CN113220003B - Attitude stabilization hybrid non-fragile control method for non-cooperative flexible assembly spacecraft - Google Patents

Attitude stabilization hybrid non-fragile control method for non-cooperative flexible assembly spacecraft Download PDF

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CN113220003B
CN113220003B CN202110350727.2A CN202110350727A CN113220003B CN 113220003 B CN113220003 B CN 113220003B CN 202110350727 A CN202110350727 A CN 202110350727A CN 113220003 B CN113220003 B CN 113220003B
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刘闯
杨子煜
岳晓奎
王时玉
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Northwestern Polytechnical University
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    • G05D1/0833—Control of attitude, i.e. control of roll, pitch, or yaw specially adapted for aircraft to ensure stability using limited authority control
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Abstract

The invention relates to a non-cooperative flexible assembly spacecraft attitude stabilization hybrid non-fragile control method. The invention aims to solve the problem of high-precision and high-stability control of the attitude of a non-cooperative flexible assembly under multi-source complex disturbance, and the multi-source disturbance comprises the problems of measurement error, actuator failure, coexistence of controller addition type/multiplication type gain perturbation and the like. Firstly, separating unknown uncertain inertial parameters from comprehensive interference and modeling attitude dynamics into a state space form; secondly, constructing a comprehensive interference item containing complex disturbances such as inertial parameters and actuator faults, and perfecting a state space equation in the first step; thirdly, considering the addition/multiplication type gain perturbation coexistence to design a hybrid non-fragile controller; and fourthly, substituting the three into the two to construct a closed-loop attitude control system. Fifthly, deducing a linear matrix inequality condition meeting the system stability and solving by using a tool box; and sixthly, realizing the integrated control of the attitude/mode of the non-cooperative flexible combination body under the condition of limited input. The method is used for the field of spacecraft attitude stabilization control.

Description

Attitude stabilization hybrid non-fragile control method for non-cooperative flexible assembly spacecraft
Technical Field
The invention relates to a hybrid non-fragile control method for attitude stabilization of a flexible assembly spacecraft after space non-cooperative target capture.
Background
With the development of human aerospace technology and the increase of aerospace activities, space failure targets, space garbage and the like are increased year by year, precious orbit resources are occupied, and the normal operation of other spacecrafts is threatened, the space targets cannot actively provide state information and inertia parameter information, the stable and high-precision in-orbit operation is influenced by complex disturbance, the space targets are typical non-cooperative targets, the capture processing of the space targets has important significance on the sustainable development of the aerospace activities, and the high-precision and high-stability control of the posture of the flexible assembly spacecraft formed after capture is a very important link.
Under actual working conditions, the control of the captured combined spacecraft faces the problem that state information and inertial parameter information are unknown, and also has the disadvantages of model parameter uncertainty, external interference, measurement error, actuator failure, input saturation, controller addition/multiplication type perturbation coexistence and the like, and simultaneously has amplitude limitation during the working of an actual actuator due to physical and safety limitations. These disadvantages can lead to reduced or even destabilization of a control system designed for an ideal situation.
At present, a posture high-precision high-stability mixing non-fragile control method for a non-cooperative flexible combination spacecraft in the presence of addition/multiplication perturbation of a controller, which considers the above adverse factors, particularly, does not exist, and the time and the precision for achieving stability cannot be guaranteed.
Disclosure of Invention
The invention aims to solve the problems of high-precision and high-stability control of the attitude of a non-cooperative flexible assembly spacecraft under the complex conditions of inertial unknown uncertainty, model parameter uncertainty, external interference, measurement error, actuator failure, input saturation, coexistence of additive/multiplicative gain perturbation of a controller and the like, and provides a non-fragile control method for attitude stability mixing of the non-cooperative flexible assembly spacecraft.
A non-cooperative flexible assembly spacecraft attitude stabilization hybrid non-fragile control method comprises the following steps:
firstly, establishing and separating an unknown uncertainty item of an inertial parameter, simultaneously considering uncertainty of a model parameter, and rewriting a non-cooperative flexible assembly spacecraft attitude dynamics model with external interference into a state space equation form;
step two, aiming at the measurement error and the fault of the actuating mechanism, constructing fault interference of the actuating mechanism and forming comprehensive interference with the unknown uncertain item of the inertial parameter and the external interference in the step one;
step three, aiming at the problem of the gain addition/multiplication perturbation coexistence of the controller, defining controller parameters and designing a hybrid non-fragile controller;
step four, substituting the hybrid non-fragile controller into a non-cooperative flexible assembly attitude dynamics state space model containing comprehensive interference to establish a closed-loop system state space model;
step five, according to the Lyapunov stability theory and a linear matrix inequality method, deriving a sufficient condition of a linear matrix inequality meeting the system stability to solve the controller parameters in step three and substitute the controller parameters into a controller, so that a state space model in step four is complete;
and step six, under the condition of controlling torque amplitude limiting, controlling the attitude angle, the attitude angular velocity and the modal displacement of the non-cooperative flexible assembly to quickly reach stability, and ensuring certain control precision.
