CN112130584A - Finite time self-adaptive control method of four-rotor aircraft based on command filtering - Google Patents

Finite time self-adaptive control method of four-rotor aircraft based on command filtering Download PDF

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CN112130584A
CN112130584A CN202011001794.5A CN202011001794A CN112130584A CN 112130584 A CN112130584 A CN 112130584A CN 202011001794 A CN202011001794 A CN 202011001794A CN 112130584 A CN112130584 A CN 112130584A
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rotor aircraft
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崔国增
杨伟
李泽
陶重犇
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Suzhou University of Science and Technology
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Abstract

The invention relates to a finite time self-adaptive control method of a four-rotor aircraft based on command filtering, aiming at the four-rotor aircraft with unknown nonlinear dynamics and external disturbance, a position and attitude trajectory tracking controller is designed by using a finite time command filtering backstepping method, so that the four-rotor aircraft can be quickly and accurately controlled; a finite time command filter is introduced to realize the rapid approximation of the derivative of the virtual control signal, thereby effectively avoiding the problem of dimension explosion; a new fractional order error compensation mechanism is designed to quickly remove the influence of filtering errors, so that the control performance of the four-rotor aircraft is further improved; strictly proving that all signals in a closed-loop system are bounded in limited time by using a finite time stability theory, and the position and attitude tracking errors are converged to a neighborhood near an origin in the limited time; the effectiveness of the control scheme was verified by a simulation comparative example.

Description

Finite time self-adaptive control method of four-rotor aircraft based on command filtering
Technical Field
The invention relates to a finite time self-adaptive control method of a four-rotor aircraft based on command filtering.
Background
The four-rotor aircraft has the characteristics of simple structure, high deployment efficiency, flexible control and the like, is widely concerned by researchers, and is widely applied to the fields of aerial photography, intelligent transportation, urban fire protection, cargo transportation and the like. However, the problems of parameter uncertainty, underactuation, strong coupling characteristics and the like exist in a four-rotor aircraft system, and how to design and realize high-quality flight is a challenging problem in the control field.
In order to improve the control performance of a four-rotor aircraft, a great deal of research has been carried out by some scholars and various effective nonlinear control algorithms have been proposed. When the aircraft is influenced by parameter uncertainty and air resistance, part of scholars provide a control algorithm of the four-rotor aircraft by using a sliding mode control technology; but the control algorithm has the phenomenon that a discontinuous switch control item is easy to generate buffeting.
Fortunately, the backstepping design method has significant advantages in the controller design of the structural uncertainty system, and in recent years, some researchers have succeeded in applying the backstepping method to the four-rotor flight controller design and have achieved results. However, when a control algorithm of the four-rotor aircraft is designed by adopting a backstepping recursion method, the virtual control signal needs to be repeatedly derived, and the problem of dimension explosion is easily caused. To solve this problem, a dynamic plane control technique and a command filter back-stepping method are successively proposed. Some scholars give their dynamic surface flight control algorithms for aircraft with lumped unknown non-linearities. Based on the dynamic surface control technology, the four-rotor aircraft cooperative fault-tolerant control is also researched. In essence, both the dynamic surface control technology and the command filtering step-back method utilize a filter to obtain the derivative of a virtual control signal, so as to reduce the computational complexity, but compared with the former method, only first-order filtering is considered, and an error compensation mechanism is also introduced into the command filtering step-back method to remove the influence of a filtering error on the control performance, so as to obtain better control performance.
It is worth noting that the above control scheme only guarantees progressive convergence and does not allow limited time tracking control of a quad-rotor aircraft. Considering that the finite time control has the advantages of high convergence rate, high tracking precision, strong robustness and the like, the research on the finite time control of the four-rotor aircraft has important practical significance.
Disclosure of Invention
The invention aims to overcome the defects in the prior art and provides a finite time self-adaptive control method of a four-rotor aircraft based on command filtering.
