprehensive control law
Figure DDA0002403148190000011
The reconstruction problem of (2) is converted into a constraint optimization problem of a bilinear inequality set; then, the constraint optimization problem is rapidly solved to obtain a comprehensive control law
Figure DDA0002403148190000012
Finally, the effective factor gamma (n) is estimated on line by adopting a Kalman filtering algorithm and is passed
Figure DDA0002403148190000013
The required gain parameter k (n) of the fault-tolerant controller is obtained after the fault is generated by the synchronous operation. The method of the invention effectively reduces the influence degree of the fault and reduces the systemThe safety risk of the system ensures that the spacecraft control system can autonomously perform real-time diagnosis and rapid reconstruction on different fault modes of the actuating mechanism, greatly reduces the on-board calculation pressure under the limited resource constraint in the on-orbit operation stage, and enhances the engineering applicability of the method.

Description

Integrated method and system for fault diagnosis and fault-tolerant control of execution mechanism
Technical Field
The invention belongs to the field of space control, and relates to a diagnosis and fault-tolerant control integrated method and system suitable for an executing mechanism in a spacecraft control system after a fault occurs.
Background
Autonomy is an important trend of future spacecraft control towards intelligent development, implementation of autonomous fault diagnosis and fault-tolerant control by an executing mechanism running in orbit is one of key support technologies for developing space intelligent autonomous control, a new way is opened for improving reliability, maintainability and effectiveness of a spacecraft, and the method becomes a research hotspot and a research difficulty in the field of current aerospace.
At present, fault diagnosis technologies applied in on-track and research models mostly use state residuals of a system for diagnosis, the correctness of the fault diagnosis method depends on a set threshold, and the setting of the value is complex, so that the accuracy of fault diagnosis is influenced. In view of this, it is necessary to introduce the idea of fault reconstruction into the research work of spacecraft fault diagnosis technology and to complete the design of fault-tolerant controllers by using reconstructed faults. In the research field, for performance degradation faults of an actuating mechanism, the traditional method is to estimate the faults and then adjust gain parameters of a controller, so that the influence degree of the faults is enlarged, the safety risk of the system is increased, and the real-time diagnosis and the rapid reconstruction of the faults by a spacecraft control system are difficult to ensure.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: the method and the system are suitable for the integrated method and the system for the autonomous diagnosis and the fault-tolerant control after the execution mechanism in the spacecraft control system breaks down, describe the specific fault mode of the execution mechanism by using a fault effective factor, take the fault effective factor and a controller gain parameter as a whole, and carry out rapid estimation and synchronous solution on the fault effective factor and the controller gain parameter by adopting an optimal estimation and regional pole configuration method, realize the integrated collaborative design of the fault diagnosis and the fault-tolerant control, and further ensure the real-time performance and the rapidity of the control system.
The technical scheme adopted by the invention is as follows: an integrated method for fault diagnosis and fault-tolerant control of an execution mechanism comprises the following steps:
(1) the method converts the design problem of the comprehensive control law into the constraint optimization problem of a bilinear inequality set by using a regional pole allocation principle, and comprises the following steps of:
step 1.1: establishing a mathematical model of a spacecraft control system when an actuating mechanism fails, wherein the model is described by adopting a state space model in a discrete time-varying form as follows:
Figure RE-GDA0002488323410000021
wherein, Γ (n) is an effective factor describing a specific failure mode of an actuating mechanism, x (n), u (n) and y (n) are respectively a state variable, an input variable and an output variable of a system, w (n) and v (n) are respectively a process noise variable and a measurement noise variable of the system, A (n), B (n) and C (n) are respectively a dynamic model matrix, an actuating mechanism installation matrix and a sensor installation matrix of the system, and n represents the nth moment of the system.
Step 1.2: according to the obtained mathematical model, based on the regional pole allocation principle, by designing a comprehensive control law
Figure RE-GDA0002488323410000022
So that the symmetric positive definite matrix X1(n)、X2(n) and X3(n) the following bilinear inequality groups are satisfied, that is, the system can be ensured to satisfy the requirements of dynamic characteristics and stability in a proper region (stable region) of the complex plane; to this end, the comprehensive control law
Figure RE-GDA0002488323410000023
The design problem of (a) is converted into a constraint optimization problem of bilinear inequality set.
