CN113220003A - 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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CN113220003A
CN113220003A CN202110350727.2A CN202110350727A CN113220003A CN 113220003 A CN113220003 A CN 113220003A CN 202110350727 A CN202110350727 A CN 202110350727A CN 113220003 A CN113220003 A CN 113220003A
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CN113220003B (en
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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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    • G05D1/08—Control of attitude, i.e. control of roll, pitch, or yaw
    • G05D1/0808—Control of attitude, i.e. control of roll, pitch, or yaw specially adapted for aircraft
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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, 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 of the space targets is influenced by complex disturbance, the space targets are typical non-cooperative targets, the capture processing of the space targets has important significance for the sustainable development of 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:
the method comprises the steps of firstly, constructing and separating an unknown uncertainty item of an inertia 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.
And step two, aiming at the measurement error and the fault of the actuating mechanism, constructing a fault interference item of the actuating mechanism and forming a comprehensive interference item with the unknown uncertain item of the inertia parameters and the external interference moment item in the step one.
And step three, aiming at the problem of coexistence of gain addition/multiplication perturbation of the controller, defining controller parameters and designing a hybrid non-fragile controller.
And step four, substituting the hybrid non-fragile controller into a non-cooperative flexible assembly attitude dynamics state space model containing the comprehensive interference item to establish a closed-loop system state space model.
And step five, deducing sufficient conditions of the linear matrix inequality meeting the system stability according to the Lyapunov stability theory and the linear matrix inequality method to solve the controller parameters in the step three and substitute the controller parameters into the controller, so that the state space model in the 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 unknown uncertainty of inertial parameters, uncertainty of model parameters, external interference, measurement errors, faults of an actuating mechanism, input saturation and coexistence of addition type/multiplication type gain perturbation of the controller, the uncooperative flexible assembly spacecraft can quickly reach a high-precision and high-stability state, the stability 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 the 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 of 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 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 variation curve of the attitude angle of the non-cooperative flexible assembly spacecraft under the action of the hybrid non-fragile controller,
Figure BDA0003002305840000021
theta and psi respectively represent a rolling angle, a yaw angle and a pitch angle of the spacecraft, and rad represents the unit of an 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, omegax，ωy，ωzRespectively 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 invention1，η2，η3，η4Four 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 of the present invention under the influence of a hybrid non-fragile controller, the accuracy being represented by a two-norm of a modal displacement vector;
FIG. 8 is a graph showing the variation of the control torque according to the present invention, ux，uy，uzRespectively 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 first embodiment is as follows: the embodiment is described by combining with figure 1, and the attitude stabilization hybrid non-fragile control method of the non-cooperative flexible assembly spacecraft of the embodiment is characterized in that,
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 inertia parameter by introducing a nominal inertia matrix, considering uncertainty of a model parameter, and rewriting a non-cooperative flexible assembly spacecraft attitude dynamics equation with external disturbance moment (such as aerodynamic moment, gravity gradient moment and geomagnetic moment) into a state space form;
step two, aiming at the measurement error and the fault of the actuating mechanism, constructing a fault interference item of the actuating mechanism and forming a comprehensive interference item with the unknown uncertain item of the inertia parameters and the external interference moment item in the step one;
step three, when the controller has additive perturbation or multiplicative perturbation, defining controller parameters and designing a hybrid non-fragile controller;
substituting the controller model into a flexible spacecraft attitude dynamics state space model containing a comprehensive interference item, and establishing a closed-loop control state space model;
and step five, solving the controller parameters in the step three and substituting the controller parameters into the controller model according to the linear matrix inequality principle and the Lyapunov stability principle to ensure that the state space model in the step four is complete.
And step six, under the condition that the control input amplitude limit is 15Nm, controlling the attitude angle, the attitude angular velocity and the modal displacement of the non-cooperative flexible combined spacecraft to be stable within 150s, and enabling the stability precision of the attitude angle to be less than 0.01 radian per second, the stability precision of the attitude angular velocity to be less than 0.01 radian per second and the stability precision of the modal displacement to be less than 0.01.