The purpose of the invention is realized by the following technical scheme:
a four-rotor aircraft finite time self-adaptive control method based on command filtering is characterized in that: the method comprises the following steps:
establishing a four-rotor aircraft dynamic model:
Figure BDA0002694583440000021
wherein x, y and z are the positions of the four-rotor aircraft in an inertial coordinate system; phi, theta and psi are respectively a roll angle, a pitch angle and a yaw angle; m is the mass of the organism; g is the acceleration of gravity; l is the distance from the center of mass of the machine body to the rotating shaft of the motor; j. the design is a squarex，Jy，JzThe rotational inertia of the four-rotor aircraft about three axes x, y and z is respectively; g(·)Is the air resistance coefficient of the system; d(·)Is the external disturbance to the system;
Figure BDA0002694583440000031
is a control input;
the following state variables are defined
Figure BDA0002694583440000032
Figure BDA0002694583440000033
The simplified model of quadrotor aircraft dynamics is then as follows:
Figure BDA0002694583440000034
wherein
Figure BDA0002694583440000035
Figure BDA0002694583440000036
Figure BDA0002694583440000037
Indicating that the quad-rotor aircraft is subject to external disturbances,
Figure BDA0002694583440000038
and
Figure BDA0002694583440000039
(II) designing a controller:
first, a tracking error variable is defined:
Figure BDA00026945834400000310
χi+1＝Ξi+1-Λi+1，c (4)
wherein i is 1, 3, 5, 7, 9, 11,
Figure BDA00026945834400000311
is xiiCorresponding reference signal, [ y ]1，y2，y3，y4，y5，y6]＝[φd，θd，ψd，zd，xd，yd]；Λi+1，cIs a virtual control signal ΛiAs a filtered output signal at the filtering input, wherein the finite time command filtering is in the form:
Figure BDA00026945834400000312
wherein phiiAnd phii+1Is a state variable; a isi，1，ai，2And eiFor design parameters；Λi+1，c＝φi，
Figure BDA0002694583440000041
For the finite time command filtering shown in equation (5), there is a constant
Figure BDA00026945834400000410
And ρ > 0 such that the following equation holds
Figure BDA0002694583440000042
Wherein
Figure BDA00026945834400000411
Is represented byiPhi and phii+1The degree of approximation therebetween;
defining a tracking error compensation variable:
κi＝χi-ηi (7)
κi+1＝χi+1-ηi+1 (8)
wherein etai，ηi+1To compensate the signal;
2.1) design attitude controller
The attitude subsystem is divided into a roll angle subsystem, a pitch angle subsystem and a yaw angle subsystem, and a controller is designed for each subsystem to realize attitude tracking control of the four-rotor aircraft;
for the attitude sub-system (i ═ 1, 3, 5)
Figure BDA0002694583440000043
Firstly, the following virtual control signals and controllers are designed:
Figure BDA0002694583440000044
Figure BDA0002694583440000045
wherein c isi，ci+1，si，si+1，liIs a normal number; 1/2 < gamma ═ gamma1/γ2＜1，γ1，γ2Is positive odd;
Figure BDA0002694583440000046
is a vector of basis functions of the fuzzy logic system;
Figure BDA0002694583440000047
is an unknown constant
Figure BDA0002694583440000048
Wherein, in
Figure BDA00026945834400000412
Is a weight vector for the fuzzy logic system,
Figure BDA0002694583440000049
estimating an error for the parameter; rate of parameter update
Figure BDA0002694583440000059
The structure is as follows:
Figure BDA0002694583440000051
wherein the design parameters
Figure BDA0002694583440000052
For eliminating filtering error lambdai+1，c-ΛiThe following fractional order error compensation signal is introduced:
Figure BDA0002694583440000053
Figure BDA0002694583440000054
wherein constant hi，hi+1Greater than 0, ηi(0)＝ηi+1(0)＝0；
2.2) design of the position controller
The position subsystem is divided into a z-height subsystem, an x-position subsystem and a y-position subsystem, and a controller is designed for each subsystem, so that the position trajectory tracking control of the four-rotor aircraft is realized;
for the location subsystem (i ═ 7, 9, 11)
Figure BDA0002694583440000055
The virtual control signals and the controller are designed as follows:
Figure BDA0002694583440000056
Figure BDA0002694583440000057
Figure BDA0002694583440000058
wherein constant ci，ci+1，si，si+1，liGreater than 0; 1/2 < gamma ═ gamma1/γ2＜1，γ1，γ2Is positive odd;
Figure BDA0002694583440000061
is a vector of basis functions of the fuzzy logic system;
Figure BDA0002694583440000062
is an unknown constant
Figure BDA0002694583440000063
Wherein, in
Figure BDA00026945834400000610
Is a weight vector for the fuzzy logic system,
Figure BDA0002694583440000064
estimating an error for the parameter; rate of parameter update
Figure BDA00026945834400000611
The structure is as follows:
Figure BDA0002694583440000065
wherein the parameters
Figure BDA00026945834400000612
Greater than 0;
the following fractional order error compensation signal is constructed:
Figure BDA0002694583440000066
Figure BDA0002694583440000067
wherein h isi，hi+1Is a normal number, ηi(0)＝ηi+1(0)＝0；
2.3) inverse solution of the desired Signal
Control input using position subsystem
Figure BDA00026945834400000613
Inverse solution to obtain the information [ phi ] needed by the attitude subsystemd，θd]Thereby realizing the four-rotor aircraft tracking reference signal [ x ]d，yd，zd，ψd]Meanwhile, the roll angle and the pitch angle are automatically stabilized;
according to the simplified model formula (2) of the dynamics of the four-rotor aircraft, it can be known that:
Figure BDA0002694583440000068
further obtain
Figure BDA0002694583440000069
Further, the finite time adaptive control method of the four-rotor aircraft based on command filtering further comprises:
(III) stability analysis:
according to the designed virtual control signal, the controller, the parameter update rate and the error compensation signal, the finite time stability theory analysis is utilized to prove that all signals of the closed-loop system are bounded within finite time;
step1, for i 1, 3, 5, 7, 9, 11, according to formula (3), formula (4) and formula (7), for κiDerived by derivation
Figure BDA0002694583440000071
Choosing Lyapunov function as
Figure BDA0002694583440000072
Based on
Figure BDA00026945834400000712
ΛiEta, andiobtaining ViDerivative of (2)