[A(n)+B(n)Γ(n)K(n)C(n)]X1(n)+X1(n)[A(n)+B(n)Γ(n)K(n)C(n)]T+2αX1(n)<0
Figure RE-GDA0002488323410000024
Figure RE-GDA0002488323410000025
Wherein:
a11＝a22＝sinθ{[A(n)+B(n)Γ(n)K(n)C(n)]X3(n)+X3(n)[A(n)+B(n)Γ(n)K(n)C(n)]T}
Figure RE-GDA0002488323410000026
X1(n)、X2(n) and X3(n) is a symmetric positive definite matrix to be solved, K (n) is a controller gain parameter to be designed, α and theta represent the included angle of a stable region, and r represents the radius of the stable region, namely α, theta and r are used for describing the appropriate region range meeting the dynamic characteristic and stability requirements of the system in a complex plane.
(2) Based on the obtained bilinear inequality set, a perturbation linearization technology is adopted to rapidly solve the bilinear inequality set, the flow is shown as a figure 2, and the method comprises the following steps:
step 2.1: let j equal to 1, arbitrarily take the initial feedback gain
Figure RE-GDA0002488323410000031
Step 2.2: order to
Figure RE-GDA0002488323410000032
Solving for t, X as followsi(n), i ═ 1,2,3 linear matrix inequality constraint minima problem:
Figure RE-GDA0002488323410000033
wherein epsilon1Denotes a preset first threshold value, and I denotes an identity matrix.
The minimum value obtained is defined as tjMint; if tj<0 and Aj(n) all poles are located in the stable region, then
Figure RE-GDA0002488323410000034
Completing solution for a required value, and entering the step (3); if tj<0 and Aj(n) if the poles are not all located in the stable region, returning to step 2.1; if tjIf not less than 0, entering the step 2.3;
step 2.3: order to
Figure RE-GDA0002488323410000037
Solving for the following amount of shooting δ X1(n)、δX2(n)、δX3(n) and
Figure RE-GDA0002488323410000036
the problem of linearization minima.
Figure RE-GDA0002488323410000041
In the formula:
Figure RE-GDA0002488323410000042
Figure RE-GDA0002488323410000043
Figure RE-GDA0002488323410000044
χ3(n)＝(ψ12(n))T,
Figure RE-GDA0002488323410000045
Figure RE-GDA0002488323410000046
find tj-1If | tj-1-tj|>ε2And j is<N (N is the maximum number of iterations), then order
Figure RE-GDA0002488323410000047
j equals j +1, and the step 2.2 is returned; otherwise, returning to the step 2.1. Wherein epsilon2To a set second threshold value, epsilon2＝0.0001。
(3) Comprehensive control law obtained by utilizing the steps
Figure RE-GDA0002488323410000048
The Kalman filtering algorithm is adopted to estimate the effective factor gamma (n) on line, and the fault-tolerant control law required after the fault is synchronously obtained
Figure RE-GDA0002488323410000049
(4) Utilizing the fault-tolerant control law obtained in the step (3)
Figure RE-GDA00024883234100000410
And controlling a spacecraft control system.
An integrated system for performing fault diagnosis and fault tolerant control of an actuator, comprising:
the first module converts the reconstruction problem of the comprehensive control law into a constraint optimization problem of a bilinear inequality group by using a regional pole allocation principle to obtain the bilinear inequality group;
the second module is used for solving the bilinear inequality group by adopting a perturbation linearization method according to the bilinear inequality group to obtain the comprehensive control law
Figure RE-GDA0002488323410000051
Third module, utilizing integrated control law
Figure RE-GDA0002488323410000052
The Kalman filtering algorithm is adopted to estimate the effective factor gamma (n) on line, and the fault-tolerant control law required after the fault is synchronously obtained
Figure RE-GDA0002488323410000053
And controlling a spacecraft control system.
