CN110794857B - Robust discrete fractional order control method of fixed wing unmanned aerial vehicle considering external wind interference - Google Patents

Robust discrete fractional order control method of fixed wing unmanned aerial vehicle considering external wind interference Download PDF

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CN110794857B
CN110794857B CN201911043190.4A CN201911043190A CN110794857B CN 110794857 B CN110794857 B CN 110794857B CN 201911043190 A CN201911043190 A CN 201911043190A CN 110794857 B CN110794857 B CN 110794857B
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discrete
unmanned aerial
aerial vehicle
interference
order
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CN110794857A (en
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邵书义
陈谋
姜斌
甄子洋
盛守照
张柯
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Nanjing University of Aeronautics and Astronautics
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Nanjing University of Aeronautics and Astronautics
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00—Control of position, course or altitude of land, water, air, or space vehicles, e.g. automatic pilot
    • G05D1/08—Control of attitude, i.e. control of roll, pitch, or yaw
    • G05D1/0808—Control of attitude, i.e. control of roll, pitch, or yaw specially adapted for aircraft
    • G05D1/0816—Control of attitude, i.e. control of roll, pitch, or yaw specially adapted for aircraft to ensure stability
    • G05D1/0825—Control of attitude, i.e. control of roll, pitch, or yaw specially adapted for aircraft to ensure stability using mathematical models

Abstract

The invention discloses a robust discrete fractional order control method of a fixed wing unmanned aerial vehicle considering external wind interference, which specifically comprises the following steps: firstly, establishing a longitudinal control system and an attitude dynamics system model of the fixed-wing unmanned aerial vehicle under external wind interference; then, converting a continuous form unmanned aerial vehicle nonlinear model with wind interference into a discrete form by using an Euler approximation method, and designing a discrete interference observer to compensate the adverse effect of external wind interference on the flight control performance of the fixed wing unmanned aerial vehicle; and finally, a control scheme based on the discrete disturbance observer is designed by combining a discrete fractional order theory and a backstepping method to solve the problem of robust discrete disturbance rejection tracking control of the unmanned aerial vehicle considering external wind disturbance. The invention provides a robust discrete fractional order control method based on an interference observer by considering the influence of wind interference on the flight control performance of the fixed-wing unmanned aerial vehicle, which not only can effectively control the flight of the fixed-wing unmanned aerial vehicle, but also can track an expected reference track.

Description

Robust discrete fractional order control method of fixed wing unmanned aerial vehicle considering external wind interference
Technical Field
The invention relates to a robust discrete fractional order control method of a fixed wing unmanned aerial vehicle considering external wind interference, and belongs to the technical field of robust control of aircrafts.
Background
A drone may be defined as an aircraft that does not carry a pilot, a drone that may be operated remotely or autonomously during the performance of a mission flight. Because unmanned aerial vehicle has advantages such as with low costs, the flexibility is strong, the range of application is wide, develops rapidly in recent years, is applied to civilian and military fields more and more. For example, aerial photography, crop monitoring and pesticide spraying, sheep flock monitoring, search and rescue of coastal police forces, shoreline and channel monitoring, pollution and land monitoring, forest fire detection, reconnaissance, monitoring of enemy activity, and positioning and destruction of mines, among other applications. Therefore, since the application fields of the unmanned aerial vehicles are wide, in recent decades, researchers at home and abroad design various types of unmanned aerial vehicles, and the research on the flight control system of the unmanned aerial vehicle is highly concerned.
The advantages and disadvantages of the flight control performance not only affect the capability of the unmanned aerial vehicle to execute tasks, but also affect the flight safety of the unmanned aerial vehicle, so that the method has very important significance for the research of the flight control method of the unmanned aerial vehicle. Because the flight environment of the unmanned aerial vehicle is changeable and the executed task is special, the design of a high-precision and high-efficiency flight control scheme plays an important role in improving the control performance of the unmanned aerial vehicle. Meanwhile, the unmanned aerial vehicle inevitably encounters the influence of disturbance such as wind disturbance in the flight process. The influence caused by external wind disturbance is not considered, and the system performance can be deteriorated. At this time, it is generally difficult for the control law based on the conventional system design to achieve the desired performance index. Therefore, the research on the robust control problem of the unmanned aerial vehicle system has important theoretical and practical significance. At present, the commonly used methods for processing interference mainly include a robust control method, an adaptive control method, an interference observer method and the like.
With the continuous development of modern industrial production technology, mathematical model systems obtained according to real engineering abstraction are more and more complex, and in order to meet the high requirements of modern industrial control, high-performance computers have been widely applied to the field of control. Since the computer can only process discrete digital signals during data storage and calculation, continuous signals need to be converted into discrete signals when the controlled system is controlled by the computer. In addition, the actual nonlinear control law is realized by a digital controller, so that the research on the control problem of the discrete nonlinear system is very important. In addition, the control performance of a digital controller designed based on an approximately discrete controlled object model may be better than the control performance of a digital controller obtained by a continuous controller designed with a continuous controlled object model. Therefore, in order to facilitate digital implementation, it is of practical significance to further study the discrete-time flight control method of the fixed-wing drone system under a discrete framework.
Therefore, in order to improve the robustness and safety and reliability of the system, the influence of external wind interference needs to be considered simultaneously when designing the nonlinear discrete fractional order controller for the fixed-wing drone.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: the robust discrete fractional order control method of the fixed-wing unmanned aerial vehicle considering the external wind interference is provided, so that the fixed-wing unmanned aerial vehicle can be kept stable under the condition of considering the influence of the external wind interference, and can also track an upper expected reference track.