Figure BDA0002694583440000073
Step2 based on equations (2), (4) andequation (8), for κi+1Derived to obtain
Figure BDA0002694583440000074
Model uncertainty term
Figure BDA00026945834400000713
Using fuzzy logic systems for unknown non-linear functions
Figure BDA0002694583440000075
To pair
Figure BDA0002694583440000076
It approaches, for any given
Figure BDA0002694583440000077
Exist of
Figure BDA0002694583440000078
Figure BDA0002694583440000079
Figure BDA00026945834400000710
Scaled according to an inequality
Figure BDA00026945834400000711
Figure BDA0002694583440000081
Choosing Lyapunov function as
Figure BDA0002694583440000082
To Vi+1The derivation is obtained by combining equations (25) to (28):
Figure BDA0002694583440000083
consider that
Figure BDA0002694583440000084
The formula (29) can be obtained by substituting the formula (12) and the formula (19)
Figure BDA0002694583440000085
Step3, selecting a Lyapunov function as
Figure BDA0002694583440000086
According to the formula (30) and
Figure BDA0002694583440000087
the derivative of V may be arranged as
Figure BDA0002694583440000091
By scaling according to the inequalities and combining equation (6)
Figure BDA0002694583440000092
Figure BDA0002694583440000093
Figure BDA0002694583440000094
Equation (31) can be converted to equation (32) to equation (34)
Figure BDA0002694583440000095
Further obtain the
Figure BDA0002694583440000096
In the formula
Figure BDA0002694583440000097
Figure BDA0002694583440000098
And is
Figure BDA0002694583440000099
Figure BDA0002694583440000101
Exist of
Figure BDA0002694583440000102
Equation (36) can be converted to:
Figure BDA0002694583440000103
or
Figure BDA0002694583440000104
According to equation (37), if
Figure BDA0002694583440000105
Then
Figure BDA0002694583440000106
Thus, kappa can be obtainedi，ηiAnd
Figure BDA00026945834400001014
at a finite time TrInner convergence to the following set
Figure BDA0002694583440000107
Convergence time TrIs composed of
Figure BDA0002694583440000108
According to the formula (38), when
Figure BDA0002694583440000109
Then
Figure BDA00026945834400001010
Let us know thati，ηiAnd
Figure BDA00026945834400001015
at a finite time TrInner convergence to the following set
Figure BDA00026945834400001011
Convergence time TrIs composed of
Figure BDA00026945834400001012
As can be seen from the equations (39) and (41), when i is 1, 3, 5, 7, 9, 11, κiAnd ηiWill eventually converge to the following set
Figure BDA00026945834400001013
Figure BDA0002694583440000111
Convergence time of
Figure BDA0002694583440000112
When T is more than or equal to T, the compound can be obtained
Figure BDA0002694583440000113
Therefore, χiConverge to a neighborhood near the origin in a finite time, and all signals in a closed loop system are bounded in finite time.
Compared with the prior art, the invention has obvious advantages and beneficial effects, and is embodied in the following aspects:
aiming at a position subsystem and an attitude subsystem of a four-rotor aircraft, a position and attitude trajectory tracking controller is designed by respectively using a finite time command filtering backstepping method, so that the four-rotor aircraft is quickly and accurately controlled; the finite time command filtering can not only quickly approximate the derivative of the virtual control signal, but also effectively avoid buffeting caused by a sign function and further weaken the limit condition of the virtual control signal;
introducing finite time command filtering, designing a fractional order error compensation mechanism based on non-smooth signals and combining a reverse step design method, and providing a four-rotor aircraft finite time control technical scheme, wherein a designed controller ensures that all signals in a closed loop system are bounded within finite time, and position and attitude tracking errors are converged into the vicinity of an origin within the finite time;
thirdly, the invention is based on the fractional order error compensation mechanism of the non-smooth signal, thereby ensuring that the influence of the filtering error is quickly compensated and having more effectiveness in practical application;
and fourthly, the obvious superiority of the finite time control scheme provided by the invention can be verified through a simulation comparison experiment.
Additional features and advantages of the invention will be set forth in the description which follows, and in part will be obvious from the description, or may be learned by the practice of the invention. The objectives and other advantages of the invention will be realized and attained by the structure particularly pointed out in the written description and claims hereof as well as the appended drawings.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings that are required to be used in the embodiments will be briefly described below, it should be understood that the following drawings only illustrate some embodiments of the present invention and therefore should not be considered as limiting the scope, and for those skilled in the art, other related drawings can be obtained according to the drawings without inventive efforts.
FIG. 1: the flow chart of the control method of the invention is shown schematically;
FIG. 2: a two-dimensional tracking curve graph of an actual gesture track and an expected signal;
FIG. 3: two-dimensional tracking curve graphs of the actual track and the expected track of the position;
FIG. 4: an attitude trajectory tracking error curve graph;
FIG. 5: position trajectory tracking error plot.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. The components of embodiments of the present invention generally described and illustrated in the figures herein may be arranged and designed in a wide variety of different configurations. Thus, the following detailed description of the embodiments of the present invention, presented in the figures, is not intended to limit the scope of the invention, as claimed, but is merely representative of selected embodiments of the invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments of the invention without making creative efforts, shall fall within the protection scope of the invention.
