CN115079574A - Distributed fault compensation method for flexible hypersonic aircraft - Google Patents

Distributed fault compensation method for flexible hypersonic aircraft Download PDF

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CN115079574A
CN115079574A CN202210844698.XA CN202210844698A CN115079574A CN 115079574 A CN115079574 A CN 115079574A CN 202210844698 A CN202210844698 A CN 202210844698A CN 115079574 A CN115079574 A CN 115079574A
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CN115079574B (en
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赵冬
任璐
吴巧云
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Anhui University
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Abstract

The invention discloses a distributed fault compensation control method for a flexible hypersonic aerocraft, which comprises the following steps: according to the structure and flight environment of the aircraft, a T-S fuzzy control technology is adopted to carry out piecewise linearization on the ordinary differential system; establishing a longitudinal dynamic system model of the flexible hypersonic aircraft under the distributed fault based on a partial differential system; constructing reversible state transformation, and transmitting all distributed faults to the boundary of a partial differential system to obtain an equivalent dynamic system model; a T-S fuzzy fault-tolerant control framework is established, and the state of the aircraft is consistent, bounded and stable under the distributed fault; introduction of robust performance indicators
Figure 437179DEST_PATH_IMAGE001
And the condition of the aircraft is gradually stabilized under the distributed fault. The distributed fault compensation control method provided by the invention can ensure that the aircraft can still complete a set flight task when a distributed fault occurs, and the reliability and safety of the operation of the aircraft are improved.

Description

Distributed fault compensation method for flexible hypersonic aircraft
Technical Field
The invention belongs to the technical field of automatic control, and particularly relates to a distributed fault compensation method for a flexible hypersonic aircraft.
Background
With the development and progress of aerospace technologies, new aerospace technologies have emerged in succession. The novel aviation application systems have the characteristics of multivariable, strong coupling, fast time variation, strong nonlinearity and the like due to the structural characteristics and the complex working environment of the novel aviation application systems. In particular, when a system component fails, the system may have large parameter or structure uncertainties, which may cause abrupt changes in the system dynamics. If the controller cannot effectively cope with dynamic sudden changes of the system, the system performance is reduced, even the system is unstable, and safety accidents are caused. When the system fails, its dynamic characteristics will change. Therefore, how to enhance the capability of the control system to effectively handle dynamic mutation to improve the safety performance of the system becomes a research hotspot.
At present, the fault-tolerant control method for the flexible hypersonic aircraft mainly focuses on the following aspects: (1) actuator fault compensation based on a disturbance observer, (2) actuator fault compensation based on adaptive control; (3) and actuator fault compensation design based on a backstepping method technology and the like. In the conventional fault compensation design process, the flexible motion of the hypersonic aircraft is generally described by a simplified second-order ordinary differential system, the accuracy and complexity of a system model are reduced, the actual dynamic characteristics of the hypersonic aircraft are difficult to describe, in addition, the fault-tolerant control problem of the hypersonic aircraft under the fault of an actuator is solved through the research, and the problem of distributed fault compensation is lack of research.
Disclosure of Invention
Aiming at a longitudinal dynamics system of a flexible hypersonic aircraft under distributed faults, the invention provides a distributed fault compensation method of the flexible hypersonic aircraft, aiming at overcoming the defects in the prior art, and the fault compensation method is based on a control separation technology and a T-S fuzzy control technology, so that the aircraft can still have expected closed-loop stability and output tracking performance when the distributed faults occur, and the performance of an aircraft control system is improved.
In order to achieve the purpose, the invention adopts the following technical scheme: a distributed fault compensation control method for a flexible hypersonic aircraft specifically comprises the following steps:
step 1: according to the structure and flight environment of the aircraft, a distribution parameter system in which an ordinary differential system and a partial differential system are mutually coupled is adopted to depict the longitudinal dynamics system characteristic of the aircraft, and a T-S fuzzy control technology is adopted to carry out piecewise linearization on the ordinary differential system; establishing a longitudinal dynamic system model of the flexible hypersonic aircraft under the distributed fault based on a partial differential system;
and 2, step: according to the longitudinal dynamic system model of the flexible hypersonic aircraft under the distributed faults, which is established in the step 1, based on structural characteristic analysis of the distributed faults, the internal dynamic state of the distributed faults existing in the partial differential system is obtained, reversible state transformation is constructed, and the distributed faults are all transmitted to the boundary of the partial differential system to obtain an equivalent dynamic system model;
and 3, step 3: establishing a T-S fuzzy fault-tolerant control framework, obtaining a control gain matrix by adopting a linear matrix inequality method based on the equivalent dynamics system model obtained in the step 2, and inputting the control gain matrix into the established T-S fuzzy fault-tolerant control framework to realize the consistent bounded stability of the state of the aircraft under the distributed fault;
and 4, step 4: introduction of robust performance indicators
Figure 110699DEST_PATH_IMAGE001
And designing a robust T-S fuzzy fault-tolerant control mechanism based on control separation based on the T-S fuzzy fault-tolerant control framework in the step 3, establishing a linear matrix inequality to obtain a control gain matrix, and inputting the control gain matrix into the established T-S fuzzy fault-tolerant control framework to realize gradual stabilization of the state of the aircraft under the distributed fault.
Further, step 1 comprises the following substeps:
step 11: the rigid motion of the aircraft is determined by the flying height according to the structure and flying environment of the aircraft
Figure 621315DEST_PATH_IMAGE002
Flying speed
Figure 869893DEST_PATH_IMAGE003
Angle of attack
Figure 609310DEST_PATH_IMAGE004
Go downElevation angle
Figure 892524DEST_PATH_IMAGE005
Angular velocity of pitch
Figure 308462DEST_PATH_IMAGE006
The system consists of five flight states, and rigid motion is expressed as a group of nonlinear ordinary differential systems:
Figure 44337DEST_PATH_IMAGE007
wherein,
Figure 85980DEST_PATH_IMAGE008
for the rate of change of the flying height,
Figure 223700DEST_PATH_IMAGE009
as is the rate of change of the flying speed,
Figure 810539DEST_PATH_IMAGE010
to be the rate of change of the angle of attack,
Figure 33710DEST_PATH_IMAGE011
is the rate of change of the pitch angle,
Figure 114930DEST_PATH_IMAGE012
the rate of change of pitch angle velocity, g is the gravitational acceleration,m 0 is the mass of the aircraft and is,
Figure 107157DEST_PATH_IMAGE013
is the lift force of the aircraft,
Figure 130476DEST_PATH_IMAGE014
，
Figure 840943DEST_PATH_IMAGE015
in order to be a coefficient of lift force,
Figure 958810DEST_PATH_IMAGE016