The invention adopts the following technical scheme for solving the technical problems:
the robust discrete fractional order control method of the fixed wing unmanned aerial vehicle considering external wind interference comprises the following steps:
step 1, establishing a longitudinal flight control system and an attitude dynamics system model of the fixed-wing unmanned aerial vehicle under the action of external wind interference, namely a continuous form unmanned aerial vehicle nonlinear model with external wind interference according to Newton-Euler's theorem;
step 2, converting the continuous form unmanned aerial vehicle nonlinear model with external wind interference into a discrete form unmanned aerial vehicle nonlinear model with external wind interference by using an Euler approximation method;
step 3, designing a nonlinear discrete disturbance observer to compensate the influence of external wind disturbance on a fixed-wing unmanned aerial vehicle system based on a discrete unmanned aerial vehicle nonlinear model with the external wind disturbance; the nonlinear discrete disturbance observer is as follows:
Figure BDA0002253417930000021
wherein the content of the first and second substances,
Figure BDA0002253417930000022
is that
Figure BDA0002253417930000023
Is estimated by the estimation of (a) a,
Figure BDA0002253417930000024
is a bounded interference
Figure BDA0002253417930000025
To (1)
Figure BDA0002253417930000026
The number of the variables is one,
Figure BDA0002253417930000027
is a normal number of the design, and,
Figure BDA0002253417930000028
is that
Figure BDA0002253417930000029
Is estimated by the estimation of (a) a,
Figure BDA00022534179300000210
is the intermediate variable that is the variable between,
Figure BDA00022534179300000211
is a state variable
Figure BDA00022534179300000212
To (1)
Figure BDA00022534179300000213
The number of the variables is one,
Figure BDA00022534179300000214
step 4, combining a discrete fractional order theory and a backstepping control method, and designing a robust discrete fractional order controller by using the nonlinear discrete disturbance observer designed in the step 3 to enable the fixed-wing unmanned aerial vehicle system to track an expected reference signal on a flight track and an attitude angle; the method specifically comprises the following steps:
aiming at a longitudinal flight control system, designing a discrete fractional order controller based on the nonlinear discrete disturbance observer in the step 3 to enable the fixed-wing unmanned aerial vehicle system to track an expected flight trajectory reference signal, wherein the specific process is as follows:
in order to eliminate the interference caused by wind to the flying height of the unmanned aerial vehicle, a nonlinear discrete interference observer is designed based on the step 3, and the expression is as follows:
Figure BDA0002253417930000031
wherein k +1 and k respectively represent the k +1 th and k th time,
Figure BDA0002253417930000032
in order to discrete the state variable of the disturbance observer,
Figure BDA0002253417930000033
for the output of a discrete disturbance observer, ζzFor the control parameters of the design and satisfy ζz＞0，
Figure BDA0002253417930000034
Uz(k)＝Gz(k)uz(k)，
Figure BDA0002253417930000035
uz(k)＝sinγ(k)，
Figure BDA0002253417930000036
Figure BDA0002253417930000037
Is the fly height, at is the sampling period,
Figure BDA0002253417930000038
is the flight speed, γ is the track inclination;
the discrete fractional order height controller is designed to:
Figure BDA0002253417930000039
wherein the content of the first and second substances,
Figure BDA00022534179300000310
Figure BDA00022534179300000311
the order of the order is a fraction of the order,
Figure BDA00022534179300000312
expression representing a fractional order definition, λzAnd λ1zAs a constant of design, ez(k) For height tracking error, nz is j-1, and j is 2, …, k +1, and
Figure BDA00022534179300000313
Figure BDA00022534179300000314
is a height reference signal;
in order to eliminate the interference caused by wind to the flight speed and the track inclination angle of the unmanned aerial vehicle, a nonlinear discrete interference observer is designed based on the step 3, and the expression is as follows:
Figure BDA00022534179300000315
wherein i0＝1,2，
Figure BDA00022534179300000316
Figure BDA00022534179300000317
For discrete disturbance observersThe state variable of (a) is changed,
Figure BDA00022534179300000318
being the ith of a discrete disturbance observer0The output of the first and second processors is,
Figure BDA00022534179300000326
for the designed control parameter to satisfy
Figure BDA00022534179300000319
Figure BDA00022534179300000320
Is FH(k) I th of (1)0The number of the variables is one,
Figure BDA00022534179300000321
Figure BDA00022534179300000322
is UH(k) Ith0Individual variable, UH(k)＝GH(k)uH(k)，
Figure BDA00022534179300000323
Figure BDA00022534179300000324
I th of (1)0The number of the variables is one,
Figure BDA00022534179300000325
m is the mass of the unmanned aerial vehicle, g is the acceleration of gravity;
the discrete fractional order velocity and track pitch controller is then designed to:
Figure BDA0002253417930000041
wherein the content of the first and second substances,
Figure BDA0002253417930000042
Figure BDA0002253417930000043
the order of the order is a fraction of the order,
Figure BDA0002253417930000044
expression representing a fractional order definition, λHAnd λ1HAs a constant of design, eH(k) For speed and track pitch angle error variables, nH is j-1, and j is 2, …, k +1 and