The second embodiment is as follows: the difference between this embodiment and the first embodiment is:
2. the non-cooperative flexible assembly spacecraft attitude stabilization hybrid non-fragile control method according to claim 1, characterized by comprising the following steps: the method comprises the following steps of firstly, constructing and separating an unknown uncertainty item of an inertia parameter, simultaneously considering uncertainty of a model parameter, and rewriting a flexible assembly attitude kinetic equation with external disturbance moment (such as aerodynamic moment, gravity gradient moment and geomagnetic moment) into a state space form, wherein the specific process comprises the following steps:
defining a local horizontal and local vertical coordinate system Fo(Xo,Yo,Zo) (LVLH) as a reference coordinate system with an origin at the non-cooperative composite centroid, a roll axis along the flight direction, a yaw axis pointing towards the geocentric, and a pitch axis completing the right hand coordinate system. Defining a body coordinate system F of the combined spacecraftB(XB,YB,ZB) 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 BDA0003002305840000031
wherein,
Figure BDA0003002305840000041
theta and psi represent the three components of the flexible composite spacecraft, i.e., roll, pitch and yaw attitude angles, omega, respectively0Indicating the angular velocity of the track on which the flexible assembly is located. When high rail assembly carries out the small-angle attitude adjustment, have:
Figure BDA0003002305840000042
if a piezoelectric actuator is incorporated into the surface of a flexible attachment of the combination to provide the input voltage upAnd 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 BDA0003002305840000043
wherein,
Figure BDA0003002305840000044
an inertia matrix representing the body of the assembly, ω ═ ωx ωy ωz]Representing attitude angular velocity vectors, including roll, pitch, and yaw attitude angle rates of change,
Figure BDA0003002305840000045
representing a matrix of coupling coefficients between the rigid body and the flexible structure of the combination,
Figure BDA0003002305840000046
a modal coordinate vector representing the relative composition ontology,
Figure BDA0003002305840000047
and
Figure BDA0003002305840000048
representing a control input torque and an external disturbance torque;
Figure BDA0003002305840000049
representing a modal damping matrix, wherein
Figure BDA00030023058400000410
And ΩiI is 1,2, …, m represents damping ratio and natural frequency respectively,
Figure BDA00030023058400000411
the stiffness matrix is represented and m is the number of flexural modes considered. Here, TdIncluding gravity gradient moment, solar radiation pressure moment and aerodynamic moment upRepresents a piezoelectric input voltage, and
Figure BDA00030023058400000412
is the corresponding coupling coefficient matrix.
Defining auxiliary variables
Figure BDA00030023058400000413
Obtaining:
Figure BDA00030023058400000414
substituting the second equation in the non-cooperative flexible assembly attitude dynamics equation set to obtain a rewritten equation:
Figure BDA00030023058400000415
using feedback of true values, piezoelectric input upExpressed as:
Figure BDA00030023058400000416
in the formula Fa，FbTo measure the feedback coefficient. Will be provided with
Figure BDA00030023058400000417
Substituting the derivative of the auxiliary variable
Figure BDA00030023058400000421
And the flexible assembly attitude kinetic equation after rewriting is obtained:
Figure BDA00030023058400000418
Figure BDA00030023058400000419
order to
Figure BDA00030023058400000420
The two equations above can be rewritten as a state space form:
Figure BDA0003002305840000051
wherein the state variable is
Figure BDA0003002305840000052
Output variable
Figure BDA0003002305840000053
u(t)＝TcIn order to control the torque, the torque is controlled,
Figure BDA0003002305840000054
is the combined interference. Coefficient matrix:
Figure BDA0003002305840000055
Figure BDA0003002305840000056
C＝I6+2m
the unknown inertial parameter information is all normalized to the following coefficient matrix:
Figure BDA0003002305840000057
Figure BDA0003002305840000058
wherein
Figure BDA0003002305840000059
JnIs a nominal inertia matrix.