In the first module, a specific method for converting the reconstruction problem of the comprehensive control law into the constraint optimization problem of the bilinear inequality set is as follows:
step 1.1: establishing a mathematical model of a spacecraft control system when an actuating mechanism fails, and describing by adopting a state space model in a discrete time-varying form as follows:
Figure RE-GDA0002488323410000054
wherein, Γ (n) is an effective factor describing a specific fault mode of an actuating mechanism, x (n), u (n) and y (n) are respectively a state variable, an input variable and an output variable of a system, w (n) and v (n) are respectively a process noise variable and a measurement noise variable of the system, A (n), B (n) and C (n) are respectively a dynamic model matrix, an actuating mechanism installation matrix and a sensor installation matrix of the system, and n represents the nth moment of the system;
step 1.2: according to the mathematical model established in step 1.1, by designing the comprehensive control law
Figure RE-GDA0002488323410000055
So that the symmetric positive definite matrix X1(n)、X2(n) and X3(n) satisfies the following bilinear inequality set of equations:
[A(n)+B(n)Γ(n)K(n)C(n)]X1(n)+X1(n)[A(n)+B(n)Γ(n)K(n)C(n)]T+2αX1(n)<0
Figure RE-GDA0002488323410000056
Figure RE-GDA0002488323410000057
wherein:
Figure RE-GDA0002488323410000058
X1(n)、X2(n) and X3(n) is a symmetric positive definite matrix to be solved, K (n) is a controller gain parameter to be set, α and theta are included angles of the stable region, and r is a radius of the stable region.
In the second module, the comprehensive control law is obtained
Figure RE-GDA0002488323410000061
The specific method comprises the following steps:
step 2.1: let j equal to 1, arbitrarily take the initial feedback gain
Figure RE-GDA0002488323410000062
Step 2.2: order to
Figure RE-GDA0002488323410000063
Solving for t, X as followsi(n) minima problem under the constraint of the linear matrix inequality:
Figure RE-GDA0002488323410000064
wherein epsilon1The first threshold value is preset, I represents an identity matrix, I is 1,2, 3; t is the amount of relaxation to be optimized; j is the step length of iterative optimization;
the minimum value obtained is defined as tjMint; if tj<0 and Aj(n) all poles are located in the stable region, then
Figure RE-GDA0002488323410000065
To obtain a desired value, a comprehensive control law
Figure RE-GDA0002488323410000066
If tj<0 and Aj(n) if the poles are not all located in the stable region, returning to step 2.1, and adjusting the initial feedback gain; if tjIf not less than 0, entering the step 2.3;
step 2.3: order to
Figure RE-GDA0002488323410000067
Solving for the following amount of shooting δ X1(n)、δX2(n)、δX3(n) and
Figure RE-GDA0002488323410000068
the linearization minima problem of (1):
Figure RE-GDA0002488323410000071
in the formula:
Figure RE-GDA0002488323410000072
Figure RE-GDA0002488323410000073
Figure RE-GDA0002488323410000074
χ3(n)＝(ψ12(n))T,
Figure RE-GDA0002488323410000075
Figure RE-GDA0002488323410000076
find tj-1If | tj-1-tj|>ε2And j is<N, then order
Figure RE-GDA0002488323410000077
j equals j +1, and the step 2.2 is returned; otherwise, returning to the step 2.1; wherein N is the maximum number of iterations, ∈2Is a preset second threshold value.
Compared with the prior art, the invention has the beneficial effects that:
(1) the method disclosed by the invention is based on an integrated technical means, realizes synchronous execution of fault estimation and processing, improves the emergency processing capacity of the fault of the executing mechanism, has great advantages in rapidity and real-time compared with the traditional technology, can ensure high performance and high quality of the attitude control level of the spacecraft when the executing mechanism is in fault, improves the on-orbit running quality of the spacecraft to a certain extent, prolongs the service life, and enriches the thinking and system of the design of the existing control system.