；
Figure 71122DEST_PATH_IMAGE017
is the resistance of the aircraft and is the resistance of the aircraft,
Figure 999764DEST_PATH_IMAGE018
，
Figure 197527DEST_PATH_IMAGE019
in order to be a coefficient of resistance,
Figure 620549DEST_PATH_IMAGE020
；
Figure 446423DEST_PATH_IMAGE021
is the thrust of the aircraft and is,
Figure 952491DEST_PATH_IMAGE022
，
Figure 480293DEST_PATH_IMAGE023
in order to be the thrust coefficient,
Figure 831640DEST_PATH_IMAGE024
，
Figure 918544DEST_PATH_IMAGE025
is the throttle opening of the aircraft;
Figure 188989DEST_PATH_IMAGE026
is the pitching moment of the aircraft and,
Figure 971131DEST_PATH_IMAGE027
，
Figure 860590DEST_PATH_IMAGE028
for the pitch moment coefficient due to the angle of attack,
Figure 926635DEST_PATH_IMAGE029
；
Figure 508926DEST_PATH_IMAGE030
for the coefficient of pitch moment due to the pitch angle rate,
Figure 276899DEST_PATH_IMAGE031
，
Figure 970049DEST_PATH_IMAGE032
is the average aerodynamic chord;
Figure 625021DEST_PATH_IMAGE033
for the pitch moment coefficient caused by the elevator,
Figure 378214DEST_PATH_IMAGE034
，
Figure 134948DEST_PATH_IMAGE035
an elevator deflection angle for an aircraft;
Figure 631788DEST_PATH_IMAGE036
is the moment of inertia of the aircraft;Sis used as a reference surface for the test piece,
Figure 406846DEST_PATH_IMAGE037
is dynamic pressure;
step 12: will be provided with
Figure 65361DEST_PATH_IMAGE038
Combined into rigid motion state of aircraft
Figure 699605DEST_PATH_IMAGE039
Will be
Figure 842879DEST_PATH_IMAGE040
Combined into control signals for aircraft
Figure 738023DEST_PATH_IMAGE041
The rigid body motion of the longitudinal dynamical system of the aircraft is represented as an affine non-linear system:
Figure 567438DEST_PATH_IMAGE042
wherein,
Figure 298765DEST_PATH_IMAGE043
is the change rate of the rigid body motion state of the aircraft,
Figure 137408DEST_PATH_IMAGE044
is the rigid motion characteristic of the aircraft,
Figure 621479DEST_PATH_IMAGE045
；
Figure 887375DEST_PATH_IMAGE046
a matrix is assigned to the control of the aircraft,
Figure 338954DEST_PATH_IMAGE047
；
step 13: the affine nonlinear system in the step 12 is expressed as follows by adopting a T-S fuzzy control technology:
Figure 981288DEST_PATH_IMAGE048
wherein,lin order to be able to determine the number of fuzzy sets,iin order to be an index into the fuzzy set,
Figure 585445DEST_PATH_IMAGE049
，
Figure 22242DEST_PATH_IMAGE050
is a rigid motion state matrix of the aircraft,
Figure 462582DEST_PATH_IMAGE051
，
Figure 643028DEST_PATH_IMAGE052
in order to control the allocation matrix,
Figure 101691DEST_PATH_IMAGE053
，
Figure 709390DEST_PATH_IMAGE054
as a function of known state and time,
Figure 135561DEST_PATH_IMAGE055
，
Figure 854118DEST_PATH_IMAGE056
，
Figure 432867DEST_PATH_IMAGE057
for the fuzzy set segment number divided by the T-S fuzzy control technology,jin order to obscure the index of the number of segments,
Figure 211467DEST_PATH_IMAGE058
is as followsiThe membership degree of the subsystem corresponding to each fuzzy set in the global system corresponding to the whole fuzzy set;
step 14: during the high-speed flight of the aircraft, flexible motion is generated, and considering the characteristic that the flexible motion is coupled by rigid motion, the flexible motion of the aircraft is described by a group of partial differential systems:
Figure 626399DEST_PATH_IMAGE059
wherein,zrepresenting the relative position to the center of mass of the aircraft,Lrepresenting the total length of the equivalent partial differential system,
Figure 148647DEST_PATH_IMAGE060
representing flexural vibrations of aircraft in relative positionszThe rate of longitudinal acceleration of the wheel or wheels,
Figure 581902DEST_PATH_IMAGE061
representing flexural vibrations of aircraft in relative positionszThe longitudinal force of the (c) is,
Figure 531404DEST_PATH_IMAGE062
boundary information representing partial differential systemThe effect of the number on the internal dynamics,
Figure 666588DEST_PATH_IMAGE063
representing flexible vibration of aircraftz=0The rate of change of the bending moment is measured,
Figure 992527DEST_PATH_IMAGE064
representing flexible vibration of aircraftz=0The shear stress of (a) is (b),mwhich represents the mass density of the material,EIrepresents the coefficient of stiffness resistance of the steel sheet,
Figure 280289DEST_PATH_IMAGE065
representing the known coefficients of the coefficients,
Figure 135112DEST_PATH_IMAGE066
representing flexible vibration of aircraftz=0The longitudinal displacement of the (c) is,
Figure 790216DEST_PATH_IMAGE067
representing flexible vibration of aircraftz=0Is rotated by the angle of rotation of (c),
Figure 388687DEST_PATH_IMAGE068
representing flexible vibration of aircraftz=LThe bending moment of the beam at (a),
Figure 796535DEST_PATH_IMAGE069
representing flexible vibration of aircraftz=LThe shear stress of (d);
step 15: the structural damage fault is characterized by a distributed fault, the homogeneous property of a partial differential system is broken, and a longitudinal dynamic system model of the flexible hypersonic aerocraft under the distributed fault is established:
Figure 87839DEST_PATH_IMAGE070
wherein:
Figure 197615DEST_PATH_IMAGE071
representing a vector of parameters that is known to be,
Figure 865357DEST_PATH_IMAGE072
represents a fault signal and is bounded.
Further, the initial state of the partial differential system is
Figure 862132DEST_PATH_IMAGE073
And
Figure 589916DEST_PATH_IMAGE074
wherein
Figure 688453DEST_PATH_IMAGE073
representing flexural vibrations of aircraft in relative positionszIs initially displaced in the longitudinal direction of the drill bit,
Figure 894307DEST_PATH_IMAGE074
representing flexural vibrations of aircraft in relative positionszThe initial longitudinal velocity of (c).
Further, step 2 comprises the following substeps:
step 21: according to the flexible hypersonic speed aircraft longitudinal dynamics system model under the distributed fault established in the step 1, based on structural characteristic analysis of the distributed fault, the internal dynamic state of the distributed fault existing in a partial differential system is obtained, and reversible state transformation is constructed
Figure 11167DEST_PATH_IMAGE075
Wherein
Figure 909853DEST_PATH_IMAGE076
representing flexible vibration of aircraftL-zThe bending moment of (a);
step 22: according to the constructed state transformation, the characteristics of the distributed faults are all transferred to the boundary of the partial differential system, and an equivalent partial differential system is obtained:
Figure 728643DEST_PATH_IMAGE077
wherein,
Figure 738187DEST_PATH_IMAGE078
representing equivalent partial differential systems in relative positionzThe rate of acceleration in the longitudinal direction of the vehicle,
Figure 975133DEST_PATH_IMAGE079
representing equivalent partial differential systems in relative positionzResultant longitudinal force, constant of
Figure 779141DEST_PATH_IMAGE080
，
Figure 852270DEST_PATH_IMAGE081
Representing equivalent partial differential systems in relative positionz=0The longitudinal vibration displacement of the (c) is,
Figure 399926DEST_PATH_IMAGE082
representing equivalent partial differential systems in relative positionz=0Is rotated by the angle of rotation of (c),
Figure 491379DEST_PATH_IMAGE083
representing equivalent partial differential systems in relative positionz=LThe bending moment of the beam at (a),
Figure 466288DEST_PATH_IMAGE084
representing equivalent partial differential systems in relative positionz=LThe shear stress of the (c) is,
Figure 525249DEST_PATH_IMAGE085
is a first vector of known constants that is,
Figure 735651DEST_PATH_IMAGE086
，
Figure 556976DEST_PATH_IMAGE087
is a second vector of known constants that is,
Figure 843732DEST_PATH_IMAGE088
，
Figure 16087DEST_PATH_IMAGE089
is the output signal vector of the equivalent partial differential system,
Figure 764601DEST_PATH_IMAGE090
is the output signal of the equivalent partial differential system,
Figure 706012DEST_PATH_IMAGE091
，
Figure 396625DEST_PATH_IMAGE092