△ApRepresenting model parameter uncertainty (except inertial uncertainty), which has a norm bound and satisfies the matching condition:
Figure BDA00030023058400000510
wherein M is1And N1Is a real constant matrix of suitable dimensions, F1(t) is a measurable matrix function of Leeberg.
Other steps and parameters are the same as those in the first embodiment.
The third concrete implementation mode: the present embodiment differs from the first or second embodiment in that:
3. the non-cooperative flexible assembly spacecraft attitude stabilization hybrid non-fragile control method of claim 2, characterized by comprising the following steps: in the second step, aiming at the conditions of measurement errors and actuator faults, an actuator fault interference item is constructed and forms a comprehensive interference item together with the inertial parameter unknown uncertain item and the external interference moment item 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, allowing E (its structure and B) with full rank1Similarly) represents the distribution matrix of the fault signals f (t) present in the input. If E ≠ B1Then a process fault is indicated; if E is equal to B1Then an actuator failure is indicated.
And constructing the complex disturbance factors into comprehensive interference:
Figure BDA0003002305840000061
wherein the matrix
Figure BDA0003002305840000062
Is B2The state space equation in the step one is rewritten as:
Figure BDA0003002305840000063
where v (t) represents the measurement error.
Other steps and parameters are the same as those in the first or second embodiment.
The fourth concrete implementation mode: the difference between this embodiment mode and one of the first to third embodiment modes is:
4. the non-cooperative flexible assembly spacecraft attitude stabilization hybrid non-fragile control method of claim 3, characterized by comprising the following steps: in the third step, when the addition/multiplication perturbation exists in the controller at the same time, the controller parameters 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 BDA0003002305840000064
Figure BDA0003002305840000065
is a state variable introduced by the controller,
Figure BDA0003002305840000066
is an estimate of the output variable without taking into account the measurement error, Ac、BcIs a matrix of controller coefficients with appropriate dimensions, and K is a matrix of controller gains. Controller errors and unknown actuator dynamics can lead to perturbation problems, when Δ K is additive perturbation, with the mathematical expression Δ K being equal to M2F2(t)N2,||F2(t) | < 1, when Δ K is multiplicative perturbation, the mathematical expression is that Δ K equals M3F3(t)N3K,||F3(t)||≤1。
Considering the controller simultaneously, the two perturbation problems exist, and the expression is as follows:
△K＝M2F2(t)N2+M3F3(t)N3K,||F2(t)||≤1,||F3(t)||≤1
M2、N2、M3、N3is a real constant matrix of suitable dimensions, F2(t)、F3(t) is a measurable matrix function of Leeberg.
Other steps and parameters are the same as those in one of the first to third embodiments.
The fifth concrete implementation mode: the difference between this embodiment and one of the first to fourth embodiments is:
5. the non-cooperative flexible assembly spacecraft attitude stabilization hybrid non-fragile control method of claim 4, characterized in that: substituting the controller into a non-cooperative flexible assembly spacecraft attitude dynamics state space equation containing a comprehensive interference item, and establishing a closed-loop attitude control 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 item in the second step to obtain:
Figure BDA0003002305840000071
wherein
Figure BDA0003002305840000072
B1＝B2B, there are:
Figure BDA0003002305840000073
y(t)＝Cx(t)＝[C 0]ζ(t)
the coefficient matrix is:
Figure BDA0003002305840000074
when-added perturbation Δ KαMultiplication-by-sum perturbation Δ KmCo-existence time coefficient matrix
Figure BDA0003002305840000075
The specific mathematical expression is as follows:
Figure BDA0003002305840000076
where σ ∈ (0,1) is a given constant.
Will matrix
Figure BDA0003002305840000077
Writing into:
Figure BDA0003002305840000078
the control moment u (t) is written as:
Figure BDA0003002305840000079
other steps and parameters are the same as in one of the first to fourth embodiments.