(2) The invention provides a fault-tolerant control method and a fault-tolerant control system with simple structural form and small on-orbit calculation amount, which move the parameters of on-orbit calculation to the ground design stage, only need to estimate effective factors in real time and synchronously adjust the control law on the orbit, greatly reduce the on-board calculation amount compared with the traditional technology, ensure the system to have good reliability, ensure the system to still have excellent applicability under the constraint of limited resources such as on-board calculation and storage, and effectively expand the application range of the existing fault diagnosis and fault-tolerant control method.
Drawings
FIG. 1 is a flow chart of the method of the present invention;
FIG. 2 is a flow chart of solving a bilinear inequality set problem by using a perturbation linearization method in the method of the present invention;
FIG. 3 is a graph of attitude angle and its variation based on the prior state feedback control method;
FIG. 4 is a graph of control torque variation based on a prior state feedback control method;
FIG. 5 is a graph of attitude angle and its variation based on the method of the present invention;
fig. 6 is a graph of the variation of the control torque obtained based on the method of the present invention.
Detailed Description
The invention is further explained by the figures and the examples.
An integrated method of fault diagnosis and fault-tolerant control of an execution mechanism comprises the following steps, and the flow is shown in fig. 1:
(1) the method converts the reconstruction problem of the comprehensive control law into the constraint optimization problem of a bilinear inequality set by using a regional pole allocation principle, and comprises the following steps of:
step 1.1: establishing a mathematical model of a spacecraft control system when an actuating mechanism fails, wherein the model is described by adopting a state space model in a discrete time-varying form as follows:
Figure RE-GDA0002488323410000081
wherein, Γ (n) is an effective factor describing a specific fault mode of an actuating mechanism, x (n), u (n) and y (n) are respectively a state variable, an input variable and an output variable of a system, w (n) and v (n) are respectively a process noise variable and a measurement noise variable of the system, and A (n), B (n) and C (n) are respectively a dynamic model matrix, an actuating mechanism installation matrix and a sensor installation matrix of the system; n represents the nth time of the system, and n is a positive integer.
Step 1.2: according to the obtained mathematical model, based on the regional pole allocation principle, by designing a comprehensive control law
Figure RE-GDA0002488323410000091
So that the symmetric positive definite matrix X1(n)、X2(n) and X3(n) the following bilinear inequality groups are satisfied, that is, the system can be ensured to satisfy the requirements of dynamic characteristics and stability in a proper region (stable region) of the complex plane; to this end, the comprehensive control law
Figure RE-GDA0002488323410000092
Is transformed into a bilinear inequality set of constraint optimizationAnd (5) problems are solved.
[A(n)+B(n)Γ(n)K(n)C(n)]X1(n)+X1(n)[A(n)+B(n)Γ(n)K(n)C(n)]T+2αX1(n)<0
Figure RE-GDA0002488323410000093
Figure RE-GDA0002488323410000094
Wherein:
a11＝a22＝sinθ{[A(n)+B(n)Γ(n)K(n)C(n)]X3(n)+X3(n)[A(n)+B(n)Γ(n)K(n)C(n)]T}
Figure RE-GDA0002488323410000095
X1(n)、X2(n) and X3(n) is a symmetric positive definite matrix to be solved, K (n) is a controller gain parameter to be designed, α and theta represent the included angle of a stable region, and r represents the radius of the stable region, namely α, theta and r are used for describing the appropriate region range meeting the dynamic characteristic and stability requirements of the system in a complex plane.
(2) Based on the obtained bilinear inequality set, a perturbation linearization technology is adopted to rapidly solve the bilinear inequality set, the flow is shown as a figure 2, and the method comprises the following steps:
step 2.1: let j equal to 1, arbitrarily take the initial feedback gain
Figure RE-GDA0002488323410000096
Step 2.2: order to
Figure RE-GDA0002488323410000097
Solving for t, X as followsi(n), i ═ 1,2,3 linear matrix inequality constraint minima problem:
Figure RE-GDA0002488323410000101
wherein epsilon1Denotes a preset first threshold value, and I denotes an identity matrix.