It should be noted that: like reference numbers and letters refer to like items in the following figures, and thus, once an item is defined in one figure, it need not be further defined and explained in subsequent figures. Meanwhile, in the description of the present invention, the directional terms and the sequence terms, etc. are used only for distinguishing the description, and are not to be construed as indicating or implying relative importance.
Aiming at the problem of trajectory tracking control of a four-rotor aircraft with parameter uncertainty and external interference, the invention provides a finite time self-adaptive control method based on command filtering, and by introducing a finite time command filter, the rapid approximation of a virtual control signal derivative is realized, so that the problem of dimension explosion existing in the traditional backstepping design method is effectively avoided; a new fractional order error compensation mechanism is designed to remove the influence of filtering errors, so that the control performance is further improved; strictly proving that all signals in a closed-loop system are bounded in limited time by using a finite time stability theory, and the position and attitude tracking errors are converged to a neighborhood near an origin in the limited time; the effectiveness of the control scheme was verified by a simulation comparative example.
As shown in fig. 1, the finite time adaptive control method of the quad-rotor aircraft based on command filtering specifically includes the following steps:
establishing a four-rotor aircraft dynamic model:
Figure BDA0002694583440000131
wherein x, y and z are the positions of the four-rotor aircraft in an inertial coordinate system; phi, theta and psi are respectively a roll angle, a pitch angle and a yaw angle; m is the mass of the organism; g is the acceleration of gravity; l is the distance from the center of mass of the machine body to the rotating shaft of the motor; j. the design is a squarex，Jy，JzThe rotational inertia of the four-rotor aircraft about three axes x, y and z is respectively; g(·)Is the air resistance coefficient of the system; d(·)Is the external disturbance to the system;
Figure BDA00026945834400001411
is a control input;
the following state variables are defined
Figure BDA0002694583440000141
Figure BDA0002694583440000142
The simplified model of quadrotor aircraft dynamics is then as follows:
Figure BDA0002694583440000143
wherein
Figure BDA0002694583440000144
Figure BDA0002694583440000145
Figure BDA0002694583440000146
Indicating that the quad-rotor aircraft is subject to external disturbances,
Figure BDA0002694583440000147
and
Figure BDA0002694583440000148
(II) designing a controller:
first, a tracking error variable is defined:
Figure BDA0002694583440000149
χi+1＝Ξi+1-Λi+1，c (4)
wherein i is 1, 3, 5, 7, 9, 11,
Figure BDA00026945834400001410
is xiiCorresponding reference signal, [ y ]1，y2，y3，y4，y5，y6]＝[φd，θd，ψd，zd，xd，yd]；Λi+1，cIs a virtual control signal ΛiAs a filtered output signal at the filtering input, wherein the finite time command filtering is in the form:
Figure BDA0002694583440000151
wherein phiiAnd phii+1Is a state variable; a isi，1，ai，2And eiIs a design parameter; lambdai+1，c＝φi，
Figure BDA0002694583440000152
For the finite time command filtering shown in equation (5), there is a constant
Figure BDA0002694583440000157
And ρ > 0 such that the following equation holds
Figure BDA0002694583440000153
Wherein
Figure BDA0002694583440000158
Is represented byiPhi and phii+1The degree of approximation therebetween;
defining a tracking error compensation variable:
κi＝χi-ηi (7)
κi+1＝χi+1-ηi+1 (8)
wherein etai，ηi+1To compensate the signal;
2.1) design attitude controller
The attitude subsystem is divided into a roll angle subsystem, a pitch angle subsystem and a yaw angle subsystem, and a controller is designed for each subsystem to realize attitude tracking control of the four-rotor aircraft;
for the attitude sub-system (i ═ 1, 3, 5)
Figure BDA0002694583440000154
Firstly, the following virtual control signals and controllers are designed:
Figure BDA0002694583440000155
Figure BDA0002694583440000156
wherein c isi，ci+1，si，si+1，liIs a normal number; 1/2 < gamma ═ gamma1/γ2＜1，γ1，γ2Is positive odd;
Figure BDA0002694583440000161
is a vector of basis functions of the fuzzy logic system;
Figure BDA0002694583440000162
is an unknown constant
Figure BDA0002694583440000163
Wherein, in
Figure BDA0002694583440000164
Is a weight vector for the fuzzy logic system,
Figure BDA0002694583440000165
estimating an error for the parameter; rate of parameter update
Figure BDA0002694583440000166
The structure is as follows:
Figure BDA0002694583440000167
wherein the design parameters
Figure BDA0002694583440000168
For eliminating filtering error lambdai+1，c-ΛiThe following fractional order error compensation signal is introduced:
Figure BDA0002694583440000169
Figure BDA00026945834400001610
wherein constant hi，hi+1Greater than 0, ηi(0)＝ηi+1(0)＝0；
2.2) design of the position controller