Figure BDA0002253417930000045
Figure BDA0002253417930000046
γd(k +1) are velocity, track inclination angle reference signals, respectively;
aiming at the attitude dynamics system, a discrete fractional order controller based on the nonlinear discrete disturbance observer in the step 3 is designed, so that the fixed wing unmanned aerial vehicle system is enabled to track an expected attitude angle reference signal, and the specific process is as follows:
in order to eliminate the interference caused by wind to the slow loop of the unmanned aerial vehicle attitude system, a nonlinear discrete interference observer is designed based on the step 3, and the expression is as follows:
Figure BDA0002253417930000047
wherein the content of the first and second substances,
Figure BDA0002253417930000048
in order to discrete the state variable of the disturbance observer,
Figure BDA0002253417930000049
is the ith output of the discrete disturbance observer, an
Figure BDA00022534179300000410
ζ1iFor the control parameters of the design and satisfy ζ1i＞0，
Figure BDA00022534179300000411
Is composed of
Figure BDA00022534179300000412
The (c) th variable of (a),
Figure BDA00022534179300000413
F1(x1(k) is a slow-loop nonlinear function, x, in the unmanned aerial vehicle attitude system1(k) Is the attitude angle of the unmanned aerial vehicle,
Figure BDA00022534179300000414
α (k) is the angle of attack, β (k) is the sideslip angle, μ (k) is the track roll angle, U1i(k) Is U1(k) The ith variable, and
Figure BDA00022534179300000415
G1(x1(k) for a slow loop control gain matrix in a drone attitude system,
Figure BDA00022534179300000416
x2(k) for the attitude of the drone, p (k) is the roll rate, q (k) is the pitch rate, r (k) is the yaw rate, x (k) is the yaw rate1i(k) Is x1(k) I ═ 1,2, 3;
then the design of unmanned aerial vehicle attitude system virtual controller is:
Figure BDA00022534179300000417
wherein x is1dFor the desired attitude angle tracking signal, N1＝diag[N11,N12,N13]And N is1iAs a constant of design, e1(k) In order to track the error, the tracking error is,
Figure BDA0002253417930000051
in the form of a discrete heelTrace the state variable of the differentiator, h11Is a designed constant;
in order to eliminate the interference caused by wind to the fast loop of the unmanned aerial vehicle attitude system, a nonlinear discrete interference observer is designed based on the step 3, and the expression is as follows:
Figure BDA0002253417930000052
wherein the content of the first and second substances,
Figure BDA0002253417930000053
in order to discrete the state variable of the disturbance observer,
Figure BDA0002253417930000054
is the ith output of the discrete disturbance observer, an
Figure BDA0002253417930000055
ζ2iFor the control parameters of the design and satisfy ζ2i＞0，
Figure BDA0002253417930000056
Is composed of
Figure BDA0002253417930000057
The (c) th variable of (a),
Figure BDA0002253417930000058
F2(x (k)) is a fast-loop nonlinear function, U, in the unmanned aerial vehicle attitude system2i(k) Is U2(k) The ith variable, and
Figure BDA0002253417930000059
G2(x (k)) is a fast loop control gain matrix, x, in the unmanned aerial vehicle attitude system2i(k) Is x2(k) I ═ 1,2, 3;
the discrete fractional attitude system controller is designed to:
Figure BDA00022534179300000510
wherein the content of the first and second substances,
Figure BDA00022534179300000511
in a discrete form tracking the state variables of the differentiator,
Figure BDA00022534179300000512
Figure BDA00022534179300000513
the order of the order is a fraction of the order,
Figure BDA00022534179300000514
expressions representing fractional order definitions, λ and λ1Constant of design, h01As a constant of design, e2(k) For tracking error, n is j-1, and j is 2, …, k +1 and
Figure BDA00022534179300000515
as a preferred scheme of the present invention, the longitudinal flight control system and attitude dynamics system model of the fixed-wing drone under the action of external wind interference in step 1 is:
Figure BDA0002253417930000061
Figure BDA0002253417930000062
Figure BDA0002253417930000063
Figure BDA0002253417930000064
Figure BDA0002253417930000065
Figure BDA0002253417930000066
Figure BDA0002253417930000067
Figure BDA0002253417930000068
Figure BDA0002253417930000069
wherein M is the mass of the drone, g is the acceleration of gravity,
Figure BDA00022534179300000610
is the flight level of the aircraft,
Figure BDA00022534179300000611
is the flight speed, gamma is the track pitch angle,
Figure BDA00022534179300000612
is the resistance force of the water-bearing material,
Figure BDA00022534179300000613
is the engine thrust, alpha is the angle of attack, beta is the sideslip angle, mu is the track roll angle,
Figure BDA00022534179300000614
is lift, p is roll rate, q is pitch rate, r is yaw rate,
Figure BDA00022534179300000615
and
Figure BDA00022534179300000616
is the component of the thrust vector in the body coordinate system,
Figure BDA00022534179300000617
is aerodynamic, Ixx、IyyAnd IzzIs moment of inertia, IxzIs the product of inertia,/Δ0、nΔ0And mΔ0Is a function of p, q and r, Δ lΔ、ΔnΔAnd Δ mΔIs an uncertainty term caused by wind gradients, dz、dv、dγ、dα、dβAnd dμThe interference caused by wind to the unmanned aerial vehicle is shown as follows:
dz＝wWg
Figure BDA00022534179300000618
Figure BDA00022534179300000619
Figure BDA00022534179300000620
Figure BDA00022534179300000621
Figure BDA00022534179300000622
wherein, wWg、uWgAnd vWgIs the external wind speed, χ is the air current coordinate system and the groundAzimuth angle between the plane coordinate systems.