The invention has the beneficial effects that:
compared with the prior art, the method has the advantages that under the conditions of the coexistence of unknown uncertainty of inertia parameters, uncertainty of model parameters, external interference, measurement errors, faults of an actuating mechanism, input saturation and controller addition/multiplication gain perturbation, the uncooperative flexible combination spacecraft can quickly reach a high-precision and high-stability state, the stabilization time is not more than 150s, the attitude angle control precision is less than 0.01rad, the attitude angular speed control precision is less than 0.01rad/s, the modal displacement control precision is less than 0.01, and the magnitude of control torque is not more than 15Nm all the time in the whole control process.
The hybrid non-fragile control method designed by the invention enables the flexible assembly spacecraft after space non-cooperative target capture to quickly reach a stable state under the complex disturbances such as unknown uncertainty of inertial parameters, uncertainty of model parameters, external interference, measurement errors, faults of an execution mechanism, input saturation, coexistence of additive/multiplicative gain perturbation of a controller and the like, and meets the task requirements.
Drawings
FIG. 1 is a flow chart of a hybrid non-fragile control method for attitude stabilization of a non-cooperative flexible assembly spacecraft of the present invention;
FIG. 2 is a change curve of the attitude angle of the non-cooperative flexible combined spacecraft under the action of a hybrid non-fragile controller, phi, theta and psi respectively represent a rolling angle, a yaw angle and a pitch angle of the spacecraft, and rad represents the unit of the angle as radian;
FIG. 3 is a graph showing the variation curve of the attitude angular velocity of a non-cooperative flexible assembly spacecraft under the action of a hybrid non-fragile controller, omega x ，ω y ，ω z Respectively representing the components of the angular velocity on three axes of a body coordinate system, and the unit of rad/s representing the angular velocity is radian per second;
FIG. 4 is a graph showing the variation of modal displacement, η, of a non-cooperative flexible composite spacecraft under the influence of a hybrid non-fragile controller in accordance with the present invention 1 ，η 2 ，η 3 ，η 4 Four components of modal displacement, respectively;
FIG. 5 is a plot of attitude angle accuracy of a non-cooperative flexible assembly spacecraft of the present invention under the influence of a hybrid non-fragile controller, the accuracy being represented by a two-norm attitude angle vector;
FIG. 6 is a plot of attitude angular velocity accuracy of a non-cooperative flexible assembly spacecraft of the present invention under the influence of a hybrid non-fragile controller, the accuracy being represented by a two-norm of the attitude angular velocity vector;
FIG. 7 is a plot of modal displacement accuracy of a non-cooperative flexible composite spacecraft under the influence of a hybrid non-fragile controller, the accuracy being represented by a two-norm modal displacement vector in accordance with the present invention;
FIG. 8 is a graph showing the variation of the control torque according to the present invention, u x ，u y ，u z Respectively represent the components of the control moment on three axes of the body coordinate system, and Nm represents the unit of the control moment in Nm.
Detailed Description
The embodiment is described with reference to fig. 1, and a non-cooperative flexible assembly spacecraft attitude stabilization hybrid non-fragile control method comprises the following steps:
firstly, establishing and separating an unknown uncertainty item of an inertial parameter, simultaneously considering uncertainty of a model parameter, and rewriting a non-cooperative flexible assembly spacecraft attitude dynamics model with external interference into a state space equation form;
step two, aiming at the measurement error and the fault of the actuating mechanism, constructing fault interference of the actuating mechanism and forming comprehensive interference with the unknown uncertain item of the inertial parameter and the external interference in the step one;
step three, aiming at the problem of the gain addition/multiplication perturbation coexistence of the controller, defining controller parameters and designing a hybrid non-fragile controller;
step four, substituting the hybrid non-fragile controller into a non-cooperative flexible assembly attitude dynamic state space model containing comprehensive interference to establish a closed-loop system state space model;
step five, according to the Lyapunov stability theory and a linear matrix inequality method, deriving a sufficient condition of a linear matrix inequality meeting the system stability to solve the controller parameters in step three and substitute the controller parameters into a controller, so that a state space model in step four is complete;
and step six, under the condition of controlling torque amplitude limiting, controlling the attitude angle, the attitude angular velocity and the modal displacement of the non-cooperative flexible assembly to quickly reach stability, and ensuring certain control precision.
Establishing and separating an unknown uncertainty item of an inertial parameter, considering uncertainty of a model parameter, and rewriting a non-cooperative flexible assembly spacecraft attitude dynamics model with external interference into a state space equation form; the specific process is
Defining a local horizontal and local vertical coordinate system F o (X o ,Y o ,Z o ) As a reference coordinate system, the origin of the coordinate system is located at the centroid of the non-cooperative complex, the roll axis is along the flight direction, the yaw axis points to the centroid, and the pitch axis completes the right-hand coordinate system. Defining a body coordinate system F of the combined spacecraft B (X B ,Y B ,Z B ) The origin is located at the center of mass of the non-cooperative combination, and the three coordinate axes are respectively superposed with the inertia main axis of the combination.