The sixth specific implementation mode: the difference between this embodiment and one of the first to fifth embodiments is:
6. the non-cooperative flexible assembly spacecraft attitude stabilization hybrid non-fragile control method of claim 5, characterized in that: 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 BDA0003002305840000081
γ>0, solving a linear matrix inequality:
Figure BDA0003002305840000082
wherein
Figure BDA0003002305840000083
Figure BDA0003002305840000084
Figure BDA0003002305840000085
Figure BDA0003002305840000086
Figure BDA0003002305840000087
Figure BDA0003002305840000088
Obtaining positive definite symmetric matrix P11，Q11And matrix Q21，
Figure BDA0003002305840000089
And
Figure BDA00030023058400000810
and further solving a controller parameter matrix in the step three:
Figure BDA00030023058400000811
Figure BDA00030023058400000812
Figure BDA00030023058400000813
and substituting the closed-loop system state space equation in the step four.
Other steps and parameters are the same as those in one of the first to fifth embodiments.
The seventh embodiment: the difference between this embodiment and one of the first to sixth embodiments is:
7. the non-cooperative flexible assembly spacecraft attitude stabilization hybrid non-fragile control method of claim 6, characterized in that: under the condition of controlling input amplitude limiting, the attitude angle, the attitude angular velocity and the modal displacement of the flexible combined spacecraft are controlled to be stable quickly, and certain precision is ensured; the specific process is as follows:
due to physical and safety constraints, there are constraints on the actuators and saturation of control inputs, which negatively impacts 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(ui＝1,2,3(t))＝sign(ui(t))min{|ui(t)|,umi}
wherein u ismiIs the upper limit of the control torque provided by the actuator.
Other steps and parameters are the same as those in one of the first to sixth embodiments.
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 BDA0003002305840000091
order to
Figure BDA0003002305840000092
The two equations above can be rewritten as a state space form:
Figure BDA0003002305840000093
wherein the state variable is
Figure BDA0003002305840000094
Output variable
Figure BDA0003002305840000095
u(t)＝TcIn order to control the torque, the torque is controlled,
Figure BDA0003002305840000096
is an external disturbance. Coefficient matrix:
Figure BDA0003002305840000097
Figure BDA0003002305840000098
C＝I6+2m
the unknown uncertain inertial parameter information is all normalized to the following coefficient matrix:
Figure BDA0003002305840000101
Figure BDA0003002305840000102
wherein
Figure BDA0003002305840000103
JnIs a nominal inertia matrix.
△ApRepresenting the uncertainty of the model parameters (except for inertial uncertainty), which has a norm bound and satisfies the matching condition:
Figure BDA0003002305840000104
step two: and (3) aiming at the conditions of measurement errors and actuator faults, constructing an actuator fault interference item and forming a comprehensive interference item with the inertial parameter unknown uncertain item and the external interference moment item in the step one.
Constructing the complex disturbance as a comprehensive disturbance:
Figure BDA0003002305840000109
substituting the state space model in the step one:
Figure BDA0003002305840000105
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 BDA0003002305840000106
Figure BDA0003002305840000107
is a state variable introduced by the controller,
Figure BDA0003002305840000108
is an estimate of the output variable without taking into account the measurement error, Ac、BcIs a controller parameter matrix with appropriate dimensions, and K is a controller gain matrix. Considering the existence of the above two types of perturbation of the controller, the expression is:
△K＝M2F2(t)N2+M3F3(t)N3K,||F2(t)||≤1,||F3(t)||≤1
M2、N2、M3、N3is a real constant matrix of suitable dimensions, F2(t)、F3(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 a comprehensive interference term 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 item in the second step to obtain:
Figure BDA0003002305840000111
wherein:
Figure BDA0003002305840000112
the coefficient matrix is:
Figure BDA0003002305840000113
when-added perturbation Δ KαMultiplication-by-sum perturbation Δ KmCoexistence ofTime uncertainty coefficient matrix
Figure BDA0003002305840000114
The specific mathematical expression is as follows:
Figure BDA0003002305840000115
where σ ∈ (0,1) is a given constant.