As a preferable scheme of the present invention, the discrete form unmanned aerial vehicle nonlinear model with external wind interference in step 2 is:
Figure BDA0002253417930000071
Figure BDA0002253417930000072
Figure BDA0002253417930000073
Figure BDA0002253417930000074
Figure BDA0002253417930000075
y(k)＝x1(k)
where Δ T is the sampling period, k +1 and k are the k +1 and k times, respectively,
Figure BDA0002253417930000076
Figure BDA0002253417930000077
Figure BDA0002253417930000078
F1(x1(k) ) is a slow-loop non-linear function in the unmanned aerial vehicle attitude system,
Figure BDA0002253417930000079
G1(x1(k) for a slow loop control gain matrix in a drone attitude system,
Figure BDA00022534179300000710
F2(x (k)) is a fast loop non-linear function in the unmanned aerial vehicle attitude system,
Figure BDA00022534179300000711
G2(x (k)) is a fast loop control gain matrix in the unmanned aerial vehicle attitude system, and is defined
Figure BDA00022534179300000712
Figure BDA00022534179300000713
Then there is
Figure BDA00022534179300000714
Figure BDA00022534179300000715
Figure BDA00022534179300000716
Figure BDA00022534179300000717
Figure BDA0002253417930000081
Figure BDA0002253417930000082
Compared with the prior art, the invention adopting the technical scheme has the following technical effects:
the invention establishes a fixed wing unmanned aerial vehicle longitudinal control system and an attitude dynamics system model under external wind interference; the method comprises the steps of converting a continuous form unmanned aerial vehicle nonlinear model with wind interference into a discrete form by using an Euler approximation method, and designing a discrete interference observer to compensate the adverse effect of external wind interference on the flight control performance of the fixed wing unmanned aerial vehicle; a control scheme based on a discrete disturbance observer is designed by combining a discrete fractional order theory and a backstepping method to solve the problem of robust discrete disturbance rejection tracking control of the unmanned aerial vehicle considering external wind disturbance. The influence of wind interference on the flight control performance of the fixed-wing unmanned aerial vehicle is considered, and the robust discrete fractional order control method based on the interference observer is provided, so that the flight of the fixed-wing unmanned aerial vehicle can be effectively controlled, and an expected reference track can be tracked.
Drawings
Fig. 1 is a flow chart of the drone system control of the present invention.
Detailed Description
Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings. The embodiments described below with reference to the accompanying drawings are illustrative only for the purpose of explaining the present invention, and are not to be construed as limiting the present invention.
As shown in fig. 1, the robust discrete fraction set control method provided by the present invention can enable a fixed-wing drone to not only remain stable under the consideration of the influence of external wind interference, but also track an upper expected reference trajectory. The control method comprises the following steps:
(1) establishing a fixed wing unmanned aerial vehicle longitudinal flight control system and an attitude dynamics system model under the action of external wind interference according to Newton-Euler theorem;
(2) converting a continuous form unmanned aerial vehicle nonlinear model with wind interference into a discrete form by using an Euler approximation method;
(3) respectively designing discrete disturbance observers to compensate the adverse effect of external wind disturbance on the fixed-wing unmanned aerial vehicle system;
(4) and (4) combining a discrete fractional order theory and a backstepping control method, and designing a robust discrete fractional order controller by using the discrete disturbance observer designed in the step (3) so that the flight trajectory and the attitude angle of the fixed-wing unmanned aerial vehicle system track an expected reference signal.
1. Unmanned aerial vehicle system model with wind interference
The invention considers a fixed wing unmanned aerial vehicle longitudinal flight control system and an attitude dynamics system model under the action of external wind interference:
Figure BDA0002253417930000091
Figure BDA0002253417930000092
Figure BDA0002253417930000093
Figure BDA0002253417930000094
Figure BDA0002253417930000095
Figure BDA0002253417930000096
Figure BDA0002253417930000097
wherein M is the mass of the unmanned aerial vehicle, g is the acceleration of gravity,
Figure BDA0002253417930000098
is the flight level of the aircraft,
Figure BDA0002253417930000099
is the flight speed, gamma is the track pitch angle,
Figure BDA00022534179300000910
is the resistance force of the water-bearing material,
Figure BDA00022534179300000911
is the engine thrust, alpha is the angle of attack, beta is the sideslip angle, mu is the track roll angle,
Figure BDA00022534179300000912
is lift, p is roll rate, q is pitch rate, r is yaw rate,
Figure BDA00022534179300000913
and
Figure BDA00022534179300000914
is the component of the thrust vector in the body coordinate system,
Figure BDA00022534179300000915
is aerodynamic, Ixx、IyyAnd IzzIs moment of inertia, IxzIs the product of inertia,/Δ0、nΔ0And mΔ0Is a function of p, q and r, Δ lΔ、ΔnΔAnd Δ mΔIs an uncertainty term caused by wind gradients, dz、dv、dγ、dα、dβAnd dμThe interference caused by wind to the unmanned aerial vehicle is shown as follows:
Figure BDA0002253417930000101
where χ is the azimuth angle between the air and ground coordinate systems, wWg、uWgAnd vWgIs the external wind speed.