The position subsystem is divided into a z-height subsystem, an x-position subsystem and a y-position subsystem, and a controller is designed for each subsystem, so that the position trajectory tracking control of the four-rotor aircraft is realized;
for the location subsystem (i ═ 7, 9, 11)
Figure BDA00026945834400001611
The virtual control signals and the controller are designed as follows:
Figure BDA00026945834400001612
Figure BDA00026945834400001613
Figure BDA0002694583440000171
wherein constant ci，ci+1，si，si+1，liGreater than 0; 1/2 < gamma ═ gamma1/γ2＜1，γ1，γ2Is positive odd;
Figure BDA0002694583440000172
is a vector of basis functions of the fuzzy logic system;
Figure BDA0002694583440000173
is an unknown constant
Figure BDA0002694583440000174
Wherein, in
Figure BDA0002694583440000175
Is a weight vector for the fuzzy logic system,
Figure BDA0002694583440000176
estimating an error for the parameter; rate of parameter update
Figure BDA0002694583440000177
The structure is as follows:
Figure BDA0002694583440000178
wherein the parameters
Figure BDA0002694583440000179
Greater than 0;
the following fractional order error compensation signal is constructed:
Figure BDA00026945834400001710
Figure BDA00026945834400001711
wherein h isi，hi+1Is a normal number, ηi(0)＝ηi+1(0)＝0；
2.3) inverse solution of the desired Signal
Control input using position subsystem
Figure BDA00026945834400001712
Inverse solution to obtain the information [ phi ] needed by the attitude subsystemd，θd]Thereby realizing the four-rotor aircraft tracking reference signal [ x ]d，yd，zd，ψd]Meanwhile, the roll angle and the pitch angle are automatically stabilized;
according to the simplified model formula (2) of the dynamics of the four-rotor aircraft, it can be known that:
Figure BDA00026945834400001713
further obtain
Figure BDA0002694583440000181
(III) stability analysis:
according to the designed virtual control signal, the controller, the parameter update rate and the error compensation signal, the finite time stability theory analysis is utilized to prove that all signals of the closed-loop system are bounded within finite time;
step1, for i 1, 3, 5, 7, 9, 11, according to formula (3), formula (4) and formula (7), for κiDerived by derivation
Figure BDA0002694583440000182
Choosing Lyapunov function as
Figure BDA0002694583440000183
Based on
Figure BDA0002694583440000184
ΛiAnd ηiObtaining ViDerivative of (2)
Figure BDA0002694583440000185
Step2 based on equation (2), equation (4) and equation (8), for kappai+1Derived to obtain
Figure BDA0002694583440000186
Model uncertainty term
Figure BDA0002694583440000187
Using fuzzy logic systems for unknown non-linear functions
Figure BDA0002694583440000188
To pair
Figure BDA0002694583440000189
It approaches, for any given
Figure BDA00026945834400001810
Exist of
Figure BDA00026945834400001811
Figure BDA00026945834400001812
Figure BDA00026945834400001813
Scaled according to an inequality
Figure BDA0002694583440000191
Figure BDA0002694583440000192
Selecting Lyapunov function of
Figure BDA0002694583440000193
To Vi+1The derivation is obtained by combining equations (25) to (28):
Figure BDA0002694583440000194
consider that
Figure BDA0002694583440000195
The formula (29) can be obtained by substituting the formula (12) and the formula (19)
Figure BDA0002694583440000196
Step3, selecting a Lyapunov function as
Figure BDA0002694583440000197
According to the formula (30) and
Figure BDA0002694583440000198
the derivative of V may be arranged as
Figure BDA0002694583440000201
By scaling according to the inequalities and combining equation (6)
Figure BDA0002694583440000202
Figure BDA0002694583440000203
Figure BDA0002694583440000204
Equation (31) can be converted to equation (32) to equation (34)
Figure BDA0002694583440000205
Further obtain the
Figure BDA0002694583440000206
In the formula
Figure BDA0002694583440000207
Figure BDA0002694583440000208
And is
Figure BDA0002694583440000209
Figure BDA0002694583440000211
Exist of
Figure BDA0002694583440000212
Equation (36) can be converted to:
Figure BDA0002694583440000213
or
Figure BDA0002694583440000214
According to equation (37), if
Figure BDA0002694583440000215
Then
Figure BDA0002694583440000216
Thus, kappa can be obtainedi，ηiAnd
Figure BDA00026945834400002114
at a finite time TrInner convergence to the following set
Figure BDA0002694583440000217
Convergence time TrIs composed of
Figure BDA0002694583440000218
According to the formula (38), when
Figure BDA0002694583440000219
Then
Figure BDA00026945834400002110
Let us know thati，ηiAnd
Figure BDA00026945834400002115
at a finite time TrInner convergence to the following set
Figure BDA00026945834400002111
Convergence time TrIs composed of
Figure BDA00026945834400002112
As can be seen from the equations (39) and (41), when i is 1, 3, 5, 7, 9, 11, κiAnd ηiWill eventually converge to the following set
Figure BDA00026945834400002113
Figure BDA0002694583440000221
Convergence time of
Figure BDA0002694583440000222
When T is more than or equal to T, the compound can be obtained
Figure BDA0002694583440000223
Therefore, χiConverge to a neighborhood near the origin in a finite time, and all signals in a closed loop system are bounded in finite time.