The minimum value obtained is defined as tjMint; if tj<0 and Aj(n) all poles are located in the stable region, then
Figure RE-GDA0002488323410000102
Completing solution for a required value, and entering the step (3); if tj<0 and Aj(n) if the poles are not all located in the stable region, returning to step 2.1; if tjIf not less than 0, entering the step 2.3;
step 2.3: order to
Figure RE-GDA0002488323410000103
Solving for the following amount of shooting δ X1(n)、δX2(n)、δX3(n) and
Figure RE-GDA0002488323410000104
the problem of linearization minima.
Figure RE-GDA0002488323410000105
In the formula:
Figure RE-GDA0002488323410000106
Figure RE-GDA0002488323410000107
Figure RE-GDA0002488323410000108
χ3(n)＝(ψ12(n))T,
Figure RE-GDA0002488323410000111
Figure RE-GDA0002488323410000112
find tj-1If | tj-1-tj|>ε2And j is<N (N is the maximum number of iterations), then order
Figure RE-GDA0002488323410000113
j equals j +1, and the step 2.2 is returned; otherwise, returning to the step 2.1. Wherein epsilon2Is a preset second threshold value.
(3) Comprehensive control law obtained by utilizing the steps
Figure RE-GDA0002488323410000114
The Kalman filtering algorithm is adopted to estimate the effective factor gamma (n) on line, and the fault-tolerant control law required after the fault is synchronously obtained
Figure RE-GDA0002488323410000115
(4) Utilizing the fault-tolerant control law obtained in the step (3)
Figure RE-GDA0002488323410000116
The on-orbit fault of the actuating mechanism can be diagnosed in real time and reconstructed quickly, so that the influence degree of the fault is effectively reduced, the safety risk of the system is reduced, the autonomous viability of the spacecraft control system is greatly improved, and the operation cost of ground measurement and control is reduced.
An integrated system for performing fault diagnosis and fault tolerant control of an actuator, comprising:
the first module converts the reconstruction problem of the comprehensive control law into a constraint optimization problem of a bilinear inequality group by using a regional pole allocation principle to obtain the bilinear inequality group;
the second module is used for solving the bilinear inequality group by adopting a perturbation linearization method according to the bilinear inequality group to obtain the comprehensive control law
Figure RE-GDA0002488323410000117
Third module, utilizing integrated control law
Figure RE-GDA0002488323410000118
The Kalman filtering algorithm is adopted to estimate the effective factor gamma (n) on line, and the fault-tolerant control law required after the fault is synchronously obtained
Figure RE-GDA0002488323410000119
And controlling a spacecraft control system.
In the first module, a specific method for converting the reconstruction problem of the comprehensive control law into the constraint optimization problem of the bilinear inequality set is as follows:
step 1.1: establishing a mathematical model of a spacecraft control system when an actuating mechanism fails, and describing by adopting a state space model in a discrete time-varying form as follows:
Figure RE-GDA00024883234100001110
wherein, Γ (n) is an effective factor describing a specific fault mode of an actuating mechanism, x (n), u (n) and y (n) are respectively a state variable, an input variable and an output variable of a system, w (n) and v (n) are respectively a process noise variable and a measurement noise variable of the system, A (n), B (n) and C (n) are respectively a dynamic model matrix, an actuating mechanism installation matrix and a sensor installation matrix of the system, and n represents the nth moment of the system;
step 1.2: according to the mathematical model established in step 1.1, by designing the comprehensive control law
Figure RE-GDA0002488323410000121
So that the symmetric positive definite matrix X1(n)、X2(n) and X3(n) satisfies the following bilinear inequality set of equations:
[A(n)+B(n)Γ(n)K(n)C(n)]X1(n)+X1(n)[A(n)+B(n)Γ(n)K(n)C(n)]T+2αX1(n)<0
Figure RE-GDA0002488323410000122
Figure RE-GDA0002488323410000123
wherein:
Figure RE-GDA0002488323410000124
X1(n)、X2(n) and X3(n) is a symmetric positive definite matrix to be solved, K (n) is a controller gain parameter to be set, α and theta are included angles of the stable region, and r is a radius of the stable region.