The attitude kinematic equation of the flexible assembly spacecraft is as follows:
Figure GDA0003744245730000031
where phi, theta and psi denote the three components of the flexible composite spacecraft, i.e., roll, pitch and yaw attitude angles, omega, respectively 0 Indicating the angular velocity, omega, of the track on which the flexible assembly is located x 、ω y 、ω z The components of the attitude angular velocity of the flexible assembly spacecraft on three coordinate axes are respectively represented, the components are respectively roll attitude angular velocity, pitch attitude angular velocity and yaw attitude angular velocity, and the components are as follows when the high-orbit assembly is adjusted in small-angle attitude:
Figure GDA0003744245730000041
if a piezoelectric actuator is incorporated into the surface of a flexible attachment of a composite body to provide an input voltage u p Thereby producingGenerating the deformation which causes the control moment, the body of the assembly and the flexible dynamic equation can be expressed as follows:
Figure GDA0003744245730000042
wherein,
Figure GDA0003744245730000043
an inertia matrix representing the body of the assembly, ω ═ ω x ω y ω z ]Representing the attitude angular velocity vector, ω × An anti-symmetric matrix representing the vector omega,
Figure GDA0003744245730000044
representing a matrix of coupling coefficients between the rigid body and the flexible structure of the combination,
Figure GDA0003744245730000045
a modal coordinate vector representing the relative composition ontology,
Figure GDA0003744245730000046
and
Figure GDA0003744245730000047
representing a control input torque and an external disturbance torque;
Figure GDA0003744245730000048
represents a modal damping matrix wherein
Figure GDA0003744245730000049
And Ω i Where i is 1,2, …, m represents damping ratio and natural frequency,
Figure GDA00037442457300000410
the stiffness matrix is represented and m is the number of flexural modes considered. Here, T d Including gravity gradient moment, solar radiation pressure moment and aerodynamic moment u p Represents a piezoelectric input voltage, and
Figure GDA00037442457300000411
is the corresponding coupling coefficient matrix;
defining auxiliary variables
Figure GDA00037442457300000412
Obtaining:
Figure GDA00037442457300000413
substituting the second equation in the non-cooperative flexible assembly attitude dynamics equation system to obtain a rewritten equation:
Figure GDA00037442457300000414
using feedback of true values, piezoelectric input u p Expressed as:
Figure GDA00037442457300000415
in the formula F a ，F b To measure the feedback coefficient. Will be provided with
Figure GDA00037442457300000416
Substituting the derivative of the auxiliary variable
Figure GDA00037442457300000417
And the flexible assembly attitude kinetic equation after rewriting is obtained:
Figure GDA00037442457300000418
Figure GDA00037442457300000419
order to
Figure GDA00037442457300000420
The two equations above can be rewritten as a state space equation form:
Figure GDA00037442457300000421
wherein the state variable
Figure GDA00037442457300000422
Output variable
Figure GDA00037442457300000423
u(t)＝T c In order to control the torque, the torque is controlled,
Figure GDA00037442457300000424
is the preliminary synthetic interference, coefficient matrix:
Figure GDA0003744245730000051
Figure GDA0003744245730000052
the unknown inertial parameter information is all normalized to the following coefficient matrix:
Figure GDA0003744245730000053
Figure GDA0003744245730000054
wherein
Figure GDA0003744245730000055
J n Is a nominal inertia matrix;
△A p representing model parametersUncertainty, which has a norm bound and satisfies a match condition:
Figure GDA0003744245730000056
wherein M is 1 And N 1 Is a real constant matrix of suitable dimensions, F 1 (t) is a matrix function measurable by Leeberg.
In the second step, aiming at the measurement error and the fault of the actuating mechanism, the fault interference of the actuating mechanism is constructed and forms comprehensive interference with the unknown uncertain item of the inertial parameter and the external interference in the first step; the specific process is as follows:
improper actuation of the actuator can severely affect the performance of the attitude control system, leaving E with column full rank representing the distribution matrix of fault signals f (t) present in the input. If E ≠ B 1 Then a process fault is indicated; if E is equal to B 1 Then an actuator failure is indicated.
And constructing the complex disturbance factors into comprehensive interference:
Figure GDA0003744245730000057
wherein the matrix
Figure GDA0003744245730000058
Is B 2 The state space equation in the step one is rewritten as:
Figure GDA0003744245730000061
where v (t) represents the measurement error.