representing equivalent partial differential systems in relative positionz=LThe longitudinal velocity of the beam of light at (c),
Figure 790697DEST_PATH_IMAGE093
representing equivalent partial differential systems in relative positionz=LIs rotated by the angle of rotation of (c),
Figure 608480DEST_PATH_IMAGE094
is a third vector of known constants that is,
Figure 404398DEST_PATH_IMAGE095
，
Figure 32957DEST_PATH_IMAGE096
is a known distributed fault parameter vector;
step 23: the distributed fault is transferred to the boundary of the partial differential system from the inside of the partial differential system, the characteristics of the partial differential system are not changed, and an equivalent dynamic system model under the distributed fault is obtained:
Figure 914325DEST_PATH_IMAGE097
wherein,
Figure 270220DEST_PATH_IMAGE098
is a system matrix of rigid body motion of the aircraft,
Figure 920644DEST_PATH_IMAGE099
，
Figure 218639DEST_PATH_IMAGE100
a matrix is assigned to the control of rigid body motion of the aircraft,
Figure 587304DEST_PATH_IMAGE101
。
further, step 3 comprises the following sub-steps:
step 31: designing a T-S fuzzy fault-tolerant control framework to have the following structure: if it is not
Figure 746890DEST_PATH_IMAGE102
Belong to
Figure 251820DEST_PATH_IMAGE103
，…，
Figure 222181DEST_PATH_IMAGE104
Belong to
Figure 78142DEST_PATH_IMAGE105
Then, then
Figure 775840DEST_PATH_IMAGE106
Wherein
Figure 400856DEST_PATH_IMAGE107
representing the state feedback control gain matrix to be solved,
Figure 775074DEST_PATH_IMAGE108
，
Figure 852752DEST_PATH_IMAGE109
representing the output feedback control gain matrix to be solved,
Figure 619720DEST_PATH_IMAGE110
，
Figure 99242DEST_PATH_IMAGE111
representing a fault compensation matrix to be solved，
Figure 411406DEST_PATH_IMAGE112
，
Figure 976380DEST_PATH_IMAGE113
Represents the dimension of the distributed fault that occurred,
Figure 15880DEST_PATH_IMAGE114
for achieving desired aircraft system stability and output tracking,
Figure 615488DEST_PATH_IMAGE115
for ensuring compensation of distributed faults, the T-S fuzzy fault tolerant control framework is expressed as:
Figure 620526DEST_PATH_IMAGE116
wherein,
Figure 531850DEST_PATH_IMAGE117
，
Figure 250408DEST_PATH_IMAGE118
，
Figure 579889DEST_PATH_IMAGE119
；
step 32: and (3) substituting the T-S fuzzy fault-tolerant control framework into an equivalent dynamic system model to obtain a closed-loop system as follows:
Figure 358489DEST_PATH_IMAGE120
wherein,
Figure 22689DEST_PATH_IMAGE121
is a system matrix of the rigid body motion closed-loop system of the aircraft,
Figure 544937DEST_PATH_IMAGE122
；
Figure 227460DEST_PATH_IMAGE123
is a gain matrix of the rigid body motion closed-loop system of the aircraft,
Figure 176961DEST_PATH_IMAGE124
；
Figure 62878DEST_PATH_IMAGE125
a fault compensation matrix of the rigid body motion closed-loop system of the aircraft,
Figure 388817DEST_PATH_IMAGE126
；
step 33: according to the closed loop system in step 2, the following Lyapunov function is selected:
Figure 161732DEST_PATH_IMAGE127
wherein:
Figure 547714DEST_PATH_IMAGE128
Figure 186506DEST_PATH_IMAGE129
representing the first constant to be solved for,
Figure 50556DEST_PATH_IMAGE130
representing equivalent partial differential systems in relative positionzThe rotation angle is measured, and the rotation angle is measured,
Figure 176513DEST_PATH_IMAGE131
representing the second constant to be solved for,zrepresenting the relative displacement of the equivalent partial differential system from the center of mass,
Figure 733396DEST_PATH_IMAGE132
representing equivalent partial differential systems in relative positionzThe longitudinal velocity of the beam of light at (c),
Figure 593905DEST_PATH_IMAGE133
represents a third constant to be solved for,
Figure 996068DEST_PATH_IMAGE134
representing equivalent partial differential systems in relative positionzThe bending moment of the beam at (a),
Figure 9154DEST_PATH_IMAGE135
is a constant matrix;
step 34: establishing a group of linear matrix inequality constraints according to the positive nature of the Lyapunov function and the negative nature of the derivative thereof in the step 33, and solving an output feedback control gain matrix to be solved
Figure 736939DEST_PATH_IMAGE109
Fault compensation matrix to be solved
Figure 819164DEST_PATH_IMAGE111
(ii) a The set of linear matrix inequalities is constrained by:
Figure 290597DEST_PATH_IMAGE136
wherein,
Figure 656725DEST_PATH_IMAGE137
，
Figure 289832DEST_PATH_IMAGE138
represents the symmetric elements of the matrix and,
Figure 124932DEST_PATH_IMAGE139
in the form of a vector of known constants,
Figure 134477DEST_PATH_IMAGE140
，
Figure 590997DEST_PATH_IMAGE141
and
Figure 926163DEST_PATH_IMAGE142
for the coefficients to be solved for the data,
Figure 717402DEST_PATH_IMAGE143
for the first constant matrix to be solved for,
Figure 796216DEST_PATH_IMAGE144
a second constant matrix to be solved;
step 35: based on the first constant matrix solved in step 34
Figure 871357DEST_PATH_IMAGE145
And a second constant matrixWTo obtain a state feedback control gain matrix
Figure 970900DEST_PATH_IMAGE146
；
Step 36: state feedback control gain matrix to be solved
Figure 655960DEST_PATH_IMAGE107
Output feedback control gain matrix
Figure 882673DEST_PATH_IMAGE109
Fault compensation matrix
Figure 703998DEST_PATH_IMAGE111
And inputting the state of the aircraft into the T-S fuzzy fault-tolerant control framework in the step 31, and realizing consistent bounded stability of the state of the aircraft under the distributed fault.
Further, step 4 comprises the following sub-steps:
step 41: introduction of robust performance indicators
Figure 974443DEST_PATH_IMAGE001
Figure 881219DEST_PATH_IMAGE147
Wherein
Figure 410158DEST_PATH_IMAGE148
representing robust performance indicators
Figure 85990DEST_PATH_IMAGE001
A coefficient;
step 42: according to the positive nature of the Lyapunov function and the negative nature of the derivative thereof and the introduced robust performance index
Figure 933860DEST_PATH_IMAGE001
Establishing linear matrix inequality constraint to obtain output feedback control gain matrix to be solved
Figure 186987DEST_PATH_IMAGE109
Fault compensation matrix to be solved
Figure 755503DEST_PATH_IMAGE111
(ii) a The linear matrix inequality constraint is:
Figure 551420DEST_PATH_IMAGE149
wherein,
Figure 429247DEST_PATH_IMAGE150
，
Figure 45036DEST_PATH_IMAGE151
for the third constant matrix to be solved,
Figure 807455DEST_PATH_IMAGE152
for the fourth matrix of constants to be solved,
step 43: based on the third constant matrix solved in step 42
Figure 566202DEST_PATH_IMAGE153
And a fourth constant matrix Z to obtain a state feedback control gain matrix
Figure 614929DEST_PATH_IMAGE154
；
And step 44: state feedback control gain matrix to be solved
Figure 983594DEST_PATH_IMAGE107
Output feedback control gain matrix
Figure 893912DEST_PATH_IMAGE109
Fault compensation matrix
Figure 398843DEST_PATH_IMAGE111
Inputting the state of the aircraft into the T-S fuzzy fault-tolerant control framework in the step 31 to realize gradual stabilization of the state of the aircraft under the distributed fault.
Compared with the prior art, the invention has the following beneficial effects: the T-S fuzzy fault-tolerant control framework is established in the distributed fault compensation method of the flexible hypersonic aircraft, on one hand, the closed loop stability and the output tracking of the system can be guaranteed, on the other hand, the influence caused by the distributed fault can be compensated, and therefore the safety and the reliability of the operation of the longitudinal dynamic system of the flexible hypersonic aircraft are improved.
Drawings
FIG. 1 is a block diagram of the distributed fault compensation method of the flexible hypersonic aircraft of the present invention;
FIG. 2 is a rigid motion closed loop response curve of a flexible hypersonic aircraft under a distributed fault;
FIG. 3 is a flexible motion closed loop response curve for a flexible hypersonic aircraft under a distributed fault.
Detailed Description
The following description will further describe the embodiments of the present invention with reference to the drawings.