According to the formula (1), an affine nonlinear fixed-wing drone attitude dynamics mathematical model of the following form can be obtained:
Figure BDA0002253417930000102
in the formula (I), the compound is shown in the specification,
Figure BDA0002253417930000103
is the attitude angle of the unmanned aerial vehicle,
Figure BDA0002253417930000104
is the angular velocity vector of the drone,
Figure BDA0002253417930000105
is the control plane control vector of the unmanned aerial vehicle, deltaeIs the elevator yaw angle, deltaaIs the aileron rudder angle, deltarIs the rudder deflection angle and,
Figure BDA0002253417930000106
is the output signal of the unmanned aerial vehicle,
Figure BDA0002253417930000107
and
Figure BDA0002253417930000108
is a known non-linear state function vector,
Figure BDA0002253417930000109
and
Figure BDA00022534179300001010
is a known drone control matrix that,
Figure BDA00022534179300001011
and
Figure BDA00022534179300001012
is the effect of wind interference on the drone. Non-linear function F1(x1)＝[F11,F12,F13]TAnd F2(x)＝[F21,F22,F23]TControl matrix G1(x1) And G2(x) And external interference
Figure BDA00022534179300001013
The specific expression of (a) is as follows:
Figure BDA00022534179300001014
Figure BDA00022534179300001015
Figure BDA00022534179300001016
Figure BDA0002253417930000111
Figure BDA0002253417930000112
Figure BDA0002253417930000113
Figure BDA0002253417930000114
Figure BDA0002253417930000115
Figure BDA0002253417930000116
in the formula (I), the compound is shown in the specification,
Figure BDA0002253417930000117
Figure BDA0002253417930000118
heis the angular momentum of the engine and is,
Figure BDA0002253417930000119
is the length of the wings of the unmanned aerial vehicle,
Figure BDA00022534179300001110
is the average aerodynamic chord length,
Figure BDA00022534179300001111
is the aerodynamic pressure, SrIs the wing area of the unmanned aerial vehicle,
Figure BDA00022534179300001112
and
Figure BDA00022534179300001113
respectively a total roll moment coefficient, a total pitch moment coefficient and a total yaw moment coefficient,
Figure BDA00022534179300001114
and
Figure BDA00022534179300001115
is the coefficient of the moment of force,
Figure BDA00022534179300001116
Figure BDA00022534179300001117
and
Figure BDA00022534179300001118
the Euler approximation method is utilized to convert the continuous form unmanned aerial vehicle nonlinear models (1) and (2) with wind interference into the following discrete forms:
Figure BDA00022534179300001119
where, at is the sampling period,
Figure BDA00022534179300001120
uz(k)＝sinγ(k)，
Figure BDA0002253417930000121
Figure BDA0002253417930000122
and
Figure BDA0002253417930000123
definition of
Figure BDA0002253417930000124
Figure BDA0002253417930000125
Figure BDA0002253417930000126
And
Figure BDA0002253417930000127
is that
Figure BDA0002253417930000128
The variable of (a) is selected,
Figure BDA0002253417930000129
Figure BDA00022534179300001225
and
Figure BDA00022534179300001211
is that
Figure BDA00022534179300001212
The variable of (a) is selected,
Figure BDA00022534179300001213
Figure BDA00022534179300001214
and are available
Figure BDA00022534179300001215
Figure BDA00022534179300001216
Figure BDA00022534179300001217
Figure BDA00022534179300001218
Figure BDA00022534179300001219
Figure BDA00022534179300001220
For the drone system model (13) to account for the presence of external wind disturbances, the following assumptions are necessary in order to achieve the desired control objectives.
Assume that 1: suppose that
Figure BDA00022534179300001221
And
Figure BDA00022534179300001222
is bounded, and
Figure BDA00022534179300001223
Figure BDA00022534179300001224
and i0＝1,2。
2. Design of discrete disturbance observer
Considering an unmanned aerial vehicle discrete system model (13) with external wind interference, a discrete interference observer is designed to suppress the influence of the wind interference on the system.
Based on equation (13), then
Figure BDA0002253417930000131
In the formula (I), the compound is shown in the specification,
Figure BDA0002253417930000132
the state variable of the system (20) is
Figure BDA0002253417930000133
Is a wind-induced differentially bounded disturbance, a known non-linear function
Figure BDA0002253417930000134
Defining bounded interference
Figure BDA0002253417930000135
Non-linear function
Figure BDA0002253417930000136
Variable of state
Figure BDA0002253417930000137
In the system (20) of the present invention,
Figure BDA0002253417930000138
to (1) a
Figure BDA0002253417930000139
A variable can be written as
Figure BDA00022534179300001310
In the formula (I), the compound is shown in the specification,
Figure BDA00022534179300001311
to design a non-linear discrete disturbance observer, the following intermediate variables are defined:
Figure BDA00022534179300001312
in the formula (I), the compound is shown in the specification,
Figure BDA00022534179300001313
is a design normal number.
According to the formulae (21) and (22),
Figure BDA00022534179300001314
can be described as
Figure BDA00022534179300001315
Furthermore, an intermediate variable M is definedi(k) Is estimated as
Figure BDA00022534179300001316
In the formula (I), the compound is shown in the specification,
Figure BDA00022534179300001317
is that
Figure BDA00022534179300001318
Is estimated.
According to equation (22), a nonlinear discrete disturbance observer of the form:
Figure BDA00022534179300001319
in the formula (I), the compound is shown in the specification,
Figure BDA00022534179300001320
is that
Figure BDA00022534179300001321
Is estimated.
Definition of
Figure BDA00022534179300001322
And
Figure BDA00022534179300001323
and considering equations (22) and (25), there are
Figure BDA00022534179300001324
Combining the formulas (23) and (24) to obtain
Figure BDA0002253417930000141
In the formula (I), the compound is shown in the specification,
Figure BDA0002253417930000142
the design process of the nonlinear discrete disturbance observer can be summarized as the following theorem 1:
theorem 1: considering a longitudinal control system and an attitude dynamics system model (13) in a discrete form with external wind interference influence, a nonlinear discrete interference observer is designed as shown in formulas (24) and (25). The non-linear discrete disturbance observer is designed to ensure that the error between the estimated value of the disturbance observer and the external disturbance is bounded.
Proof 1: to analyze interference estimation errors
Figure BDA0002253417930000143
The following Lyapunov function is selected for the boundedness:
Figure BDA0002253417930000144
according to the formula (27),
Figure BDA0002253417930000145
can be written as
Figure BDA0002253417930000146
In the formula (I), the compound is shown in the specification,
Figure BDA0002253417930000147
Figure BDA0002253417930000148
is a normal number.
According to equation (29), to ensure interference estimation error
Figure BDA0002253417930000149
Is bounded, selected control parameters of a discrete disturbance observer
Figure BDA00022534179300001410
Must satisfy
Figure BDA00022534179300001411
Therefore, by selecting the appropriate control parameters,the non-linear discrete disturbance observers (24) and (25) are designed to ensure disturbance estimation errors
Figure BDA00022534179300001412
Is bounded.