(IV) simulation result and analysis:
the Matlab/Simulink software is used for carrying out simulation verification on the proposed finite time control scheme, and the model parameters of the four-rotor aircraft are selected as follows:
m＝2kg，g＝9.8m/s2，l＝0.325m，
Jx＝0.082kg·m2，Jy＝0.082kg·m2，
Jz＝0.149kg·m2.
Gx＝Gy＝Gz＝0.6kg/s，
Gφ＝Gθ＝Gψ＝0.6kg/rad.
in the simulation, the desired reference signal for the quad-rotor aircraft was set to
Figure BDA0002694583440000224
The external interference is selected as
Figure BDA0002694583440000225
The initial conditions of the system are [ phi (0), theta (0), psi (0), x (0), y (0), z (0)]＝[0，0，0，1，0，0](ii) a The control design parameters are selected as follows:
∈1＝∈3＝∈5＝5×10-4，
∈7＝∈9＝∈11＝2.5×10-3.
c2i-1＝0.6，c2i＝0.8，li＝mi＝2，
s2i-1＝h2i-1＝0.8，s2i＝h2i＝1.2，
ri＝0.8，ai，1＝8，ai，2＝5，i＝1，...，6.
and further, a finite time self-adaptive tracking control simulation result of the four-rotor aircraft can be obtained.
Simulation results of the four-rotor aircraft of the finite time command filtering backstepping method and the traditional command filtering backstepping method are shown in fig. 2-5, fig. 2 illustrates a two-dimensional tracking curve of an actual attitude track and an expected signal, fig. 3 illustrates a two-dimensional tracking curve of an actual position track and an expected position track, fig. 4 illustrates an attitude track tracking error curve, and fig. 5 illustrates a position track tracking error curve. It can be seen that the tracking error of the limited time tracking control of the present invention is not only smaller than that of the asymptotic tracking control, but also has a faster convergence rate, and the tracking error is well maintained at a smaller degree.
In conclusion, the position and attitude trajectory tracking controller is designed by using a finite time command filtering backstepping method aiming at the position subsystem and the attitude subsystem of the four-rotor aircraft, so that the four-rotor aircraft can be quickly and accurately controlled; the finite time command filtering can not only quickly approximate the derivative of the virtual control signal, but also effectively avoid buffeting caused by a sign function and further weaken the limit condition of the virtual control signal; the method is based on a fractional order error compensation mechanism of the non-smooth signal, ensures that the influence of the filtering error is quickly compensated, and has higher effectiveness in practical application.
Finite time command filtering is introduced, a fractional order error compensation mechanism based on non-smooth signals is designed, a backstepping design method is combined, and a four-rotor aircraft finite time control technical scheme is provided; the significant superiority of the limited time control scheme provided by the invention can be verified through simulation comparison experiments.
The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention. It should be noted that: like reference numbers and letters refer to like items in the following figures, and thus, once an item is defined in one figure, it need not be further defined and explained in subsequent figures.
The above description is only for the specific embodiments of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art can easily conceive of the changes or substitutions within the technical scope of the present invention, and shall be covered by the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.
It is noted that, herein, relational terms such as first and second, and the like may be used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Also, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising an … …" does not exclude the presence of other identical elements in a process, method, article, or apparatus that comprises the element.

Claims (2)

1. Four-rotor aircraft finite time self-adaptive control method based on command filtering is characterized in that: the method comprises the following steps:
establishing a four-rotor aircraft dynamic model:
Figure FDA0002694583430000011
wherein x, y and z are the positions of the four-rotor aircraft in an inertial coordinate system; phi, theta and psi are respectively a roll angle, a pitch angle and a yaw angle; m is the mass of the organism; g is the acceleration of gravity; l is the distance from the center of mass of the machine body to the rotating shaft of the motor; j. the design is a squarex，Jy，JzThe rotational inertia of the four-rotor aircraft about three axes x, y and z is respectively; g(·)Is the air resistance coefficient of the system; d(·)Is the external disturbance to the system; tau isF，τφ，τθ，τψIs a control input;
the following state variables are defined
Figure FDA0002694583430000012
Figure FDA0002694583430000013
The simplified model of quadrotor aircraft dynamics is then as follows:
Figure FDA0002694583430000014
wherein
Figure FDA0002694583430000021
Figure FDA0002694583430000022
Figure FDA0002694583430000023
Indicating external disturbance to the four-rotor aircraft, [ tau ]1，τ2，τ3，τ4]＝[τφ，τθ，τψ，τF]And τ5＝cosφsinθcosψ+sinφsinψ，τ6＝cosφsinθsinψ-sinφcosψ；