Fig. 1 is a frame diagram of a distributed fault compensation method for a flexible hypersonic aircraft according to the present invention, and the distributed fault compensation control method for the flexible hypersonic aircraft specifically includes the following steps:
step 1: according to the structure and flight environment of the aircraft, a distribution parameter system formed by mutually coupling a normal differential system and a partial differential system is adopted to depict the longitudinal dynamic system characteristic of the aircraft, and as the elastic deformation of the aircraft body can cause the disturbance of the aircraft attack angle in a certain range, the lift force and the resistance of the aircraft and the thrust of an engine are further influenced; on the contrary, the change of the rigid motion state also directly affects the stress of the aircraft, and further affects the elastic deformation of the fuselage, so that the ordinary differential system and the partial differential system present strong coupling characteristics. The ordinary differential system is subjected to piecewise linearization by adopting a T-S fuzzy control technology; the structural damage fault of the aircraft can be characterized by a type of uncertain distributed fault, so that a flexible hypersonic aircraft longitudinal dynamics system model under the distributed fault is established based on a partial differential system, the influence of the distributed fault on the aircraft longitudinal dynamics system is analyzed, and the structural characteristics of the distributed fault are revealed; the method specifically comprises the following substeps:
step 11: the rigid motion of the aircraft is determined by the flying height according to the structure and flying environment of the aircraft
Figure 618471DEST_PATH_IMAGE002
Flying speed of the aircraft
Figure 208853DEST_PATH_IMAGE003
Angle of attack
Figure 421397DEST_PATH_IMAGE004
And a pitch angle
Figure 46413DEST_PATH_IMAGE005
Angular velocity of pitch
Figure 436943DEST_PATH_IMAGE006
The system comprises five flight states, wherein the five flight states have strong coupling characteristics and show high nonlinear characteristics, and rigid motion is expressed as a group of nonlinear ordinary differential systems:
Figure 514621DEST_PATH_IMAGE007
wherein,
Figure 766742DEST_PATH_IMAGE008
to be the rate of change of the fly height,
Figure 246265DEST_PATH_IMAGE009
as is the rate of change of the flying speed,
Figure 807696DEST_PATH_IMAGE010
is the rate of change of the angle of attack,
Figure 372670DEST_PATH_IMAGE011
is the rate of change of the pitch angle,
Figure 927016DEST_PATH_IMAGE012
the rate of change of pitch angle velocity, g is the gravitational acceleration,m 0 is the mass of the aircraft and is,
Figure 261046DEST_PATH_IMAGE013
is the lift force of the aircraft,
Figure 258958DEST_PATH_IMAGE014
，
Figure 780069DEST_PATH_IMAGE015
in order to be a coefficient of lift force,
Figure 905151DEST_PATH_IMAGE016
；
Figure 93687DEST_PATH_IMAGE017
is the resistance of the aircraft and is,
Figure 996921DEST_PATH_IMAGE018
，
Figure 270907DEST_PATH_IMAGE019
as a system of resistanceThe number of the first and second groups is,
Figure 167057DEST_PATH_IMAGE020
；
Figure 475678DEST_PATH_IMAGE021
is the thrust of the aircraft and is,
Figure 549814DEST_PATH_IMAGE022
，
Figure 576675DEST_PATH_IMAGE023
in order to be the thrust coefficient,
Figure 512402DEST_PATH_IMAGE024
，
Figure 941109DEST_PATH_IMAGE025
is the throttle opening of the aircraft;
Figure 451725DEST_PATH_IMAGE026
is the pitching moment of the aircraft and,
Figure 434724DEST_PATH_IMAGE027
，
Figure 672676DEST_PATH_IMAGE028
for the pitch moment coefficient due to the angle of attack,
Figure 955890DEST_PATH_IMAGE029
；
Figure 371828DEST_PATH_IMAGE030
for the coefficient of pitch moment due to the pitch angle rate,
Figure 107703DEST_PATH_IMAGE031
，
Figure 650811DEST_PATH_IMAGE032
is the average aerodynamic chord;
Figure 788531DEST_PATH_IMAGE033
for the pitch moment coefficient caused by the elevator,
Figure 375370DEST_PATH_IMAGE155
，
Figure 598541DEST_PATH_IMAGE035
an elevator deflection angle for an aircraft;
Figure 912717DEST_PATH_IMAGE036
is the moment of inertia of the aircraft;Sis used as a reference surface for the test piece,
Figure 29577DEST_PATH_IMAGE037
is dynamic pressure;
step 12: will be provided with
Figure 662684DEST_PATH_IMAGE038
Combined into rigid motion state of aircraft
Figure 248517DEST_PATH_IMAGE039
Will be
Figure 258061DEST_PATH_IMAGE040
Combined into control signals for aircraft
Figure 229428DEST_PATH_IMAGE041
The rigid body motion of the longitudinal dynamical system of the aircraft is represented as an affine non-linear system:
Figure 299016DEST_PATH_IMAGE042
wherein,
Figure 605101DEST_PATH_IMAGE043
is the change rate of the rigid body motion state of the aircraft,
Figure 277391DEST_PATH_IMAGE044
is the rigid motion characteristic of the aircraft,
Figure 244210DEST_PATH_IMAGE045
；
Figure 484698DEST_PATH_IMAGE046
a matrix is assigned to the control of the aircraft,
Figure 779544DEST_PATH_IMAGE047
；
step 13: the affine nonlinear system in the step 12 is expressed as follows by adopting a T-S fuzzy control technology:
Figure 130891DEST_PATH_IMAGE048
wherein,lin order to be able to determine the number of fuzzy sets,iin order to be an index into the fuzzy set,
Figure 76851DEST_PATH_IMAGE049
，
Figure 488240DEST_PATH_IMAGE050
is a rigid motion state matrix of the aircraft,
Figure 768918DEST_PATH_IMAGE051
，
Figure 923956DEST_PATH_IMAGE052
in order to control the allocation matrix,
Figure 458842DEST_PATH_IMAGE053
，
Figure 916499DEST_PATH_IMAGE054
as a function of known state and time,
Figure 310572DEST_PATH_IMAGE055
，
Figure 128355DEST_PATH_IMAGE056
，
Figure 924273DEST_PATH_IMAGE057
for the number of fuzzy stages divided by the T-S fuzzy control technology,jin order to obscure the index of the number of segments,
Figure 785787DEST_PATH_IMAGE058
is as followsiThe membership degree of the subsystem corresponding to each fuzzy set in the global system corresponding to the whole fuzzy set;
step 14: in the high-speed flight process of the aircraft, the rigidity of the fuselage is reduced by the generated aerodynamic heat, so that the fuselage is elastically deformed to a certain degree, the stress of the aircraft is directly influenced by the change of the motion state of the rigid body, the elastic deformation of the fuselage is further influenced, the flexible motion is generated, the coupling characteristic that the flexible motion is subjected to the rigid body motion is considered, and the flexible motion of the aircraft is described by a group of partial differential systems:
Figure 667156DEST_PATH_IMAGE059
wherein,zrepresenting the relative position to the center of mass of the aircraft,Lrepresenting the total length of the equivalent partial differential system,
Figure 288630DEST_PATH_IMAGE060
representing flexural vibrations of aircraft in relative positionszThe rate of longitudinal acceleration of the wheel or wheels,
Figure 939054DEST_PATH_IMAGE061
representing flexural vibrations of aircraft in relative positionszThe longitudinal force of the (c) is,
Figure 738514DEST_PATH_IMAGE062
representing the influence of the boundary signal of a partial differential system on the internal dynamics,
Figure 841599DEST_PATH_IMAGE063
representing flexible vibration of aircraftz=0Change of bending momentThe ratio of the content to the content,
Figure 1185DEST_PATH_IMAGE064
representing flexible vibration of aircraftz=0The shear stress of the (c) is,mwhich represents the mass density of the material,EIrepresents the coefficient of stiffness resistance of the steel sheet,
Figure 771695DEST_PATH_IMAGE065
representing the known coefficients of the coefficients,
Figure 975012DEST_PATH_IMAGE066
representing flexible vibration of aircraftz=0The longitudinal displacement of the (c) is,
Figure 830972DEST_PATH_IMAGE067
representing flexible vibration of aircraftz=0Is rotated by a rotation angle of (c),
Figure 794249DEST_PATH_IMAGE068
representing flexible vibration of aircraftz=LThe bending moment of the beam at (a),
Figure 153686DEST_PATH_IMAGE069
representing flexible vibration of aircraftz=LThe shear stress of (d); the initial state of the partial micro-division system is
Figure 294949DEST_PATH_IMAGE073
And
Figure 372626DEST_PATH_IMAGE074
wherein
Figure 874015DEST_PATH_IMAGE073
representing flexural vibrations of aircraft in relative positionszIs initially displaced in the longitudinal direction of the drill bit,
Figure 619117DEST_PATH_IMAGE074
representing flexural vibrations of aircraft in relative positionszThe initial longitudinal velocity of (c).
Step 15: the structural damage fault is characterized by a distributed fault, the occurrence of the distributed fault can cause the internal dynamic characteristics of the partial differential system to be mutated, so that the homogeneous property of the partial differential system is broken, and a longitudinal dynamic system model of the flexible hypersonic aircraft under the distributed fault is established:
Figure 187674DEST_PATH_IMAGE070
wherein:
Figure 752648DEST_PATH_IMAGE071
representing a vector of parameters that is known to be,
Figure 57727DEST_PATH_IMAGE072
represents a fault signal and is bounded.