In the second module, the comprehensive control law is obtained
Figure RE-GDA0002488323410000125
The specific method comprises the following steps:
step 2.1: let j equal to 1, arbitrarily take the initial feedback gain
Figure RE-GDA0002488323410000126
Step 2.2: order to
Figure RE-GDA0002488323410000127
Solving for t, X as followsi(n) minima problem under the constraint of the linear matrix inequality:
Figure RE-GDA0002488323410000131
wherein epsilon1The first threshold value is preset, I represents an identity matrix, I is 1,2, 3; t is the amount of relaxation to be optimized; j is the step length of iterative optimization;
the minimum value obtained is defined as tjMint; if tj<0 and Aj(n) all poles are located in the stable region, then
Figure RE-GDA0002488323410000132
To obtain a desired value, a comprehensive control law
Figure RE-GDA0002488323410000133
If tj<0 and Aj(n) if the poles are not all located in the stable region, returning to step 2.1, and adjusting the initial feedback gain; if tjIf not less than 0, entering the step 2.3;
step 2.3: order to
Figure RE-GDA0002488323410000134
Solving for the following amount of shooting δ X1(n)、δX2(n)、δX3(n) and
Figure RE-GDA0002488323410000135
the linearization minima problem of (1):
Figure RE-GDA0002488323410000136
in the formula:
Figure RE-GDA0002488323410000137
Figure RE-GDA0002488323410000138
Figure RE-GDA0002488323410000141
χ3(n)＝(ψ12(n))T,
Figure RE-GDA0002488323410000142
Figure RE-GDA0002488323410000143
find tj-1If | tj-1-tj|>ε2And j is<N, then order
Figure RE-GDA0002488323410000144
j equals j +1, and the step 2.2 is returned; otherwise, returning to the step 2.1; wherein N is the maximum number of iterations, ∈2Is a preset second threshold value.
Example (b):
relevant simulation parameters of the spacecraft attitude control system are as follows; meanwhile, a momentum wheel is adopted as an actuating mechanism, the maximum control torque of the momentum wheel is set to be 1N m, and the fault occurrence time is 15 s.
(1) The satellite principal inertia matrix is taken as
Figure RE-GDA0002488323410000145
(2) Initial attitude angular velocity of
ω0＝[0.3 0.3 0.3]°/s
(3) Initial attitude angle of
α0＝[3 4 5]°
(4) Covariance matrix of process noise and observation noise as
W＝diag([0.0320.0320.0320.0320.0320.032])
V＝0.52W
(5) The parameters for the stable region are set to α -1.5, θ -0.8, and r-5
By the ground design, the closed loop poles of the system can be obtained as follows:
λ1,2＝-1.5076±0.3474i
λ3,4＝-1.5076±0.3238i
λ5,6＝-1.5097±0.0107i
fig. 3 and 4 are an attitude angle and attitude angular velocity change simulation curve and a control moment change simulation curve obtained by the existing state feedback control method, respectively; fig. 5 and fig. 6 are an attitude angle and attitude angular velocity change simulation curve and a control moment change simulation curve respectively obtained by the autonomous fault diagnosis and reconfiguration control integrated method designed by the present invention.
Comparing the simulation curve results of fig. 3 to fig. 6, it can be known that, when the momentum wheel has a serious failure, the state feedback controller designed based on the prior art can cause the attitude of the spacecraft to diverge, that is, the prior art cannot ensure that the stability of the attitude is realized after the executing mechanism has a failure, and thus it is difficult to ensure that the spacecraft provides safe, reliable, continuous and stable services. The integrated control method obtained by the invention can effectively diagnose and reconstruct the controller aiming at the faults of the actuating mechanism, thereby ensuring the stability of the system, having good response process and having more advantages in performance compared with the prior state feedback control method. Moreover, the integrated control method designed by the invention is not only applicable to single actuator faults, but also can be popularized and applied to the condition of multiple actuator faults.