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 BDA0003002305840000116
γ>0, solving a linear matrix inequality:
Figure BDA0003002305840000121
wherein
Figure BDA0003002305840000122
Figure BDA0003002305840000123
Figure BDA0003002305840000124
Figure BDA0003002305840000125
Figure BDA0003002305840000126
Figure BDA0003002305840000127
Obtaining positive definite symmetric matrix P11，Q11And matrix Q21，
Figure BDA0003002305840000128
And
Figure BDA0003002305840000129
and further solving a controller parameter matrix in the step three:
Figure BDA00030023058400001210
Figure BDA00030023058400001211
Figure BDA00030023058400001212
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(ui＝1,2,3(t))＝sign(ui(t))min{|ui(t)|,umi}
wherein u ismiIs 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 BDA00030023058400001213
the unknown uncertain inertia matrix is: Δ J ═ J (0.05+0.01sin (tt)) Jn
The number of flexible modes considered m-4
Coupling coefficient matrix between rigid body and flexible structure:
Figure BDA0003002305840000131
damping ratio xi1 ξ2 ξ3 ξ4]＝[0.005607 0.008620 0.01283 0.02516]
Natural frequency [ omega ]1 Ω2 Ω3 Ω4]＝[0.7681 1.1038 1.8733 2.5496]
Coupling matrix:
Figure BDA0003002305840000132
feedback coefficient matrix: fa＝[3.1533 -0.5714 5.3674 9.3389]，Fb＝[1.0976 0.1965 1.8086 3.0873]
External environment moment:
Figure BDA0003002305840000133
the Lenberg matrix function and its corresponding real constant matrix:
M1＝0.01×[8 11 13 15 16 -18 8 11 13 15 16 18 8 11]T，
N1＝0.01×[1 2 3 4 2 10 1 2 3 4 2 10 1 2]，F1(t)＝sin(0.11πt)
M2＝0.1×ones(3,1)N2＝0.01×ones(1,14)，F2(t)＝sin(0.11πt+π/4)
M3＝0.1×ones(3,1)N3＝0.01×ones(1,3)，F3(t)＝cos(0.11πt)
initial value of angle: Θ (0) ═ 0.18,0.15, -0.15]Trad
Initial value of angular velocity: ω (0) [ -0.02, -0.02,0.02]Trad/s
Initial value of modal displacement:
Figure BDA0003002305840000134
initial value of modal displacement derivative:
Figure BDA0003002305840000135
actuator fault signal:
Figure BDA0003002305840000136
associated normal numbers:
Figure BDA0003002305840000137
ξ1＝0.025,ξ2＝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. ofm1＝um2＝um3＝15Nm
Solving the linear matrix inequality with the LMI toolkit yields:
Figure BDA0003002305840000141
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 execution 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 (7)

1. A non-cooperative flexible assembly spacecraft attitude stabilization hybrid non-fragile control method is characterized by comprising the following steps: a hybrid non-fragile attitude stabilization control method of a flexible assembly spacecraft is specifically carried out according to the following steps:
the method comprises the steps of firstly, constructing and separating an unknown uncertainty item of an inertia 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.
And step two, aiming at the measurement error and the fault of the actuating mechanism, constructing a fault interference item of the actuating mechanism and forming a comprehensive interference item with the unknown inertial parameter item, the uncertain model parameter interference item and the external interference moment item in the step one.
And step three, aiming at the problem of coexistence of gain addition/multiplication perturbation of the controller, defining controller parameters and designing a hybrid non-fragile controller.
And step four, substituting the hybrid non-fragile controller into a non-cooperative flexible assembly attitude dynamics state space model containing the comprehensive interference item to establish a closed-loop system state space model.
And step five, deducing sufficient conditions of the linear matrix inequality meeting the system stability according to the Lyapunov stability theory and the linear matrix inequality method to solve the controller parameters in the step three and substitute the controller parameters into the controller, so that the state space model in the 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.