Step 2: according to the longitudinal dynamic system model of the flexible hypersonic aircraft under the distributed faults, which is established in the step 1, based on structural characteristic analysis of the distributed faults, the internal dynamic state of the distributed faults existing in the partial differential system is obtained, reversible state transformation is constructed, and the distributed faults are all transmitted to the boundary of the partial differential system to obtain an equivalent dynamic system model; the method specifically comprises the following substeps:
step 21: according to the flexible hypersonic speed aircraft longitudinal dynamics system model under the distributed fault established in the step 1, based on structural characteristic analysis of the distributed fault, the internal dynamic state of the distributed fault existing in a partial differential system is obtained, and reversible state transformation is constructed
Figure 391756DEST_PATH_IMAGE075
Wherein
Figure 874822DEST_PATH_IMAGE076
representing flexible vibration of aircraftL-zThe bending moment of (a);
step 22: according to the constructed state transformation, the characteristics of the distributed faults are all transferred to the boundary of the partial differential system, and an equivalent partial differential system is obtained:
Figure 927091DEST_PATH_IMAGE077
wherein,
Figure 35861DEST_PATH_IMAGE078
representing equivalent partial differential systems in relative positionzThe rate of longitudinal acceleration of the wheel or wheels,
Figure 224397DEST_PATH_IMAGE079
representing equivalent partial differential systems in relative positionzResultant longitudinal force, constant of
Figure 376899DEST_PATH_IMAGE080
，
Figure 916465DEST_PATH_IMAGE081
Representing equivalent partial differential systems in relative positionz=0The longitudinal vibration displacement of the (c) is,
Figure 563347DEST_PATH_IMAGE082
representing equivalent partial differential systems in relative positionz=0Is rotated by the angle of rotation of (c),
Figure 871968DEST_PATH_IMAGE083
representing equivalent partial differential systems in relative positionz=LThe bending moment of the (c) is,
Figure 696836DEST_PATH_IMAGE084
representing equivalent partial differential systems in relative positionz=LThe shear stress of the (c) is,
Figure 723698DEST_PATH_IMAGE085
is a first vector of known constants that is,
Figure 908691DEST_PATH_IMAGE086
，
Figure 71819DEST_PATH_IMAGE087
is a second vector of known constants that is,
Figure 831703DEST_PATH_IMAGE088
，
Figure 80282DEST_PATH_IMAGE089
is the output signal vector of the equivalent partial differential system,
Figure 68966DEST_PATH_IMAGE090
is the output signal of an equivalent partial differential system,
Figure 352180DEST_PATH_IMAGE091
，
Figure 518850DEST_PATH_IMAGE092
representing equivalent partial differential systems in relative positionz=LThe longitudinal velocity of the beam of light at (c),
Figure 254725DEST_PATH_IMAGE093
representing equivalent partial differential systems in relative positionz=LIs rotated by the angle of rotation of (c),
Figure 47101DEST_PATH_IMAGE094
is a third vector of known constants that is,
Figure 184821DEST_PATH_IMAGE095
，
Figure 20928DEST_PATH_IMAGE096
is a known distributed fault parameter vector;
step 23: the distributed fault is transferred to the boundary of the partial differential system from the inside of the partial differential system, the characteristics of the partial differential system are not changed, namely the partial differential systems before and after transformation have the same infinite dimension internal characteristics, and an equivalent dynamic system model under the distributed fault is obtained:
Figure 244098DEST_PATH_IMAGE097
wherein,
Figure 309006DEST_PATH_IMAGE098
is a system matrix of rigid body motion of the aircraft,
Figure 566812DEST_PATH_IMAGE099
，
Figure 75285DEST_PATH_IMAGE100
a matrix is assigned to the control of rigid body motion of the aircraft,
Figure 51332DEST_PATH_IMAGE101
。
and step 3: in the traditional fault-tolerant control, a control separation thought is introduced, and a fault-tolerant control signal structure is decomposed into two parts and is independently designed, wherein one part is used for ensuring the consistency and stability of a closed-loop system, and the other part is used for distributed fault compensation; and (3) establishing a T-S fuzzy fault-tolerant control framework to realize expected closed-loop stability and output tracking, obtaining a control gain matrix by adopting a linear matrix inequality method based on the equivalent dynamical system model obtained in the step (2), and inputting the control gain matrix into the established T-S fuzzy fault-tolerant control framework to realize consistent bounded stability of the state of the aircraft under distributed faults, thereby being easy to realize. The method specifically comprises the following substeps:
step 31: according to the coupling action between rigid motion and flexible motion of the flexible hypersonic aircraft, namely, the elastic deformation of the aircraft body can cause the disturbance of the attack angle of the aircraft in a certain range, thereby influencing the lift force and the resistance of the aircraft and the thrust of an engine; on the contrary, the change of the rigid motion state can also directly influence the stress of the aircraft, and further influence the elastic deformation of the fuselage, so that the rigid motion state and the elastic deformation of the fuselage have strong coupling characteristics, and the T-S fuzzy fault-tolerant control frame is designed to have the following structure: if it is not
Figure 654351DEST_PATH_IMAGE102
Belong to
Figure 140565DEST_PATH_IMAGE103
，…，
Figure 944573DEST_PATH_IMAGE104
Belong to
Figure 266970DEST_PATH_IMAGE105
Then, then
Figure 814626DEST_PATH_IMAGE106
Wherein, in the process,
Figure 656811DEST_PATH_IMAGE107
representing the state feedback control gain matrix to be solved,
Figure 897300DEST_PATH_IMAGE108
，
Figure 441413DEST_PATH_IMAGE109
representing the output feedback control gain matrix to be solved,
Figure 792760DEST_PATH_IMAGE110
，
Figure 987987DEST_PATH_IMAGE111
representing the fault compensation matrix to be solved,
Figure 399377DEST_PATH_IMAGE112
，
Figure 430787DEST_PATH_IMAGE113
represents the dimension of the distributed fault that occurred,
Figure 320246DEST_PATH_IMAGE114
for achieving desired aircraft system stability and output tracking,
Figure 137023DEST_PATH_IMAGE115
for ensuring compensation of distributed faults, the T-S fuzzy fault tolerant control framework is expressed as:
Figure 719314DEST_PATH_IMAGE116
wherein,
Figure 238020DEST_PATH_IMAGE117
，
Figure 931170DEST_PATH_IMAGE118
，
Figure 835409DEST_PATH_IMAGE119
；
step 32: and (3) substituting the T-S fuzzy fault-tolerant control framework into an equivalent dynamic system model to obtain a closed-loop system as follows:
Figure 588602DEST_PATH_IMAGE120
wherein,
Figure 594604DEST_PATH_IMAGE121
is a system matrix of the rigid body motion closed-loop system of the aircraft,
Figure 91444DEST_PATH_IMAGE122
；
Figure 617235DEST_PATH_IMAGE123
is a gain matrix of the rigid body motion closed-loop system of the aircraft,
Figure 275749DEST_PATH_IMAGE124
；
Figure 909993DEST_PATH_IMAGE125
a fault compensation matrix of the rigid body motion closed-loop system of the aircraft,
Figure 803999DEST_PATH_IMAGE126
；
step 33: according to the closed loop system in step 2, the following Lyapunov function is selected:
Figure 948411DEST_PATH_IMAGE127
wherein:
Figure 777826DEST_PATH_IMAGE128
Figure 899366DEST_PATH_IMAGE129
representing the first constant to be solved for,
Figure 597064DEST_PATH_IMAGE130
representing equivalent partial differential systems in relative positionzIs rotated by the angle of rotation of the rotating shaft,
Figure 831867DEST_PATH_IMAGE131
represents the second constant to be solved for,zrepresenting the relative displacement of the equivalent partial differential system from the center of mass,
Figure 97763DEST_PATH_IMAGE132
representing equivalent partial differential systems in relative positionzThe longitudinal velocity of the beam of light at (c),
Figure 441020DEST_PATH_IMAGE133
represents a third constant to be solved for,
Figure 942409DEST_PATH_IMAGE134
representing equivalent partial differential systems in relative positionzThe bending moment of the beam at (a),
Figure 687511DEST_PATH_IMAGE135
is a constant matrix;
step 34: in order to ensure the closed loop stability and tracking performance of the longitudinal dynamic system of the flexible hypersonic aircraft under the distributed fault, a group of linear matrix inequality constraints are established according to the positive nature of the Lyapunov function and the negative nature of the derivative thereof in the step 33, and the output feedback control gain matrix to be solved is solved
Figure 232630DEST_PATH_IMAGE109
Fault compensation matrix to be solved
Figure 922238DEST_PATH_IMAGE111
(ii) a In the invention, a group of linear matrix inequalities are constrained as follows:
Figure 102683DEST_PATH_IMAGE136
wherein,
Figure 312079DEST_PATH_IMAGE137
，
Figure 919778DEST_PATH_IMAGE138
represents the symmetric elements of the matrix and,
Figure 96681DEST_PATH_IMAGE139
in the form of a vector of known constants,
Figure 815238DEST_PATH_IMAGE140
，
Figure 643255DEST_PATH_IMAGE141
and
Figure 421855DEST_PATH_IMAGE142
for the coefficients to be solved for,
Figure 86055DEST_PATH_IMAGE143
for the first constant matrix to be solved,
Figure 608303DEST_PATH_IMAGE144
a second constant matrix to be solved;
step 35: based on the first constant matrix solved in step 34
Figure 792291DEST_PATH_IMAGE145
And a second constant matrixWTo obtain a state feedback control gain matrix
Figure 741792DEST_PATH_IMAGE146
；
Step 36: state feedback control gain matrix to be solved
Figure 627708DEST_PATH_IMAGE156
Output feedback control gain matrix
Figure 953648DEST_PATH_IMAGE157
Fault compensation matrix
Figure 490677DEST_PATH_IMAGE111
And inputting the state of the aircraft into the T-S fuzzy fault-tolerant control framework in the step 31, and realizing consistent bounded stability of the state of the aircraft under the distributed fault.