(II) designing a controller:
first, a tracking error variable is defined:
Figure FDA0002694583430000024
χi+1＝Ξi+1-Λi+1，c (4)
wherein i is 1, 3, 5, 7, 9, 11,
Figure FDA0002694583430000025
is xiiCorresponding reference signal, [ y ]1，y2，y3，y4，y5，y6]＝[φd，θd，ψd，zd，xd，yd]；Λi+1，cIs a virtual control signal ΛiAs a filtered output signal at the filtering input, wherein the finite time command filtering is in the form:
Figure FDA0002694583430000026
wherein phiiAnd phii+1Is a state variable; a isi，1，ai，2And eiIs a design parameter; lambdai+1，c＝φi，
Figure FDA0002694583430000027
For the finite time command filtering shown in equation (5), the constants τ > 0 and ρ > 0 exist such that the following holds
Figure FDA0002694583430000028
Wherein O isi(∈ρτ) Is represented byiPhi and phii+1The degree of approximation therebetween;
defining a tracking error compensation variable:
κi＝χi-ηi (7)
κi+1＝χi+1-ηi+1 (8)
wherein etai，ηi+1To compensate the signal;
2.1) design attitude controller
The attitude subsystem is divided into a roll angle subsystem, a pitch angle subsystem and a yaw angle subsystem, and a controller is designed for each subsystem to realize attitude tracking control of the four-rotor aircraft;
for the attitude sub-system (i ═ 1, 3, 5)
Figure FDA0002694583430000031
Firstly, the following virtual control signals and controllers are designed:
Figure FDA0002694583430000032
Figure FDA0002694583430000033
wherein c isi，ci+1，si，si+1，liIs a normal number; 1/2 < gamma ═ gamma1/γ2＜1，γ1，γ2Is positive odd;
Figure FDA0002694583430000034
being basis functions of fuzzy logic systemsVector quantity;
Figure FDA0002694583430000035
is an unknown constant
Figure FDA0002694583430000036
Wherein, in
Figure FDA0002694583430000037
Is a weight vector for the fuzzy logic system,
Figure FDA0002694583430000038
estimating an error for the parameter; rate of parameter update
Figure FDA0002694583430000039
The structure is as follows:
Figure FDA00026945834300000310
wherein the design parameters
Figure FDA00026945834300000311
For eliminating filtering error lambdai+1，c-ΛiThe following fractional order error compensation signal is introduced:
Figure FDA00026945834300000312
Figure FDA00026945834300000313
wherein constant hi，hi+1Greater than 0, ηi(0)＝ηi+1(0)＝0；
2.2) design of the position controller
The position subsystem is divided into a z-height subsystem, an x-position subsystem and a y-position subsystem, and a controller is designed for each subsystem, so that the position trajectory tracking control of the four-rotor aircraft is realized;
for the location subsystem (i ═ 7, 9, 11)
Figure FDA0002694583430000041
The virtual control signals and the controller are designed as follows:
Figure FDA0002694583430000042
Figure FDA0002694583430000043
Figure FDA0002694583430000044
wherein constant ci，ci+1，si，si+1，liGreater than 0; 1/2 < gamma ═ gamma1/γ2＜1，γ1，γ2Is positive odd;
Figure FDA0002694583430000045
is a vector of basis functions of the fuzzy logic system;
Figure FDA0002694583430000046
is an unknown constant
Figure FDA0002694583430000047
Wherein, in
Figure FDA0002694583430000048
As a fuzzy logic systemThe weight vector of (2) is calculated,
Figure FDA0002694583430000049
estimating an error for the parameter; rate of parameter update
Figure FDA00026945834300000410
The structure is as follows:
Figure FDA00026945834300000411
wherein the parameters
Figure FDA00026945834300000412
Greater than 0;
the following fractional order error compensation signal is constructed:
Figure FDA0002694583430000051
Figure FDA0002694583430000052
wherein h isi，hi+1Is a normal number, ηi(0)＝ηi+1(0)＝0；
2.3) inverse solution of the desired Signal
Using control input [ tau ] of the position subsystem5，τ6]Inverse solution to obtain the information [ phi ] needed by the attitude subsystemd，θd]Thereby realizing the four-rotor aircraft tracking reference signal [ x ]d，yd，zd，ψd]Meanwhile, the roll angle and the pitch angle are automatically stabilized;
according to the simplified model formula (2) of the dynamics of the four-rotor aircraft, it can be known that:
Figure FDA0002694583430000053
further obtain
Figure FDA0002694583430000054
2. The command-filtering-based finite-time adaptive control method for a quad-rotor aircraft according to claim 1, wherein: further comprising:
(III) stability analysis:
according to the designed virtual control signal, the controller, the parameter update rate and the error compensation signal, the finite time stability theory analysis is utilized to prove that all signals of the closed-loop system are bounded within finite time;
step1: for i ═ 1, 3, 5, 7, 9, 11, according to formula (3), formula (4) and formula (7), for κiDerived by derivation
Figure FDA0002694583430000055
Choosing Lyapunov function as
Figure FDA0002694583430000056
Based on
Figure FDA0002694583430000057
ΛiAnd ηiObtaining ViDerivative of (2)
Figure FDA0002694583430000061
Step2: based on formula (2), formula (4) and formula (8), for ki+1Derived to obtain
Figure FDA0002694583430000062
Model uncertainty term
Figure FDA0002694583430000063
Using fuzzy logic systems for unknown non-linear functions