2. The non-cooperative flexible assembly spacecraft attitude stabilization hybrid non-fragile control method according to claim 1, characterized by comprising the following steps: the method comprises the following steps of firstly, constructing and separating an unknown uncertainty item of an inertia parameter, simultaneously considering uncertainty of a model parameter, and rewriting a non-cooperative flexible assembly attitude dynamics equation with external disturbance moment into a state space equation form, wherein the specific process comprises the following steps:
defining a local horizontal and local vertical coordinate system Fo(Xo,Yo,Zo) (LVLH) as a reference coordinate system with an origin at the non-cooperative composite centroid, a roll axis along the flight direction, a yaw axis pointing towards the geocentric, and a pitch axis completing the right hand coordinate system. Defining a body coordinate system F of the combined spacecraftB(XB,YB,ZB) 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 FDA0003002305830000011
wherein,
Figure FDA0003002305830000012
theta and psi represent the three components of the flexible composite spacecraft, i.e., roll, pitch and yaw attitude angles, omega, respectively0Indicating the angular velocity of the track on which the flexible assembly is located. When high rail assembly carries out the small-angle attitude adjustment, have:
Figure FDA0003002305830000013
if a piezoelectric actuator is incorporated into the surface of a flexible attachment of the combination to provide the input voltage upAnd 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 FDA0003002305830000021
wherein,
Figure FDA0003002305830000022
an inertia matrix representing the body of the assembly, ω ═ ωx ωy ωz]Representing attitude angular velocity vectors, including roll, pitch, and yaw attitude angle rates of change,
Figure FDA0003002305830000023
representing a matrix of coupling coefficients between the rigid body and the flexible structure of the combination,
Figure FDA0003002305830000024
a modal coordinate vector representing the relative composition ontology,
Figure FDA0003002305830000025
and
Figure FDA0003002305830000026
representing a control input torque and an external disturbance torque;
Figure FDA0003002305830000027
representing a modal damping matrix, wherein
Figure FDA0003002305830000028
And ΩiI is 1,2, …, m represents damping ratio and natural frequency respectively,
Figure FDA0003002305830000029
the stiffness matrix is represented and m is the number of flexural modes considered. Here, TdIncluding gravity gradient moment, solar radiation pressure moment and aerodynamic moment upRepresents a piezoelectric input voltage, and
Figure FDA00030023058300000210
is the corresponding coupling coefficient matrix.
Defining auxiliary variables
Figure FDA00030023058300000211
Obtaining:
Figure FDA00030023058300000212
substituting the second equation in the non-cooperative flexible assembly attitude dynamics equation set to obtain a rewritten equation:
Figure FDA00030023058300000213
using feedback of true values, piezoelectric input upExpressed as:
Figure FDA00030023058300000214
in the formula Fa，FbTo measure the feedback coefficient. Will be provided with
Figure FDA00030023058300000215
Substituting the derivative of the auxiliary variable
Figure FDA00030023058300000216
And the flexible assembly attitude kinetic equation after rewriting is obtained:
Figure FDA00030023058300000217
Figure FDA00030023058300000218
order to
Figure FDA00030023058300000219
The two equations above can be rewritten as a state space form:
Figure FDA00030023058300000220
wherein the state variable is
Figure FDA0003002305830000031
Output variable
Figure FDA0003002305830000032
u(t)＝TcIn order to control the torque, the torque is controlled,
Figure FDA0003002305830000033
is an external disturbance. Coefficient matrix：
Figure FDA0003002305830000034
Figure FDA0003002305830000035
C＝I6+2m
The unknown uncertain inertial parameter information is all normalized to the following coefficient matrix:
Figure FDA0003002305830000036
Figure FDA0003002305830000037
wherein
Figure FDA0003002305830000038
JnIs a nominal inertia matrix.
△ApRepresenting model parameter uncertainty (except inertial uncertainty), which has a norm bound and satisfies the matching condition:
Figure FDA0003002305830000039
wherein M is1And N1Is a real constant matrix of suitable dimensions, F1(t) is a measurable matrix function of Leeberg.