And 4, step 4: introducing a robust performance index, designing a robust T-S fuzzy fault-tolerant control mechanism based on control separation based on the T-S fuzzy fault-tolerant control framework in the step 3, establishing a linear matrix inequality to obtain a control gain matrix, and inputting the control gain matrix into the established T-S fuzzy fault-tolerant control framework to realize gradual stabilization of the state of the aircraft under distributed faults; the method specifically comprises the following substeps:
step 41: in order to realize the gradual stability performance of the flexible hypersonic aircraft under the distributed fault, a robust performance index is introduced
Figure 611080DEST_PATH_IMAGE001
Figure 984292DEST_PATH_IMAGE158
Wherein
Figure 848343DEST_PATH_IMAGE148
representing robust performance indicators
Figure 741344DEST_PATH_IMAGE001
A coefficient;
step 42: in order to ensure the closed loop stability and the tracking performance of a longitudinal dynamic system of a flexible hypersonic aircraft under distributed faults, the method is based on the positive nature of a Lyapunov function, the negative nature of a derivative of the Lyapunov function and an introduced robust performance index
Figure 298227DEST_PATH_IMAGE001
Establishing linear matrix inequality constraint to obtain output feedback control gain matrix to be solved
Figure 158736DEST_PATH_IMAGE157
Fault compensation matrix to be solved
Figure 826478DEST_PATH_IMAGE111
(ii) a The linear matrix inequality constraint in the invention is:
Figure 72520DEST_PATH_IMAGE149
wherein,
Figure 800305DEST_PATH_IMAGE150
，
Figure 148109DEST_PATH_IMAGE151
for the third constant matrix to be solved,
Figure 353963DEST_PATH_IMAGE152
for the fourth matrix of constants to be solved,
step 43: based on the third constant matrix solved in step 42
Figure 221556DEST_PATH_IMAGE153
And a fourth constant matrix Z to obtain a state feedback control gain matrix
Figure 120242DEST_PATH_IMAGE154
；
Step 44: state to be solved forState feedback control gain matrix
Figure 689763DEST_PATH_IMAGE107
Output feedback control gain matrix
Figure 699307DEST_PATH_IMAGE109
Fault compensation matrix
Figure 919942DEST_PATH_IMAGE111
Inputting the state of the aircraft into the T-S fuzzy fault-tolerant control framework in the step 31 to realize gradual stabilization of the state of the aircraft under the distributed fault.
Examples
In the embodiment, the distributed fault compensation method of the flexible hypersonic aircraft is subjected to simulation experiments:
step 1: considering a rigid motion model of a longitudinal dynamic system of the flexible hypersonic aircraft as follows:
Figure 848584DEST_PATH_IMAGE159
wherein:
Figure 46347DEST_PATH_IMAGE160
Figure 469369DEST_PATH_IMAGE161
Figure 436188DEST_PATH_IMAGE162
Figure 535731DEST_PATH_IMAGE163
。
the system parameters of the flexible motion of the longitudinal dynamic system of the flexible hypersonic aerocraft under the distributed fault are respectively as follows:
Figure 220790DEST_PATH_IMAGE164
，
Figure 946039DEST_PATH_IMAGE165
，
Figure 767364DEST_PATH_IMAGE166
，
Figure 37809DEST_PATH_IMAGE167
，
Figure 944585DEST_PATH_IMAGE168
，
Figure 709409DEST_PATH_IMAGE169
(ii) a The distributed fault is represented as:
Figure 650821DEST_PATH_IMAGE170
step 2: at the equilibrium point
Figure 92166DEST_PATH_IMAGE171
Nearby and defining a tracking error as
Figure 486239DEST_PATH_IMAGE172
The tracking error equation can be derived as:
Figure 553289DEST_PATH_IMAGE173
wherein:
Figure 349207DEST_PATH_IMAGE174
and
Figure 227033DEST_PATH_IMAGE175
definition of
Figure 108402DEST_PATH_IMAGE176
，
Figure 215029DEST_PATH_IMAGE177
And
Figure 865453DEST_PATH_IMAGE178
then, then
Figure 648601DEST_PATH_IMAGE179
Wherein:
Figure 391167DEST_PATH_IMAGE180
，
Figure 426119DEST_PATH_IMAGE181
。
the following fuzzy rule is established:
if it is not
Figure 196629DEST_PATH_IMAGE182
Belong to
Figure 150679DEST_PATH_IMAGE183
Then, then
Figure 882006DEST_PATH_IMAGE184
，
If it is not
Figure 455069DEST_PATH_IMAGE182
Belong to
Figure 345665DEST_PATH_IMAGE185
Then, then
Figure 470616DEST_PATH_IMAGE186
，
Wherein:
Figure 813872DEST_PATH_IMAGE187
. Then, the T-S fuzzy tracking error model is:
Figure 587966DEST_PATH_IMAGE188
and step 3: the initial conditions of the longitudinal dynamic system of the flexible hypersonic aircraft are respectively as follows:
Figure 192123DEST_PATH_IMAGE189
，
Figure 628920DEST_PATH_IMAGE190
，
Figure 69260DEST_PATH_IMAGE191
。
and 4, step 4: and (3) adopting Matlab/Simulink simulation, building an aircraft system model and a corresponding actuator fault model in Matlab/Simulink, designing a corresponding adaptive controller based on the aircraft system model and the corresponding actuator fault model, and further performing simulation verification.
Simulating the distributed fault compensation control method of the flexible hypersonic aircraft according to the designed parameters to obtain an output tracking error curve of a rigid body motion system of the flexible hypersonic aircraft as shown in figure 2, wherein the error curve of the flying altitude and the expected altitude of the aircraft, the error curve of the flying speed and the expected speed of the aircraft, the error curve of the attack angle and the expected attack angle of the aircraft, the error curve of the pitch angle and the expected pitch angle of the aircraft and the error curve of the pitch angle speed and the expected pitch angle speed of the aircraft are sequentially arranged from top to bottom in the figure 2; the vibration response of the flexible motion system of the flexible hypersonic aircraft is shown in fig. 3, and the longitudinal displacement of the flexible vibration of the aircraft and the longitudinal speed of the flexible vibration are from top to bottom in fig. 3.
The above is only a preferred embodiment of the present invention, and the protection scope of the present invention is not limited to the above-mentioned embodiments, and all technical solutions belonging to the idea of the present invention belong to the protection scope of the present invention. It should be noted that modifications and embellishments within the scope of the invention may be made by those skilled in the art without departing from the principle of the invention.

Claims (6)

1. A distributed fault compensation control method for a flexible hypersonic aircraft is characterized by comprising the following steps:
step 1: according to the structure and flight environment of the aircraft, a distribution parameter system in which an ordinary differential system and a partial differential system are mutually coupled is adopted to depict the longitudinal dynamics system characteristic of the aircraft, and a T-S fuzzy control technology is adopted to carry out piecewise linearization on the ordinary differential system; establishing a longitudinal dynamic system model of the flexible hypersonic aircraft under the distributed fault based on a partial differential system;
and 2, step: according to the longitudinal dynamic system model of the flexible hypersonic aircraft under the distributed faults, which is established in the step 1, based on structural characteristic analysis of the distributed faults, the internal dynamic state of the distributed faults existing in the partial differential system is obtained, reversible state transformation is constructed, and the distributed faults are all transmitted to the boundary of the partial differential system to obtain an equivalent dynamic system model;
and step 3: establishing a T-S fuzzy fault-tolerant control framework, obtaining a control gain matrix by adopting a linear matrix inequality method based on the equivalent dynamics system model obtained in the step 2, and inputting the control gain matrix into the established T-S fuzzy fault-tolerant control framework to realize the consistent bounded stability of the state of the aircraft under the distributed fault;
and 4, step 4: introduction of robust performance indicators
Figure 432826DEST_PATH_IMAGE001
Designing a robust T-S fuzzy fault-tolerant control mechanism based on the T-S fuzzy fault-tolerant control framework of the step 3 and establishing a linear matrixAnd obtaining a control gain matrix by an inequality, and inputting the control gain matrix into the established T-S fuzzy fault-tolerant control framework to realize gradual stabilization of the state of the aircraft under the distributed fault.