In the third step, aiming at the problem of additive/multiplicative perturbation coexistence of the gain of the controller, the parameters of the controller are defined, and a hybrid non-fragile controller is designed; the specific process is as follows:
when the controller has additive/multiplicative perturbation, the form of the controller is designed as follows:
Figure GDA0003744245730000062
Figure GDA0003744245730000063
is a state variable introduced by the controller,
Figure GDA0003744245730000064
is an estimate of the output variable without taking into account the measurement error, A c 、B c Is a matrix of controller coefficients with appropriate dimensions, K is a matrix of controller gains,
Figure GDA0003744245730000065
the expectation value of the probability of controller gain perturbation DeltaK occurring in the system is represented, the value range of the expectation value is (0,1), controller errors and unknown dynamic characteristics of an actuating mechanism can cause perturbation problems, and when the DeltaK is additive perturbation, the mathematical expression is that the DeltaK is equal to M 2 F 2 (t)N 2 ,||F 2 (t) | ≦ 1, and when Δ K is multiplicative perturbation, the mathematical expression is that Δ K ≦ M 3 F 3 (t)N 3 K,||F 3 (t)||≤1。
Considering the controller simultaneously, the two perturbation problems exist, and the expression is as follows:
△K＝M 2 F 2 (t)N 2 +M 3 F 3 (t)N 3 K,||F 2 (t)||≤1,||F 3 (t)||≤1
M 2 、N 2 、M 3 、N 3 is a real constant matrix of suitable dimensions, F 2 (t)、F 3 (t) is a measurable matrix function of Leeberg.
Substituting the hybrid non-fragile controller into a non-cooperative flexible assembly attitude dynamics state space model containing comprehensive interference to establish a closed-loop system state space model; the specific process is as follows:
substituting the controller obtained in the third step into the non-cooperative flexible assembly spacecraft attitude dynamics model containing the comprehensive interference in the second step to obtain:
Figure GDA0003744245730000066
wherein
Figure GDA0003744245730000067
B 1 ＝B 2 B, there are:
Figure GDA0003744245730000068
y(t)＝Cx(t)＝[C 0]ζ(t)
the coefficient matrix is:
Figure GDA0003744245730000069
wherein B and B 1 The definitions are the same;
when-added perturbation Δ K α Multiplication-by-sum perturbation Δ K m Co-existence time coefficient matrix
Figure GDA0003744245730000071
The specific mathematical expression is as follows:
Figure GDA0003744245730000072
where σ is a constant, ranging from (0, 1).
Will matrix
Figure GDA0003744245730000073
Writing into:
Figure GDA0003744245730000074
the control moment u (t) is written as:
Figure GDA0003744245730000075
in the fifth step, according to the Lyapunov stability theory and a linear matrix inequality method, deriving a sufficient condition of a linear matrix inequality meeting the system stability to solve the controller parameters in the third step and substitute the controller parameters into a controller, so that a state space model in the fourth step is complete; the specific process is as follows:
when the controller addition/multiplication perturbation exists at the same time, the state space model in the step two has secondary stability under the action of the controller in the step three, and the output y (t) meets the requirement of H ∞ Performance constraint, for a given constant xi>0，
Figure GDA0003744245730000076
γ>0, solving the linear matrix inequality:
Figure GDA0003744245730000077
wherein
Figure GDA0003744245730000078
Figure GDA0003744245730000079
Figure GDA00037442457300000710
Figure GDA0003744245730000081
Figure GDA0003744245730000082
Figure GDA0003744245730000083
ξ 1 、ξ 2 Given a constant greater than 0;
obtaining positive definite symmetric matrix P 11 ，Q 11 And matrix Q 21 ，
Figure GDA0003744245730000084
And
Figure GDA0003744245730000085
and further solving a controller parameter matrix in the step three:
Figure GDA0003744245730000086
Figure GDA0003744245730000087
Figure GDA0003744245730000088
and substituting the closed-loop system state space equation in the fourth step.
In the sixth step, under the condition of controlling torque amplitude limiting, the attitude angle, the attitude angular velocity and the modal displacement of the non-cooperative flexible assembly are controlled to be stable quickly, and certain control precision is ensured; the specific process is as follows:
due to physical and safety constraints, there are constraints on the actuators, saturation of the control inputs, negative effects on the stability and performance of the attitude control system designed for "ideal" situations, for a positive scalar λ:
||u||<λ
the two-norm saturation value representing the control input is λ. And adding a saturation amplitude limit to the controller obtained in the step five, namely the actual control torque can be described as:
sat(u i＝1,2,3 (t))＝sign(u i (t))min{u i (t)|,u mi }
wherein u is mi Is the upper limit of the control torque provided by the actuator.
The following examples were used to demonstrate the beneficial effects of the present invention:
the first embodiment is as follows:
the attitude stabilization hybrid non-fragile control method for the non-cooperative flexible assembly spacecraft is specifically prepared according to the following steps:
the method comprises the following steps: and (3) constructing and separating an unknown uncertainty item of the inertial parameter, considering uncertainty of the model parameter, and rewriting a non-cooperative flexible spacecraft attitude dynamics equation with external interference into a state space equation form.