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. An integrated method for fault diagnosis and fault-tolerant control of an execution mechanism is characterized by comprising the following steps:
(1) converting the reconstruction problem of the comprehensive control law into a constraint optimization problem of a bilinear inequality set by using a regional pole allocation principle;
(2) solving the bilinear inequality group by adopting a perturbation linearization method according to the bilinear inequality group obtained in the step (1) to obtain a comprehensive control law
Figure FDA0002403148160000011
(3) Comprehensive control law obtained by using step (2)
Figure FDA0002403148160000012
The Kalman filtering algorithm is adopted to estimate the effective factor gamma (n) on line, and the fault-tolerant control law required after the fault is synchronously obtained
Figure FDA0002403148160000013
(4) Utilizing the fault-tolerant control law obtained in the step (3)
Figure FDA0002403148160000014
And controlling a spacecraft control system.
2. The integrated method for fault diagnosis and fault-tolerant control of the execution mechanism according to claim 1, wherein the specific steps of the step (1) are as follows:
step 1.1: establishing a mathematical model of a spacecraft control system when an actuating mechanism fails, and describing by adopting a state space model in a discrete time-varying form as follows:
Figure FDA0002403148160000015
wherein, Γ (n) is an effective factor describing a specific fault mode of an actuating mechanism, x (n), u (n) and y (n) are respectively a state variable, an input variable and an output variable of a system, w (n) and v (n) are respectively a process noise variable and a measurement noise variable of the system, A (n), B (n) and C (n) are respectively a dynamic model matrix, an actuating mechanism installation matrix and a sensor installation matrix of the system, and n represents the nth moment of the system;
step 1.2: according to the mathematical model established in step 1.1, by designing the comprehensive control law
Figure FDA0002403148160000016
So that the symmetric positive definite matrix X1(n)、X2(n) and X3(n) satisfies the following bilinear inequality set of equations:
[A(n)+B(n)Γ(n)K(n)C(n)]X1(n)+X1(n)[A(n)+B(n)Γ(n)K(n)C(n)]T+2αX1(n)<0
Figure FDA0002403148160000021
Figure FDA0002403148160000022
wherein:
Figure FDA0002403148160000023
X1(n)、X2(n) and X3(n) is a symmetric positive definite matrix to be solved, K (n) is a controller gain parameter to be set, α and theta are included angles of the stable region, and r is a radius of the stable region.
3. The integrated method for fault diagnosis and fault-tolerant control of the execution mechanism according to claim 2, wherein the specific method of the step (2) is as follows:
step 2.1: let j equal to 1, arbitrarily take the initial feedback gain
Figure FDA0002403148160000024
Step 2.2: order to
Figure FDA0002403148160000025
Solving for t, X as followsi(n) minima problem under the constraint of the linear matrix inequality:
min t
Figure FDA0002403148160000026
wherein epsilon1The first threshold value is preset, I represents an identity matrix, I is 1,2, 3; t is the amount of relaxation to be optimized; j is the step length of iterative optimization;
the minimum value obtained is defined as tjMint; if tj<0 and Aj(n) all poles are located in the stable region, then
Figure FDA0002403148160000027
Entering the step (3) for the required value; if tj<0 and Aj(n) if the poles are not all located in the stable region, returning to step 2.1, and adjusting the initial feedback gain; if tjIf not less than 0, entering the step 2.3;
step 2.3: order to
Figure FDA0002403148160000031
Solving for the following amount of shooting δ X1(n)、δX2(n)、δX3(n) and
Figure FDA0002403148160000032
the linearization minima problem of (1):
min t
Figure FDA0002403148160000033
in the formula:
Figure FDA0002403148160000034
Figure FDA0002403148160000035
Figure FDA0002403148160000036
χ3(n)＝(ψ12(n))T,
Figure FDA0002403148160000037
Figure FDA0002403148160000038
find tj-1If | tj-1-tj|>ε2And j is<N, then order
Figure FDA0002403148160000039
j equals j +1, and the step 2.2 is returned; otherwise, returning to the step 2.1; wherein N is the maximum number of iterations, ∈2Is a preset second threshold value.