3. The method of claim 2, wherein the non-cooperative flexible assembly attitude stabilization hybrid non-fragile control method comprises: in the second step, aiming at the conditions of measurement errors and actuator faults, an actuator fault interference item is constructed and forms a comprehensive interference item together with the unknown inertial parameter item and the external interference moment item 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, allowing the matrix E (its structure and B) with full rank1Similarly) represents the distribution matrix of the fault signals f (t) present in the input. If E ≠ B1Then a process fault is indicated; if E is equal to B1Then an actuator failure is indicated.
Constructing the complex disturbance as a comprehensive disturbance:
Figure FDA0003002305830000041
wherein the matrix
Figure FDA0003002305830000042
Is B2The state space equation in the step one is rewritten as:
Figure FDA0003002305830000043
where v (t) represents the measurement error vector.
4. The non-cooperative flexible assembly spacecraft attitude stabilization hybrid non-fragile control method of claim 3, characterized by comprising the following steps: in the third step, when the addition/multiplication perturbation exists in the controller at the same time, the controller parameters 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 FDA0003002305830000044
Figure FDA0003002305830000045
is a state variable introduced by the controller,
Figure FDA0003002305830000046
is an estimate of the output variable without taking into account the measurement error, Ac，BcIs a matrix of controller coefficients with appropriate dimensions, and K is a matrix of controller gains. Controller errors and unknown actuator dynamics can cause perturbation problems, and when Δ K is an additive perturbation, the mathematical expression is:
△K＝M2F2(t)N2,||F2(t)||≤1
when Δ K is a multiplicative perturbation, the mathematical expression is:
△K＝M3F3(t)N3K,||F3(t)||≤1
considering the existence of the two disturbances of the controller at the same time, the expression is:
△K＝M2F2(t)N2+M3F3(t)N3K,||F2(t)||≤1,||F3(t)||≤1
M2、N2、M3、N3is a real constant matrix of suitable dimensions, F2(t)、F3(t) is a measurable matrix function of Leeberg.
5. The non-cooperative flexible assembly spacecraft attitude stabilization hybrid non-fragile control method of claim 4, characterized in that: substituting the controller model into a non-cooperative flexible assembly attitude dynamics state space equation containing a comprehensive interference item, and establishing a closed-loop attitude control system state space equation; 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 item in the second step to obtain:
Figure FDA0003002305830000051
wherein:
Figure FDA0003002305830000052
the coefficient matrix is:
Figure FDA0003002305830000053
when-added perturbation Δ KαMultiplication-by-sum perturbation Δ KmMatrix of uncertainty coefficients when all exist
Figure FDA0003002305830000054
The specific mathematical expression is as follows:
Figure FDA0003002305830000055
where σ ∈ (0,1) is a given constant.
6. The non-cooperative flexible assembly spacecraft attitude stabilization hybrid non-fragile control method of claim 5, characterized in that: deducing a linear matrix inequality sufficient condition meeting the system stability in the step five, solving the controller parameters in the step three and substituting the controller parameters into the hybrid non-fragile controller to complete the state space equation in the step four; 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 FDA0003002305830000056
γ>0, solving a linear matrix inequality:
Figure FDA0003002305830000061
wherein
Figure FDA0003002305830000062
Figure FDA0003002305830000063
Figure FDA0003002305830000064
Figure FDA0003002305830000065
Figure FDA0003002305830000066
Figure FDA0003002305830000067
Obtaining positive definite symmetric matrix P11，Q11And matrix Q21，
Figure FDA0003002305830000068
And
Figure FDA0003002305830000069
and further solving a controller parameter matrix in the step three:
Figure FDA00030023058300000610
Figure FDA00030023058300000611
Figure FDA00030023058300000612
and substituting the closed-loop system state space equation in the step four.