3. Discrete fractional order trajectory control scheme based on discrete disturbance observer
Designing discrete fractional order controller based on discrete disturbance observer to drive output signal
Figure BDA00022534179300001413
Gamma (k) and x1(k) And a reference signal
Figure BDA00022534179300001414
γd(k) And xd(k) The error between is bounded. Firstly, aiming at a longitudinal control system, a discrete fractional order control method based on a discrete disturbance observer is designed, and a height tracking error is defined as
Figure BDA00022534179300001415
According to formula (13), there are
Figure BDA00022534179300001416
To deal with external disturbances in equation (30)
Figure BDA00022534179300001417
A nonlinear discrete disturbance observer is designed based on the formulas (24) and (25), and the expression of the nonlinear discrete disturbance observer can be expressed as
Figure BDA0002253417930000151
Wherein the content of the first and second substances,
Figure BDA0002253417930000152
as the output of a discrete disturbance observer；
Figure BDA0002253417930000153
Is a state variable of a discrete disturbance observer; designed control parameter ζzSatisfy ζzIs greater than 0; furthermore, an interference estimation error is defined as
Figure BDA0002253417930000154
Uz(k)＝Gz(k)uz(k) And is provided with
Figure BDA0002253417930000155
And DzIs a normal number.
In addition, the discrete fractional order height controller is designed as
Figure BDA0002253417930000156
In the formula (I), the compound is shown in the specification,
Figure BDA0002253417930000157
Figure BDA0002253417930000158
the order of the order is a fraction of the order,
Figure BDA0002253417930000159
expression representing a fractional order definition, λzAnd λ1zFor the designed constants, nz is j-1 and j is 2, …, k +1 and
Figure BDA00022534179300001510
combining equations (30) and (32), one can obtain
Figure BDA00022534179300001511
Further, equation (33) can be written as
Figure BDA00022534179300001512
According to the definition of fractional order, then there are
Figure BDA00022534179300001513
Figure BDA00022534179300001514
Based on the formula (33) - (36), ezThe expression of (k +1) can be written as
Figure BDA00022534179300001515
From equation (37), it can be found
Figure BDA00022534179300001516
In the formula (I), the compound is shown in the specification,
Figure BDA0002253417930000161
and deltazAnd
Figure BDA0002253417930000162
is a normal number.
In order to demonstrate the non-linear discrete disturbance observer (31) and the controller uz(k) And (32) selecting the following Lyapunov function according to the effectiveness:
Figure BDA0002253417930000163
based on equation (39), Lyapunov function Vz(k) Can be expressed as a first order difference
Figure BDA0002253417930000164
From equation (29), the following expression can be obtained:
Figure BDA0002253417930000165
combining equations (38) and (41), then there are
Figure BDA0002253417930000166
In the formula (I), the compound is shown in the specification,
Figure BDA0002253417930000167
and
Figure BDA0002253417930000168
following relative velocity
Figure BDA0002253417930000169
And performing control analysis on the flight path inclination angle gamma, and firstly defining an error variable eH＝H(k)-Hd(k) And is and
Figure BDA00022534179300001610
thus, according to equation (13), there is
Figure BDA00022534179300001611
To deal with the external interference in equation (43)
Figure BDA00022534179300001612
A nonlinear discrete disturbance observer is designed based on the formulas (24) and (25), and the expression of the nonlinear discrete disturbance observer can be expressed as
Figure BDA00022534179300001613
Wherein i0＝1,2，Hi0(k) I of H (k)0A variable, FHi0(k) Is FH(k) I th of (1)0A variable;
Figure BDA00022534179300001614
being the ith of a discrete disturbance observer0An output, and
Figure BDA00022534179300001615
Figure BDA00022534179300001616
is a state variable of a discrete disturbance observer; control parameters of the design
Figure BDA00022534179300001617
Satisfy the requirement of
Figure BDA00022534179300001618
Furthermore, an interference estimation error is defined as
Figure BDA00022534179300001619
And is
Figure BDA00022534179300001620
Figure BDA00022534179300001621
Is UH(k) Ith0A variable, and UH(k)＝GH(k)uH(k) In that respect In addition, the first and second substrates are,
Figure BDA00022534179300001622
Figure BDA00022534179300001623
is a normal number and defines
Figure BDA00022534179300001624
In addition, control law u is designedH(k) Is composed of
Figure BDA0002253417930000171
In the formula (I), the compound is shown in the specification,
Figure BDA0002253417930000172
Figure BDA0002253417930000173
is of fractional order, λHAnd λ1HFor the designed constants, nH is j-1 and j is 2, …, k +1 and
Figure BDA0002253417930000174
combining equations (43) and (45), one can obtain
Figure BDA0002253417930000175
Further, equation (46) can be written as
Figure BDA0002253417930000176
According to the definition of fractional order, then there are
Figure BDA0002253417930000177
Figure BDA0002253417930000178
Based on the formula (46) — (49), eHThe expression of (k +1) can be written as
Figure BDA0002253417930000179
Furthermore, eHIth of (k +1)0The expression of the individual variables can be described as
Figure BDA00022534179300001710
In the formula (I), the compound is shown in the specification,
Figure BDA00022534179300001711
is eH(k) I th of (1)0And (4) a variable.
From equation (51), one obtains
Figure BDA00022534179300001712
In the formula (I), the compound is shown in the specification,
Figure BDA00022534179300001713
and is
Figure BDA00022534179300001714
And
Figure BDA00022534179300001715
is a normal number.