The flexible assembly spacecraft attitude dynamics equation can be expressed in the form:
Figure GDA0003744245730000089
order to
Figure GDA00037442457300000810
The two equations above can be rewritten as a state space equation form:
Figure GDA0003744245730000091
wherein the state variable is
Figure GDA0003744245730000092
Output variable
Figure GDA0003744245730000093
u(t)＝T c In order to control the torque, the torque is controlled,
Figure GDA0003744245730000094
is an external disturbance. Coefficient matrix:
Figure GDA0003744245730000095
Figure GDA0003744245730000096
the unknown uncertain inertial parameter information is all normalized to the following coefficient matrix:
Figure GDA0003744245730000097
Figure GDA0003744245730000098
wherein
Figure GDA0003744245730000099
J n Is a nominal inertia matrix.
△A p Representing the uncertainty of the model parameters, which have norm bounds and satisfy the matching condition:
Figure GDA00037442457300000910
step two: and (4) aiming at the conditions of measurement errors and actuator faults, constructing actuator fault interference and forming comprehensive interference with the unknown uncertain item of the inertial parameters and the external interference item in the step one.
Constructing the complex disturbance as a comprehensive disturbance:
Figure GDA00037442457300000911
substituting the state space model in the step one:
Figure GDA0003744245730000101
v (t) is the measurement error.
Step three: and when the additive/multiplicative perturbation exists in the controller, defining controller parameters and designing a hybrid non-fragile controller.
When the controller has additive/multiplicative perturbation, the form of the controller is designed as follows:
Figure GDA0003744245730000102
Figure GDA0003744245730000103
is a state variable introduced by the controller,
Figure GDA0003744245730000104
is an estimate of the output variable without taking into account the measurement error, A c 、B c Is a controller parameter matrix with appropriate dimensions, and K is a controller gain matrix. Considering the controller to have the above two types of perturbation, the expression is:
△K＝M 2 F 2 (t)N 2 +M 3 F 3 (t)N 3 K,||F 2 (t)||≤1,||F 3 (t)||≤1
M 2 、N 2 、M 3 、N 3 is a real constant matrix of suitable dimensions, F 2 (t)、F 3 (t) is a measurable matrix function of Leeberg.
Step four: and substituting the controller into a non-cooperative flexible assembly spacecraft attitude dynamics state space equation containing comprehensive interference to establish a state space equation of a closed-loop attitude control system.
Substituting the controller obtained in the third step into the flexible assembly attitude dynamics equation containing the comprehensive interference in the second step to obtain:
Figure GDA0003744245730000105
wherein:
Figure GDA0003744245730000106
the coefficient matrix is:
Figure GDA0003744245730000107
when-added perturbation Δ K α Multiplication-by-sum perturbation Δ K m Co-existence time uncertainty coefficient matrix
Figure GDA0003744245730000108
The specific mathematical expression is as follows:
Figure GDA0003744245730000111
where σ is a constant in the range of (0, 1).
Step five: according to the Lyapunov stability theory and the linear matrix inequality method, the sufficient conditions of the linear matrix inequality meeting the system stability are deduced to solve the controller parameters in the third step and substitute the controller parameters into the controller, so that the state space model in the fourth step is complete.
When the additive/multiplicative perturbation exists at the same time, the state space model in the second step has secondary stability under the action of the controller in the third step, and the output y (t) meets the requirement of H ∞ Performance constraint, for a given constant xi>0，
Figure GDA0003744245730000112
γ>0, solving a linear matrix inequality:
Figure GDA0003744245730000113
wherein
Figure GDA0003744245730000114
Figure GDA0003744245730000115
Figure GDA0003744245730000116
Figure GDA0003744245730000117
Figure GDA0003744245730000118
Figure GDA0003744245730000119
Obtaining positive definite symmetric matrix P 11 ，Q 11 And matrix Q 21 ，
Figure GDA00037442457300001110
And
Figure GDA00037442457300001111
and further solving a controller parameter matrix in the step three:
Figure GDA0003744245730000121
Figure GDA0003744245730000122
Figure GDA0003744245730000123
step six: under the condition of controlling input amplitude limiting, the attitude angle, the attitude angular velocity and the modal displacement of the non-cooperative flexible assembly spacecraft are controlled to be quickly stable, and certain precision is ensured.
And adding amplitude limitation to the controller obtained in the step five, namely the actual control torque can be described as:
sat(u i＝1,2,3 (t))＝sign(u i (t))min{|u i (t)|,u mi }
wherein u is mi Is the upper limit of the control torque provided by the actuator.