2. The distributed fault compensation method for the flexible hypersonic aircraft according to claim 1, characterized in that step 1 comprises the following substeps:
step 11: the rigid motion of the aircraft is determined by the flying height according to the structure and flying environment of the aircraft
Figure 235697DEST_PATH_IMAGE002
Flying speed
Figure 279614DEST_PATH_IMAGE003
Angle of attack
Figure 394201DEST_PATH_IMAGE004
And a pitch angle
Figure 50441DEST_PATH_IMAGE005
Angular velocity of pitch
Figure 566873DEST_PATH_IMAGE006
The system consists of five flight states, and rigid motion is expressed as a group of nonlinear ordinary differential systems:
Figure 283157DEST_PATH_IMAGE007
wherein,
Figure 150618DEST_PATH_IMAGE008
for the rate of change of the flying height,
Figure 610550DEST_PATH_IMAGE009
as is the rate of change of the flying speed,
Figure 981488DEST_PATH_IMAGE010
to be the rate of change of the angle of attack,
Figure 367208DEST_PATH_IMAGE011
is the rate of change of the pitch angle,
Figure 190807DEST_PATH_IMAGE012
the rate of change of pitch angle velocity, g is the gravitational acceleration,m 0 is the mass of the aircraft and is,
Figure 720009DEST_PATH_IMAGE013
is the lift force of the aircraft,
Figure 820820DEST_PATH_IMAGE014
，
Figure 269119DEST_PATH_IMAGE015
in order to be a coefficient of lift force,
Figure 720960DEST_PATH_IMAGE016
；
Figure 647328DEST_PATH_IMAGE017
is the resistance of the aircraft and is,
Figure 101180DEST_PATH_IMAGE018
，
Figure 720381DEST_PATH_IMAGE019
in order to be a coefficient of resistance,
Figure 393939DEST_PATH_IMAGE020
；
Figure 858418DEST_PATH_IMAGE021
is the thrust of the aircraft and is,
Figure 933821DEST_PATH_IMAGE022
，
Figure 723923DEST_PATH_IMAGE023
in order to be the thrust coefficient,
Figure 619198DEST_PATH_IMAGE024
，
Figure 152947DEST_PATH_IMAGE025
is the throttle opening of the aircraft;
Figure 581392DEST_PATH_IMAGE026
is the pitching moment of the aircraft and,
Figure 276816DEST_PATH_IMAGE027
，
Figure 190545DEST_PATH_IMAGE028
for the pitch moment coefficient due to the angle of attack,
Figure 668931DEST_PATH_IMAGE029
；
Figure 453347DEST_PATH_IMAGE030
for the coefficient of pitch moment due to the pitch angle rate,
Figure 585251DEST_PATH_IMAGE031
，
Figure 242670DEST_PATH_IMAGE032
is the average aerodynamic chord;
Figure 118222DEST_PATH_IMAGE033
for the pitch moment coefficient caused by the elevator,
Figure 22725DEST_PATH_IMAGE034
，
Figure 59951DEST_PATH_IMAGE035
an elevator deflection angle for an aircraft;
Figure 682693DEST_PATH_IMAGE036
is the moment of inertia of the aircraft;Sis used as a reference surface for the test piece,
Figure 96357DEST_PATH_IMAGE037
is dynamic pressure;
step 12: will be provided with
Figure 855365DEST_PATH_IMAGE038
Combined into rigid motion state of aircraft
Figure 63493DEST_PATH_IMAGE039
Will be
Figure 406487DEST_PATH_IMAGE040
Combined into control signals for aircraft
Figure 623842DEST_PATH_IMAGE041
The rigid body motion of the longitudinal dynamical system of the aircraft is represented as an affine non-linear system:
Figure 502936DEST_PATH_IMAGE042
wherein,
Figure 22910DEST_PATH_IMAGE043
is the change rate of the rigid body motion state of the aircraft,
Figure 479300DEST_PATH_IMAGE044
is the rigid motion characteristic of the aircraft,
Figure 906870DEST_PATH_IMAGE045
；
Figure 139006DEST_PATH_IMAGE046
a matrix is assigned to the control of the aircraft,
Figure 95461DEST_PATH_IMAGE047
；
step 13: the affine nonlinear system in the step 12 is expressed as follows by adopting a T-S fuzzy control technology:
Figure 773567DEST_PATH_IMAGE048
wherein,lin order to be able to determine the number of fuzzy sets,iin order to be an index to the fuzzy set,
Figure 208090DEST_PATH_IMAGE049
，
Figure 920831DEST_PATH_IMAGE050
is a rigid motion state matrix of the aircraft,
Figure 782608DEST_PATH_IMAGE051
，
Figure 213589DEST_PATH_IMAGE052
in order to control the allocation matrix,
Figure 684760DEST_PATH_IMAGE053
，
Figure 252007DEST_PATH_IMAGE054
as a function of known state and time,
Figure 284685DEST_PATH_IMAGE055
，
Figure 937383DEST_PATH_IMAGE056
，
Figure 979289DEST_PATH_IMAGE057
for the fuzzy set segment number divided by the T-S fuzzy control technology,jin order to obscure the index of the number of segments,
Figure 401043DEST_PATH_IMAGE058
is as followsiThe membership degree of the subsystem corresponding to each fuzzy set in the global system corresponding to the whole fuzzy set;
step 14: during the high-speed flight of the aircraft, flexible motion is generated, and considering the characteristic that the flexible motion is coupled by rigid motion, the flexible motion of the aircraft is described by a group of partial differential systems:
Figure 870201DEST_PATH_IMAGE059
wherein,zrepresenting the relative position to the center of mass of the aircraft,Lrepresenting the total length of the equivalent partial differential system,
Figure 10196DEST_PATH_IMAGE060
representing flexural vibrations of aircraft in relative positionszThe rate of acceleration in the longitudinal direction of the vehicle,
Figure 823169DEST_PATH_IMAGE061
representing flexural vibrations of aircraft in relative positionszThe longitudinal force of the (c) is,
Figure 365009DEST_PATH_IMAGE062
representing the influence of the boundary signal of a partial differential system on the internal dynamics,
Figure 739489DEST_PATH_IMAGE063
representing flexible vibration of aircraftz=0The rate of change of the bending moment is measured,
Figure 366780DEST_PATH_IMAGE064
representing flexible vibration of aircraftz=0The shear stress of the (c) is,mwhich represents the mass density of the material,EIrepresents the coefficient of stiffness resistance of the steel sheet,
Figure 484908DEST_PATH_IMAGE065
representing the known coefficients of the coefficients,
Figure 881255DEST_PATH_IMAGE066
representing flexible vibration of aircraftz=0The longitudinal displacement of the (c) is,
Figure 692216DEST_PATH_IMAGE067
representing flexible vibration of aircraftz=0Is rotated by the angle of rotation of (c),
Figure 541223DEST_PATH_IMAGE068
representing flexible vibration of aircraftz=LThe bending moment of the beam at (a),
Figure 961578DEST_PATH_IMAGE069
representing flexible vibration of aircraftz=LThe shear stress of (d);
step 15: the structural damage fault is characterized by a distributed fault, the homogeneous property of a partial differential system is broken, and a longitudinal dynamic system model of the flexible hypersonic aerocraft under the distributed fault is established:
Figure 478010DEST_PATH_IMAGE070
wherein:
Figure 194293DEST_PATH_IMAGE071
representing a vector of parameters that is known to be,
Figure 530597DEST_PATH_IMAGE072
represents a fault signal, andthe barrier signal is bounded.
3. The distributed fault compensation method for flexible hypersonic aircraft according to claim 2, characterized in that the initial state of the partial differential system is
Figure 990528DEST_PATH_IMAGE073
And
Figure 361466DEST_PATH_IMAGE074
wherein
Figure 248651DEST_PATH_IMAGE073
representing flexural vibrations of aircraft in relative positionszIs initially displaced in the longitudinal direction of the drill bit,
Figure 337830DEST_PATH_IMAGE074
representing flexural vibrations of aircraft in relative positionszThe initial longitudinal velocity of (c).