To demonstrate a non-linear discrete disturbance observer (44) and controller uH(k) (45) selecting the following Lyapunov function according to the effectiveness:
Figure BDA0002253417930000181
based on the formula (53), the Lyapunov function VH(k) Can be expressed as a first order difference
Figure BDA0002253417930000182
From equation (29), the following expression can be obtained:
Figure BDA0002253417930000183
when combined with formulas (52) and (55), then have
Figure BDA0002253417930000184
In the formula (I), the compound is shown in the specification,
Figure BDA0002253417930000185
and
Figure BDA0002253417930000186
and min (-) represents the minimum value.
4. Discrete fractional order attitude control scheme based on discrete disturbance observer
Aiming at the attitude dynamics system, a discrete fractional order attitude control scheme based on a discrete disturbance observer is designed by utilizing a backstepping control method.
The first step is as follows: defining the tracking error as e1(k)＝x1(k)-x1d(k) And e2(k)＝x2(k)-xvd(k)，xvd(k) Is a virtual controller. According to formula (13), there are
Figure BDA0002253417930000187
For variable x1d(k +1), predicting x using a tracking differentiator in discrete form1d(k + 1). Discrete form tracking differentiators can be written as
Figure BDA0002253417930000188
Wherein i is 1,2,3, h11iAnd r11iAnd is and
Figure BDA0002253417930000189
and
Figure BDA00022534179300001810
the state variable of the tracking differentiator is in a discrete form.
According to equation (58) and the characteristics of the discrete differentiator, there is
Figure BDA00022534179300001811
In the formula (I), the compound is shown in the specification,
Figure BDA00022534179300001812
h11＝diag[h111,h112,h113]，r11＝diag[r111,r112,r113]，
Figure BDA0002253417930000191
to estimate an error vector, an
Figure BDA0002253417930000192
Is bounded while
Figure BDA0002253417930000193
And
Figure BDA0002253417930000194
is a normal number.
Substituting the formula (59) into the formula (57) can obtain
Figure BDA0002253417930000195
To deal with external interference in equation (60)
Figure BDA0002253417930000196
A nonlinear discrete disturbance observer is designed based on the formulas (24) and (25), and the expression of the nonlinear discrete disturbance observer can be expressed as
Figure BDA0002253417930000197
Wherein i is 1,2,3, x1i(k) Is x1(k) The (c) th variable of (a),
Figure BDA0002253417930000198
is composed of
Figure BDA0002253417930000199
The ith variable of (1);
Figure BDA00022534179300001910
is the ith output of the discrete disturbance observer, an
Figure BDA00022534179300001911
Figure BDA00022534179300001912
Is a state variable of a discrete disturbance observer; designed control parameter ζ1iSatisfy ζ1iIs greater than 0; furthermore, an interference estimation error is defined as
Figure BDA00022534179300001913
And is
Figure BDA00022534179300001914
U1i(k) Is U1(k) The ith variable, an
Figure BDA00022534179300001915
In addition, the first and second substrates are,
Figure BDA00022534179300001916
D1iis a normal number and defines
Figure BDA00022534179300001917
Designing a virtual controller xvd(k) Is composed of
Figure BDA00022534179300001918
In the formula, N1＝diag[N11,N12,N13]And N is1iIs a designed constant.
Combining equations (60) and (62), one can obtain
Figure BDA00022534179300001919
According to formula (63), e1The expression of the ith variable of (k +1) can be described as
Figure BDA00022534179300001920
In the formula, e1i(k) Is e1(k) The ith variable of (1), E1i(k) Is composed of
Figure BDA00022534179300001921
The ith variable of (1).
From equation (64), one can obtain
Figure BDA00022534179300001922
To demonstrate a non-linear discrete disturbance observer (61) and a virtual controller xvd(k) And (62) selecting the following Lyapunov function according to the effectiveness:
Figure BDA0002253417930000201
based on the formula (66), the Lyapunov function V1(k) Can be expressed as a first order difference
Figure BDA0002253417930000202
According to the formula (65), then
Figure BDA0002253417930000203
From equation (29), the following expression can be obtained:
Figure BDA0002253417930000204
in combination with equations (68) and (69), there are
Figure BDA0002253417930000205
In the formula (I), the compound is shown in the specification,
Figure BDA0002253417930000206
and
Figure BDA0002253417930000207
max (-) represents the maximum value, and
Figure BDA0002253417930000208
the second step is that: consider equations (13) and e2(k)＝x2(k)-xvd(k) Is obtained by
Figure BDA0002253417930000209
To deal with the external interference in equation (71)
Figure BDA00022534179300002010
A nonlinear discrete disturbance observer is designed based on the formulas (24) and (25), and the expression of the nonlinear discrete disturbance observer can be expressed as
Figure BDA00022534179300002011
Wherein i is 1,2,3, x2i(k) Is x2(k) The (c) th variable of (a),
Figure BDA00022534179300002012
is composed of
Figure BDA00022534179300002013
The ith variable of (1);
Figure BDA00022534179300002014
is the ith output of the discrete disturbance observer, an
Figure BDA00022534179300002015
Figure BDA00022534179300002016
Is a state variable of a discrete disturbance observer; designed control parameter ζ2iSatisfy ζ2iIs greater than 0; furthermore, an interference estimation error is defined as
Figure BDA00022534179300002017
And is
Figure BDA00022534179300002018
U2i(k) Is U2(k) The ith variable, an
Figure BDA00022534179300002019
In addition, the first and second substrates are,
Figure BDA0002253417930000211
D2iis a normal number and defines
Figure BDA0002253417930000212
For variable xvd(k +1), predicting x using a tracking differentiator in discrete formvd(k + 1). Discrete form tracking differentiators can be written as
Figure BDA0002253417930000213
Wherein i is 1,2,3, h01iAnd r01iAnd is and
Figure BDA0002253417930000214
and
Figure BDA0002253417930000215
the state variable of the tracking differentiator is in a discrete form.