7. The non-cooperative flexible assembly spacecraft attitude stabilization hybrid non-fragile control method of claim 6, characterized in that: under the condition of control input saturation, 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; the specific process is as follows:
due to physical and safety constraints, there are constraints on the actuators and saturation of control inputs, which negatively impacts 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(ui＝1,2,3(t))＝sign(ui(t))min{|ui(t)|,umi}
wherein u ismiIs the upper limit of the control torque provided by the actuator.
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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113859588A (en) * 2021-09-30 2021-12-31 西北工业大学 Spacecraft attitude/fault/interference cooperative observation and fault-tolerant anti-interference control method

Citations (9)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN102073280A (en) * 2011-01-13 2011-05-25 北京科技大学 Fuzzy singular perturbation modeling and attitude control method for complex flexible spacecraft
CN103412571A (en) * 2013-07-22 2013-11-27 西北工业大学 Spacecraft relative posture control method based on feedback linearization technology
CN104406598A (en) * 2014-12-11 2015-03-11 南京航空航天大学 Non-cooperative spacecraft attitude estimation method based on virtual sliding mode control
CN105068425A (en) * 2015-08-12 2015-11-18 哈尔滨工业大学 State feedback robustnon-fragile control method applicable for determination of agile satellite postures
CN106628257A (en) * 2016-09-28 2017-05-10 西北工业大学 Method for keeping relative motion orbit of near-earth spacecraft in earth's perturbation gravitational field
US9663252B1 (en) * 2016-12-07 2017-05-30 Beihang University Method for attitude controlling based on finite time friction estimation for flexible spacecraft
CN106814746A (en) * 2017-03-24 2017-06-09 哈尔滨工业大学 A kind of spacecraft appearance rail integration Backstepping Tracking Control
CN108804846A (en) * 2018-06-20 2018-11-13 哈尔滨工业大学 A kind of data-driven attitude controller design method of noncooperative target assembly spacecraft
CN109164816A (en) * 2018-07-25 2019-01-08 西北工业大学 A kind of noncooperative target Attitude tracking control method of controller failure and saturated characteristic

Patent Citations (9)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN102073280A (en) * 2011-01-13 2011-05-25 北京科技大学 Fuzzy singular perturbation modeling and attitude control method for complex flexible spacecraft
CN103412571A (en) * 2013-07-22 2013-11-27 西北工业大学 Spacecraft relative posture control method based on feedback linearization technology
CN104406598A (en) * 2014-12-11 2015-03-11 南京航空航天大学 Non-cooperative spacecraft attitude estimation method based on virtual sliding mode control
CN105068425A (en) * 2015-08-12 2015-11-18 哈尔滨工业大学 State feedback robustnon-fragile control method applicable for determination of agile satellite postures
CN106628257A (en) * 2016-09-28 2017-05-10 西北工业大学 Method for keeping relative motion orbit of near-earth spacecraft in earth's perturbation gravitational field
US9663252B1 (en) * 2016-12-07 2017-05-30 Beihang University Method for attitude controlling based on finite time friction estimation for flexible spacecraft
CN106814746A (en) * 2017-03-24 2017-06-09 哈尔滨工业大学 A kind of spacecraft appearance rail integration Backstepping Tracking Control
CN108804846A (en) * 2018-06-20 2018-11-13 哈尔滨工业大学 A kind of data-driven attitude controller design method of noncooperative target assembly spacecraft
CN109164816A (en) * 2018-07-25 2019-01-08 西北工业大学 A kind of noncooperative target Attitude tracking control method of controller failure and saturated characteristic

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
刘闯: "航天器姿态鲁棒控制方法研究", 《中国优秀博硕士学位论文全文数据库(博士)工程科技Ⅱ辑》 *

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113859588A (en) * 2021-09-30 2021-12-31 西北工业大学 Spacecraft attitude/fault/interference cooperative observation and fault-tolerant anti-interference control method
CN113859588B (en) * 2021-09-30 2023-07-25 西北工业大学 Spacecraft collaborative observation and fault-tolerant anti-interference control method

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