4. An integrated system for performing fault diagnosis and fault tolerant control of an actuator, comprising:
the first module converts the reconstruction problem of the comprehensive control law into a constraint optimization problem of a bilinear inequality group by using a regional pole allocation principle to obtain the bilinear inequality group;
the second module is used for solving the bilinear inequality group by adopting a perturbation linearization method according to the bilinear inequality group to obtain the comprehensive control law
Figure FDA0002403148160000041
Third module, utilizing integrated control law
Figure FDA0002403148160000042
The Kalman filtering algorithm is adopted to estimate the effective factor gamma (n) on line, and the fault-tolerant control law required after the fault is synchronously obtained
Figure FDA0002403148160000043
And controlling a spacecraft control system.
5. The system of claim 4, wherein the specific method for transforming the reconstruction problem of the integrated control law into the constrained optimization problem of the bilinear inequality set in the first module is as follows:
step 1.1: establishing a mathematical model of a spacecraft control system when an actuating mechanism fails, and describing by adopting a state space model in a discrete time-varying form as follows:
Figure FDA0002403148160000044
wherein, Γ (n) is an effective factor describing a specific fault mode of an actuating mechanism, x (n), u (n) and y (n) are respectively a state variable, an input variable and an output variable of a system, w (n) and v (n) are respectively a process noise variable and a measurement noise variable of the system, A (n), B (n) and C (n) are respectively a dynamic model matrix, an actuating mechanism installation matrix and a sensor installation matrix of the system, and n represents the nth moment of the system;
step 1.2: according to the mathematical model established in step 1.1, by designing the comprehensive control law
Figure FDA0002403148160000045
So that the symmetric positive definite matrix X1(n)、X2(n) and X3(n) satisfies the following bilinear inequality set of equations:
[A(n)+B(n)Γ(n)K(n)C(n)]X1(n)+X1(n)[A(n)+B(n)Γ(n)K(n)C(n)]T+2αX1(n)<0
Figure FDA0002403148160000046
Figure FDA0002403148160000047
wherein:
Figure FDA0002403148160000048
X1(n)、X2(n) and X3(n) is a symmetric positive definite matrix to be solved, K (n) is a controller gain parameter to be set, α and theta are included angles of the stable region, and r is a radius of the stable region.
6. The integrated system for fault diagnosis and fault-tolerant control of actuator of claim 5, wherein the second moduleIn the middle, get the comprehensive control law
Figure FDA0002403148160000051
The specific method comprises the following steps:
step 2.1: let j equal to 1, arbitrarily take the initial feedback gain
Figure FDA0002403148160000052
Step 2.2: order to
Figure FDA0002403148160000053
Solving for t, X as followsi(n) minima problem under the constraint of the linear matrix inequality:
min t
Figure FDA0002403148160000054
wherein epsilon1The first threshold value is preset, I represents an identity matrix, I is 1,2, 3; t is the amount of relaxation to be optimized; j is the step length of iterative optimization;
the minimum value obtained is defined as tjMint; if tj<0 and Aj(n) all poles are located in the stable region, then
Figure FDA0002403148160000055
To obtain a desired value, a comprehensive control law
Figure FDA0002403148160000056
If tj<0 and Aj(n) if the poles are not all located in the stable region, returning to step 2.1, and adjusting the initial feedback gain; if tjIf not less than 0, entering the step 2.3;
step 2.3: order to
Figure FDA0002403148160000059
Solving for the following amount of shooting δ X1(n)、δX2(n)、δX3(n) and
Figure FDA0002403148160000058
the linearization minima problem of (1):
min t
Figure FDA0002403148160000061
in the formula:
Figure FDA0002403148160000062
Figure FDA0002403148160000063
Figure FDA0002403148160000064
χ3(n)＝(ψ12(n))T,
Figure FDA0002403148160000065
Figure FDA0002403148160000066
find tj-1If | tj-1-tj|>ε2And j is<N, then order
Figure FDA0002403148160000067
j equals j +1, and the step 2.2 is returned; otherwise, returning to the step 2.1; wherein N is the maximum number of iterations, ∈2Is a preset second threshold value.
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