The attitude stabilization hybrid non-fragile control method for the non-cooperative flexible assembly spacecraft of the embodiment is verified through numerical simulation as follows:
nominal inertial parameters of the non-cooperative flexible assembly spacecraft:
Figure GDA0003744245730000124
the unknown uncertain inertia matrix is: Δ J ═ J (0.05+0.01sin (tt)) J n
Number of flexible modes considered m-4
Coupling coefficient matrix between rigid body and flexible structure:
Figure GDA0003744245730000125
damping ratio xi 1 ξ 2 ξ 3 ξ 4 ]＝[0.005607 0.008620 0.01283 0.02516]
Natural frequency [ omega ] 1 Ω 2 Ω 3 Ω 4 ]＝[0.7681 1.1038 1.8733 2.5496]
Coupling matrix:
Figure GDA0003744245730000126
a feedback coefficient matrix: f a ＝[3.1533 -0.5714 5.3674 9.3389]，F b ＝[1.0976 0.1965 1.8086 3.0873]
External environment moment:
Figure GDA0003744245730000127
the Lenberg matrix function and its corresponding real constant matrix:
M 1 ＝0.01×[8 11 13 15 16 -18 8 11 13 15 16 18 8 11] T ，
N 1 ＝0.01×[1 2 3 4 2 10 1 2 3 4 2 10 1 2]，F 1 (t)＝sin(0.11πt)
M 2 ＝0.1×ones(3,1)N 2 ＝0.01×ones(1,14)，F 2 (t)＝sin(0.11πt+π/4)
M 3 ＝0.1×ones(3,1)N 3 ＝0.01×ones(1,3)，F 3 (t)＝cos(0.11πt)
initial value of angle: Θ (0) ═ 0.18,0.15, -0.15] T rad
Initial value of angular velocity: omega (0) [ -0.02, -0.02,0.02] T rad/s
Initial value of modal displacement:
Figure GDA0003744245730000131
initial value of modal displacement derivative:
Figure GDA0003744245730000132
actuator fault signal:
Figure GDA0003744245730000133
associated normal numbers:
Figure GDA0003744245730000134
ξ 1 ＝0.025,ξ 2 ＝0.025,γ＝3.2,σ＝0.5.
measurement error:
v(t)＝10 -4 ×[4 5 6 0.2 0.2 0.2 0.2 0.1 0.2 0.2 0.2 0.2 0.1 0.2]sin(0.01πt)
controlling torque amplitude limiting: u. of m1 ＝u m2 ＝u m3 ＝15Nm
Solving the linear matrix inequality with the LMI toolkit yields:
Figure GDA0003744245730000135
under a designed hybrid non-fragile controller, fig. 2 to 8 are corresponding simulation results, wherein fig. 2 is a change curve of an attitude angle of a non-cooperative flexible assembly spacecraft, fig. 3 is a change curve of an attitude angular velocity of the non-cooperative flexible assembly spacecraft, fig. 4 is a change curve of a modal displacement of the non-cooperative flexible assembly spacecraft, fig. 5 is a change curve of an attitude angular precision of the non-cooperative flexible assembly spacecraft, fig. 6 is a change curve of an attitude angular velocity precision of the non-cooperative flexible assembly spacecraft, fig. 7 is a change curve of a modal displacement precision of the non-cooperative flexible assembly spacecraft, and fig. 8 is a change curve of a control moment in a whole attitude stabilization control process. The observation shows that the attitude angle, the attitude angular velocity and the convergence time of modal displacement of the non-cooperative flexible combined spacecraft are all less than 150s, the precision is respectively less than 0.01rad, 0.01rad/s and 0.01, and the control moment is always within the range of 15Nm of amplitude limit.
Therefore, the attitude of the non-cooperative flexible assembly spacecraft can be successfully controlled in a high-precision and high-stability manner under the influence of complex disturbances such as unknown uncertainty of inertial parameters, uncertainty of model parameters, external interference, measurement errors, faults of an actuating mechanism, input saturation, additive/multiplicative perturbation coexistence of a controller and the like.
The present invention is capable of other embodiments and its several details are capable of modifications in various obvious respects, all without departing from the spirit and scope of the present invention.