4. The distributed fault compensation method for the flexible hypersonic aircraft according to claim 2, characterized in that the step 2 comprises the following sub-steps:
step 21: according to the flexible hypersonic speed aircraft longitudinal dynamics system model under the distributed fault established in the step 1, based on structural characteristic analysis of the distributed fault, the internal dynamic state of the distributed fault existing in a partial differential system is obtained, and reversible state transformation is constructed
Figure 834408DEST_PATH_IMAGE075
Wherein
Figure 325432DEST_PATH_IMAGE076
representing flexible vibration of aircraftL-zThe bending moment of (a);
step 22: according to the constructed state transformation, the characteristics of the distributed faults are all transferred to the boundary of the partial differential system, and an equivalent partial differential system is obtained:
Figure 914676DEST_PATH_IMAGE077
wherein,
Figure 100938DEST_PATH_IMAGE078
representing equivalent partial differential systems in relative positionzThe rate of longitudinal acceleration of the wheel or wheels,
Figure 27306DEST_PATH_IMAGE079
representing equivalent partial differential systems in relative positionzLongitudinal resultant force, constant
Figure 248203DEST_PATH_IMAGE080
，
Figure 601824DEST_PATH_IMAGE081
Representing equivalent partial differential systems in relative positionz=0The longitudinal vibration displacement of the (c) is,
Figure 773917DEST_PATH_IMAGE082
representing equivalent partial differential systems in relative positionz=0Is rotated by the angle of rotation of (c),
Figure 503975DEST_PATH_IMAGE083
representing equivalent partial differential systems in relative positionz=LThe bending moment of the beam at (a),
Figure 844958DEST_PATH_IMAGE084
representing equivalent partial differential systems in relative positionz=LThe shear stress of (a) is (b),
Figure 103901DEST_PATH_IMAGE085
is a first vector of known constants that is,
Figure 530334DEST_PATH_IMAGE086
，
Figure 939450DEST_PATH_IMAGE087
is a second vector of known constants that is,
Figure 993994DEST_PATH_IMAGE088
，
Figure 423838DEST_PATH_IMAGE089
is the output signal vector of the equivalent partial differential system,
Figure 836103DEST_PATH_IMAGE090
is the output signal of an equivalent partial differential system,
Figure 783330DEST_PATH_IMAGE091
，
Figure 692380DEST_PATH_IMAGE092
representing equivalent partial differential systems in relative positionz=LThe longitudinal velocity of the beam of light at (c),
Figure 965230DEST_PATH_IMAGE093
representing equivalent partial differential systems in relative positionz=LIs rotated by the angle of rotation of (c),
Figure 100676DEST_PATH_IMAGE094
is a third vector of known constants that is,
Figure 976228DEST_PATH_IMAGE095
，
Figure 113686DEST_PATH_IMAGE096
is a known distributed fault parameter vector;
step 23: the distributed fault is transferred to the boundary of the partial differential system from the inside of the partial differential system, the characteristics of the partial differential system are not changed, and an equivalent dynamic system model under the distributed fault is obtained:
Figure 416491DEST_PATH_IMAGE097
wherein,
Figure 773655DEST_PATH_IMAGE098
is a system matrix of rigid body motion of the aircraft,
Figure 187318DEST_PATH_IMAGE099
，
Figure 946327DEST_PATH_IMAGE100
a matrix is assigned to the control of rigid body motion of the aircraft,
Figure 420034DEST_PATH_IMAGE101
。
5. the distributed fault compensation method for the flexible hypersonic aircraft according to claim 4, characterized in that the step 3 comprises the following sub-steps:
step 31: designing a T-S fuzzy fault-tolerant control framework to have the following structure: if it is not
Figure 264493DEST_PATH_IMAGE102
Belong to
Figure 481848DEST_PATH_IMAGE103
，…，
Figure 593898DEST_PATH_IMAGE104
Belong to
Figure 238506DEST_PATH_IMAGE105
Then, it is
Figure 570261DEST_PATH_IMAGE106
Wherein
Figure 325727DEST_PATH_IMAGE107
representing the state feedback control gain matrix to be solved,
Figure 59328DEST_PATH_IMAGE108
，
Figure 874838DEST_PATH_IMAGE109
representing the output feedback control gain matrix to be solved,
Figure 959468DEST_PATH_IMAGE110
，
Figure 253046DEST_PATH_IMAGE111
representing the fault compensation matrix to be solved,
Figure 339689DEST_PATH_IMAGE112
，
Figure 326099DEST_PATH_IMAGE113
represents the dimension of the distributed fault that occurred,
Figure 632447DEST_PATH_IMAGE114
for achieving desired aircraft system stability and output tracking,
Figure 464137DEST_PATH_IMAGE115
for ensuring compensation of distributed faults, the T-S fuzzy fault tolerant control framework is expressed as:
Figure 437909DEST_PATH_IMAGE116
wherein,
Figure 329641DEST_PATH_IMAGE117
，
Figure 123285DEST_PATH_IMAGE118
，
Figure 398146DEST_PATH_IMAGE119
；
step 32: and (3) substituting the T-S fuzzy fault-tolerant control framework into an equivalent dynamic system model to obtain a closed-loop system as follows:
Figure 85480DEST_PATH_IMAGE120
wherein,
Figure 289059DEST_PATH_IMAGE121
is a system matrix of the rigid body motion closed-loop system of the aircraft,
Figure 429053DEST_PATH_IMAGE122
；
Figure 743491DEST_PATH_IMAGE123
is a gain matrix of the rigid body motion closed-loop system of the aircraft,
Figure 285331DEST_PATH_IMAGE124
；
Figure 659812DEST_PATH_IMAGE125
a fault compensation matrix of the rigid body motion closed-loop system of the aircraft,
Figure 287102DEST_PATH_IMAGE126
；
step 33: according to the closed loop system in step 2, the following Lyapunov function is selected:
Figure 903766DEST_PATH_IMAGE127
wherein:
Figure 565691DEST_PATH_IMAGE128
Figure 845494DEST_PATH_IMAGE129
representing the first constant to be solved for,
Figure 225660DEST_PATH_IMAGE130
representing equivalent partial differential systems in relative positionzIs rotated by the angle of rotation of the rotating shaft,
Figure 147480DEST_PATH_IMAGE131
represents the second constant to be solved for,zrepresenting the relative displacement of the equivalent partial differential system from the center of mass,
Figure 398332DEST_PATH_IMAGE132
representing equivalent partial differential systems in relative positionzThe longitudinal velocity of the (c) is,
Figure 114616DEST_PATH_IMAGE133
represents a third constant to be solved for,
Figure 716498DEST_PATH_IMAGE134
representing equivalent partial differential systems in relative positionzThe bending moment of the beam at (a),
Figure 674965DEST_PATH_IMAGE135
is a constant matrix;
step 34: establishing a group of linear matrix inequality constraints according to the positive nature of the Lyapunov function and the negative nature of the derivative thereof in the step 33, and solving an output feedback control gain matrix to be solved
Figure 45903DEST_PATH_IMAGE136
To be askedFault compensation matrix of solution
Figure 933088DEST_PATH_IMAGE111
(ii) a The set of linear matrix inequalities is constrained by:
Figure 22266DEST_PATH_IMAGE137
wherein,
Figure 20309DEST_PATH_IMAGE138
，
Figure 386700DEST_PATH_IMAGE139
represents the symmetric elements of the matrix and,
Figure 569420DEST_PATH_IMAGE140
in the form of a vector of known constants,
Figure 519796DEST_PATH_IMAGE141
，
Figure 180584DEST_PATH_IMAGE142
and
Figure 667060DEST_PATH_IMAGE143
for the coefficients to be solved for,
Figure 20681DEST_PATH_IMAGE144
for the first constant matrix to be solved,
Figure 694239DEST_PATH_IMAGE145
a second constant matrix to be solved;
step 35: based on the first constant matrix solved in step 34
Figure 424298DEST_PATH_IMAGE146
And a second constant matrixWTo obtain a state feedback control gain matrix
Figure 499701DEST_PATH_IMAGE147
；
Step 36: state feedback control gain matrix to be solved
Figure 24223DEST_PATH_IMAGE107
Output feedback control gain matrix
Figure 707050DEST_PATH_IMAGE109
Fault compensation matrix
Figure 975220DEST_PATH_IMAGE111
And inputting the state of the aircraft into the T-S fuzzy fault-tolerant control framework in the step 31, and realizing consistent bounded stability of the state of the aircraft under the distributed fault.
6. The distributed fault compensation method for the flexible hypersonic aircraft according to claim 5, characterized in that the step 4 comprises the following sub-steps:
step 41: introduction of robust performance indicators
Figure 905130DEST_PATH_IMAGE001
Figure 866133DEST_PATH_IMAGE148
Wherein
Figure 514283DEST_PATH_IMAGE149
representing robust performance indicators
Figure 320565DEST_PATH_IMAGE001
A coefficient;
step 42: according to the positive nature of the Lyapunov function and the negative nature of the derivative thereof and the introduced robust performanceIndex (I)
Figure 370561DEST_PATH_IMAGE001
Establishing linear matrix inequality constraint to obtain output feedback control gain matrix to be solved
Figure 236886DEST_PATH_IMAGE109
Fault compensation matrix to be solved
Figure 870867DEST_PATH_IMAGE111
(ii) a The linear matrix inequality constraint is:
Figure 480840DEST_PATH_IMAGE150
wherein,
Figure 385342DEST_PATH_IMAGE151
，
Figure 688147DEST_PATH_IMAGE152
for the third constant matrix to be solved,
Figure 45311DEST_PATH_IMAGE153
for the fourth matrix of constants to be solved,
step 43: based on the third constant matrix solved in step 42
Figure 458974DEST_PATH_IMAGE154
And a fourth constant matrix Z to obtain a state feedback control gain matrix
Figure 217983DEST_PATH_IMAGE155
；
Step 44: state feedback control gain matrix to be solved
Figure 691690DEST_PATH_IMAGE107
And for transfusionOutput feedback control gain matrix
Figure 300263DEST_PATH_IMAGE109
Fault compensation matrix
Figure 986459DEST_PATH_IMAGE111
Inputting the state of the aircraft into the T-S fuzzy fault-tolerant control framework in the step 31 to realize gradual stabilization of the state of the aircraft under the distributed fault.
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