Figure FDA0002694583430000064
To pair
Figure FDA0002694583430000065
It approaches, for any given
Figure FDA0002694583430000066
Exist of
Figure FDA0002694583430000067
Figure FDA0002694583430000068
Figure FDA0002694583430000069
Figure FDA00026945834300000610
Scaled according to an inequality
Figure FDA00026945834300000611
Figure FDA00026945834300000612
Choosing Lyapunov function as
Figure FDA00026945834300000613
To Vi+1The derivation is obtained by combining equations (25) to (28):
Figure FDA0002694583430000071
consider that
Figure FDA0002694583430000072
The formula (29) can be obtained by substituting the formula (12) and the formula (19)
Figure FDA0002694583430000073
Step3: choosing Lyapunov function as
Figure FDA0002694583430000074
According to the formula (30) and
Figure FDA0002694583430000075
the derivative of V may be arranged as
Figure FDA0002694583430000076
By scaling according to the inequalities and combining equation (6)
Figure FDA0002694583430000077
Figure FDA0002694583430000081
Figure FDA0002694583430000082
Equation (31) can be converted to equation (32) to equation (34)
Figure FDA0002694583430000083
Further obtain the
Figure FDA0002694583430000084
In the formula
Figure FDA0002694583430000085
Figure FDA0002694583430000086
And is
Figure FDA0002694583430000087
Figure FDA0002694583430000088
Exist of
Figure FDA0002694583430000089
Equation (36) can be converted to:
Figure FDA00026945834300000810
or
Figure FDA00026945834300000811
According to equation (37), if
Figure FDA00026945834300000813
Then
Figure FDA00026945834300000812
Thereby obtaining ki，ηiAnd
Figure FDA0002694583430000091
at a finite time TrInner convergence to the following set
Figure FDA0002694583430000092
Convergence time TrIs composed of
Figure FDA0002694583430000093
According to the formula (38), when
Figure FDA0002694583430000094
Then
Figure FDA0002694583430000095
Let us know thati，ηiAnd
Figure FDA0002694583430000096
at a finite time TrInner convergence to the following set
Figure FDA0002694583430000097
Convergence time TrIs composed of
Figure FDA0002694583430000098
As can be seen from the equations (39) and (41), when i is 1, 3, 5, 7, 9, 11, κiAnd ηiWill eventually converge to the following set
Figure FDA0002694583430000099
Figure FDA00026945834300000910
Convergence time of
Figure FDA00026945834300000911
When T is more than or equal to T, the compound can be obtained
Figure FDA0002694583430000101
Therefore, χiConverge to a neighborhood near the origin in a finite time, and all signals in a closed loop system are bounded in finite time.
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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113934143A (en) * 2021-11-24 2022-01-14 苏州科技大学 Multi-rotor aircraft finite time self-adaptive event-triggered fault-tolerant tracking control method
CN114019997A (en) * 2021-11-26 2022-02-08 南京航空航天大学 Finite time control method under position tracking deviation constraint of fixed-wing unmanned aerial vehicle

Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN107688295A (en) * 2017-08-29 2018-02-13 浙江工业大学 A kind of quadrotor finite time self-adaptation control method based on fast terminal sliding formwork
CN108121354A (en) * 2017-12-19 2018-06-05 天津理工大学 Quadrotor unmanned plane tenacious tracking control method based on instruction filtering Backstepping
CN109597303A (en) * 2018-11-29 2019-04-09 南京航空航天大学 A kind of composite rotor craft syntype flight control method
CN111596679A (en) * 2020-06-03 2020-08-28 青岛大学 Finite time output feedback attitude tracking control method for aircraft

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN107688295A (en) * 2017-08-29 2018-02-13 浙江工业大学 A kind of quadrotor finite time self-adaptation control method based on fast terminal sliding formwork
CN108121354A (en) * 2017-12-19 2018-06-05 天津理工大学 Quadrotor unmanned plane tenacious tracking control method based on instruction filtering Backstepping
CN109597303A (en) * 2018-11-29 2019-04-09 南京航空航天大学 A kind of composite rotor craft syntype flight control method
CN111596679A (en) * 2020-06-03 2020-08-28 青岛大学 Finite time output feedback attitude tracking control method for aircraft

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
WEI YANG 等: ""Adaptive Practical Fixed-Time Control for a Class of Nonlinear Systems with Input Saturation"", 《PROCEEDINGS OF THE 39TH CHINESE CONTROL CONFERENCE》 *
周海亮 等: ""新型指令滤波反步及高超声速飞行器的应用"", 《控制工程》 *

Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113934143A (en) * 2021-11-24 2022-01-14 苏州科技大学 Multi-rotor aircraft finite time self-adaptive event-triggered fault-tolerant tracking control method
CN113934143B (en) * 2021-11-24 2023-08-22 苏州科技大学 Multi-rotor aircraft limited time self-adaptive event-triggered fault-tolerant tracking control method
CN114019997A (en) * 2021-11-26 2022-02-08 南京航空航天大学 Finite time control method under position tracking deviation constraint of fixed-wing unmanned aerial vehicle
CN114019997B (en) * 2021-11-26 2023-12-01 南京航空航天大学 Finite time control method under position tracking deviation constraint of fixed wing unmanned aerial vehicle

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