Claims (1)

1. A method for attitude-stable hybrid non-fragile control of a non-cooperative flexible assembly spacecraft, the method comprising the steps of:
firstly, establishing and separating an unknown uncertainty item of an inertial parameter, simultaneously considering uncertainty of a model parameter, and rewriting a non-cooperative flexible assembly spacecraft attitude dynamics model with external interference into a state space equation form;
step two, aiming at the measurement error and the fault of the actuating mechanism, constructing fault interference of the actuating mechanism and forming comprehensive interference with the unknown uncertain item of the inertial parameter and the external interference in the step one;
step three, aiming at the problem of the additive/multiplicative perturbation coexistence of the gain of the controller, defining parameters of the controller and designing a hybrid non-fragile controller;
step four, substituting the hybrid non-fragile controller into a non-cooperative flexible assembly attitude dynamics state space model containing comprehensive interference to establish a closed-loop system state space model;
step five, deducing a linear matrix inequality sufficient condition meeting the system stability according to a Lyapunov stability theory and a linear matrix inequality method to solve the controller parameters in step three and substitute the controller parameters into a controller, so that a state space model in step four is complete;
controlling the attitude angle, the attitude angular velocity and the modal displacement of the non-cooperative flexible assembly to quickly reach stability under the condition of controlling torque amplitude limiting, and ensuring certain control precision;
establishing and separating an unknown uncertainty item of an inertial parameter, considering uncertainty of a model parameter, and rewriting a non-cooperative flexible assembly spacecraft attitude dynamics model with external interference into a state space equation form; the specific process is as follows:
defining a local horizontal and local vertical coordinate system F o (X o ,Y o ,Z o ) As a reference coordinate system, the origin of the coordinate systemIn the mass center of the non-cooperative combination, the rolling axis is along the flight direction, the yawing axis points to the geocentric, and the pitching axis completes a right-hand coordinate system; defining a body coordinate system F of the combined spacecraft B (X B ,Y B ,Z B ) The origin is located at the mass center of the non-cooperative combination body, and the three coordinate axes are respectively superposed with the inertia main axis of the combination body;
the attitude kinematics equation of the flexible assembly spacecraft is as follows:
Figure FDA0003744245720000011
where phi, theta and psi denote the three components of the flexible composite spacecraft, i.e., roll, pitch and yaw attitude angles, omega, respectively 0 Indicating the angular velocity, omega, of the track on which the flexible assembly is located x 、ω y 、ω z The components of the attitude angular velocity of the flexible assembly spacecraft on three coordinate axes are respectively represented, the components are respectively roll attitude angular velocity, pitch attitude angular velocity and yaw attitude angular velocity, and the components are as follows when the high-orbit assembly is adjusted in small-angle attitude:
Figure FDA0003744245720000012
if a piezoelectric actuator is incorporated into the surface of a flexible attachment of the combination to provide the input voltage u p And thus the deformation that results in the control moment, the body of the assembly and the compliance kinetics equation can be expressed as follows:
Figure FDA0003744245720000021
wherein,
Figure FDA0003744245720000022
an inertia matrix representing the body of the assembly, ω ═ ω x ω y ω z ]Representing the attitude angular velocity vector, ω × Representative vectorThe anti-symmetric matrix of omega is,
Figure FDA0003744245720000023
representing a matrix of coupling coefficients between the rigid body and the flexible structure of the combination,
Figure FDA0003744245720000024
a modal coordinate vector representing the relative composition ontology,
Figure FDA0003744245720000025
and
Figure FDA0003744245720000026
representing a control input torque and an external disturbance torque;
Figure FDA0003744245720000027
representing a modal damping matrix, wherein
Figure FDA0003744245720000028
And Ω i I is 1,2, …, m represents damping ratio and natural frequency respectively,
Figure FDA0003744245720000029
representing the stiffness matrix and m is the number of flexural modes considered; here, T d Including gravity gradient moment, solar radiation pressure moment and aerodynamic moment u p Represents a piezoelectric input voltage, and
Figure FDA00037442457200000210
is the corresponding coupling coefficient matrix;
defining auxiliary variables
Figure FDA00037442457200000211
Obtaining:
Figure FDA00037442457200000212
substituting the second equation in the non-cooperative flexible assembly attitude dynamics equation set to obtain a rewritten equation:
Figure FDA00037442457200000213
using feedback of true values, piezoelectric input u p Expressed as:
Figure FDA00037442457200000214
in the formula F a ，F b To measure the feedback coefficient, will
Figure FDA00037442457200000215
Substituting the derivative of the auxiliary variable
Figure FDA00037442457200000216
And the flexible assembly attitude kinetic equation after rewriting is obtained:
Figure FDA00037442457200000217
Figure FDA00037442457200000218
order to
Figure FDA00037442457200000219
The two equations above can be rewritten as a state space equation form:
Figure FDA00037442457200000220
wherein the state variable is
Figure FDA00037442457200000221
Output variable
Figure FDA00037442457200000222
u(t)＝T c In order to control the torque, the torque is controlled,
Figure FDA00037442457200000223
is the preliminary comprehensive interference, coefficient matrix:
Figure FDA0003744245720000031
Figure FDA0003744245720000032
the unknown uncertain inertial parameter information is all normalized to the following coefficient matrix:
Figure FDA0003744245720000033
Figure FDA0003744245720000034
wherein,
Figure FDA0003744245720000035
J n is a nominal inertia matrix;
△A p representing model parameter uncertainty, which has a norm bound and satisfies a matching condition:
Figure FDA0003744245720000036
wherein M is 1 And N 1 Is a real constant matrix of suitable dimensions, F 1 (t) is a matrix function measurable by Leeberg;
in the second step, aiming at the measurement error and the fault of the actuating mechanism, the fault interference of the actuating mechanism is constructed and forms comprehensive interference with the unknown uncertain item of the inertial parameter and the external interference in the first step; the specific process is as follows:
improper actuation of the actuator can seriously affect the performance of the attitude control system, by letting the matrix E with full rank represent the distribution matrix of the fault signals f (t) present in the input, if E ≠ B 1 Then a process fault is indicated; if E is equal to B 1 If the fault is detected, the fault is indicated;
constructing the complex disturbance as a comprehensive disturbance:
Figure FDA0003744245720000037
wherein the matrix
Figure FDA0003744245720000038
Is a B 2 The state space equation in the step one is rewritten as:
Figure FDA0003744245720000041
wherein v (t) represents a measurement error vector;
in the third step, aiming at the problem of the additive/multiplicative perturbation coexistence of the gain of the controller, the parameters of the controller are defined, and a hybrid non-fragile controller is designed; the specific process is as follows:
when the controller has additive/multiplicative perturbation, the form of the controller is designed as follows:
Figure FDA0003744245720000042
Figure FDA0003744245720000043
is a state variable introduced by the controller,
Figure FDA0003744245720000044
is an estimate of the output variable without taking into account the measurement error, A c ，B c Is a matrix of controller coefficients with appropriate dimensions, K is a matrix of controller gains,
Figure FDA0003744245720000045
the expected value of the probability of the controller gain perturbation DeltaK occurring in the system is represented, the value range of the expected value is (0,1), the perturbation problem can be caused by controller errors and unknown dynamic characteristics of an actuating mechanism, and when the DeltaK is additive perturbation, the mathematical expression is as follows:
△K＝M 2 F 2 (t)N 2 ,||F 2 (t)||≤1
when Δ K is a multiplicative perturbation, the mathematical expression is:
△K＝M 3 F 3 (t)N 3 K,||F 3 (t)||≤1
considering the controller to have the above two disturbances at the same time, the expression is:
△K＝M 2 F 2 (t)N 2 +M 3 F 3 (t)N 3 K,||F 2 (t)||≤1,||F 3 (t)||≤1
M 2 、N 2 、M 3 、N 3 is a real constant matrix of suitable dimensions, F 2 (t)、F 3 (t) is a matrix function measurable by Leeberg;
substituting the hybrid non-fragile controller into a non-cooperative flexible assembly attitude dynamics state space model containing comprehensive interference to establish a closed-loop system state space model; the specific process is as follows:
substituting the controller obtained in the third step into the flexible assembly attitude dynamics equation containing the comprehensive interference in the second step to obtain:
Figure FDA0003744245720000046
wherein,
Figure FDA0003744245720000047
the coefficient matrix is:
Figure FDA0003744245720000051
wherein B and B 1 The definitions are the same;
when-added perturbation Δ K α Multiplication-by-sum perturbation Δ K m Matrix of uncertainty coefficients when all exist
Figure FDA0003744245720000052
The specific mathematical expression is as follows:
Figure FDA0003744245720000053
wherein σ is a constant ranging from (0, 1);
in the fifth step, according to a Lyapunov stability theory and a linear matrix inequality method, deriving a sufficient condition of a linear matrix inequality meeting the system stability to solve the controller parameters in the third step and substitute the controller parameters into a controller, so that a state space model in the fourth step is complete; the specific process is as follows:
when the additive/multiplicative perturbation exists at the same time, the state space model of the non-cooperative combination attitude system in the step two has secondary stability under the action of the controller in the step three, and the output y (t) meets the requirement of H ∞ Performance constraint, for a given constant xi>0，
Figure FDA0003744245720000054
γ>0, solving a linear matrix inequality:
Figure FDA0003744245720000055
wherein,
Figure FDA0003744245720000056
Figure FDA0003744245720000057
Figure FDA0003744245720000058
Figure FDA0003744245720000061
Figure FDA0003744245720000062
Figure FDA0003744245720000063
ξ 1 、ξ 2 given a constant greater than 0;
obtaining positive definite symmetric matrix P 11 ，Q 11 And matrix Q 21 ，
Figure FDA0003744245720000064
And
Figure FDA0003744245720000065
and further solving a controller parameter matrix in the step three:
Figure FDA0003744245720000066
Figure FDA0003744245720000067
Figure FDA0003744245720000068
substituting the closed-loop system state space equation in the step four;
in the sixth step, under the condition of controlling torque amplitude limiting, the attitude angle, the attitude angular velocity and the modal displacement of the non-cooperative flexible assembly are controlled to be stable quickly, and certain control precision is ensured; the specific process is as follows:
due to physical and safety constraints, there are constraints on the actuators, saturation of the control inputs, negative effects on the stability and performance of the attitude control system designed for "ideal" situations, for a positive scalar λ:
||u||<λ
a two-norm saturation value representing a control input is λ; and adding a saturation amplitude limit to the controller obtained in the step five, namely the actual control torque can be described as:
sat(u i＝1,2,3 (t))＝sign(u i (t))min{|u i (t)|,u mi }
wherein u is mi Is the upper limit of the control torque provided by the actuator.
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