According to equation (73) and the characteristics of the discrete differentiator, there is
Figure BDA0002253417930000216
In the formula (I), the compound is shown in the specification,
Figure BDA0002253417930000217
h01＝diag[h011,h012,h013]，r01＝diag[r011,r012,r013]，
Figure BDA0002253417930000218
to estimate an error vector, an
Figure BDA0002253417930000219
Is bounded while
Figure BDA00022534179300002110
Figure BDA00022534179300002111
Is a sum of normal numbers
Figure BDA00022534179300002112
By substituting formula (74) for formula (71), a compound having the formula
Figure BDA00022534179300002113
Furthermore, the discrete fractional order controller is designed as
Figure BDA00022534179300002114
In the formula (I), the compound is shown in the specification,
Figure BDA00022534179300002115
Figure BDA00022534179300002116
is a fractional order, λ and λ1For the designed constants, n is j-1 and j is 2, …, k +1 and
Figure BDA00022534179300002117
combining equations (75) and (76), one can obtain
Figure BDA00022534179300002118
Further, equation (77) can be written as
Figure BDA00022534179300002119
According to the definition of fractional order, then there are
Figure BDA0002253417930000221
Figure BDA0002253417930000222
Based on the formula (77) — (80), e2The expression of (k +1) can be written as
Figure BDA0002253417930000223
Furthermore, e2The expression of the ith variable of (k +1) can be described as
Figure BDA0002253417930000224
In the formula, e2i(k) Is e2(k) The ith variable of (1).
From equation (82), one obtains
Figure BDA0002253417930000225
In the formula (I), the compound is shown in the specification,
Figure BDA0002253417930000226
and delta2iAnd
Figure BDA0002253417930000227
is a normal number.
To demonstrate the effectiveness of the non-linear discrete disturbance observer (72) and the controller u (k) (76), the following Lyapunov function was chosen:
Figure BDA0002253417930000228
based on equation (84), Lyapunov function V2(k) Can be expressed as a first order difference
Figure BDA0002253417930000229
From equation (29), the following expression can be obtained:
Figure BDA00022534179300002210
combining equations (83) and (86), then
Figure BDA00022534179300002211
In the formula (I), the compound is shown in the specification,
Figure BDA00022534179300002212
and
Figure BDA00022534179300002213
5. closed loop system stability certification
For a discrete form of fixed-wing drone trajectory control system model with external wind disturbance and attitude dynamics system (13), the above process of designing a discrete fractional order controller can be summarized as the following theorem:
theorem 2: considering a discrete form of a fixed wing drone trajectory control system model and attitude dynamics system (13) in the presence of external wind disturbances, if one can select the appropriate control parameter ζz、ζHi0、ζ1i、ζ2i、λz、λ1z、λH，λ1H、λ、λ1、
Figure BDA0002253417930000231
And N1iAnd using the designed discrete disturbance observers (31), (44), (61) and (72), the altitude controller (32), the speed and track inclination angle control law (45), the virtual controller (62) and the discrete fractional order attitude controller (76),all signals in the closed loop system are bounded.
And (3) proving that: for the whole closed-loop system, the following Lyapunov function is selected:
Figure BDA0002253417930000232
from the equations (42), (56), (70) and (87), it can be found
Figure BDA0002253417930000233
According to the formula (89), if the control parameter is selected, χ can be set11＞0、χ12＞0、χz1＞0、χz2＞0、χH1＞0、χH2＞0、χ21-χ13> 0 and χ22> 0, tracking error ez(k)、eH(k) And e1(k) Will be bounded. In addition, equation (89) further indicates the interference estimation error
Figure BDA0002253417930000234
And
Figure BDA0002253417930000235
is also bounded.
The above embodiments are only for illustrating the technical idea of the present invention, and the protection scope of the present invention is not limited thereby, and any modifications made on the basis of the technical scheme according to the technical idea of the present invention fall within the protection scope of the present invention.

Claims (3)

1. The robust discrete fractional order control method of the fixed wing unmanned aerial vehicle considering external wind interference is characterized by comprising the following steps of:
step 1, establishing a longitudinal flight control system and an attitude dynamics system model of the fixed-wing unmanned aerial vehicle under the action of external wind interference, namely a continuous form unmanned aerial vehicle nonlinear model with external wind interference according to Newton-Euler's theorem;
step 2, converting the continuous form unmanned aerial vehicle nonlinear model with external wind interference into a discrete form unmanned aerial vehicle nonlinear model with external wind interference by using an Euler approximation method;
step 3, designing a nonlinear discrete disturbance observer to compensate the influence of external wind disturbance on a fixed-wing unmanned aerial vehicle system based on a discrete unmanned aerial vehicle nonlinear model with the external wind disturbance; the nonlinear discrete disturbance observer is as follows:
Figure FDA0002764395670000011
wherein the content of the first and second substances,
Figure FDA0002764395670000012
is that
Figure FDA0002764395670000013
Is estimated by the estimation of (a) a,
Figure FDA0002764395670000014
is a bounded interference
Figure FDA0002764395670000015
To (1)
Figure FDA0002764395670000016
The number of the variables is one,
Figure FDA00027643956700000116
is a normal number of the design, and,
Figure FDA0002764395670000017
is that
Figure FDA0002764395670000018
Is estimated by the estimation of (a) a,
Figure FDA0002764395670000019
is the intermediate variable that is the variable between,
Figure FDA00027643956700000110
is a state variable
Figure FDA00027643956700000111
To (1)
Figure FDA00027643956700000112
The number of the variables is one,
Figure FDA00027643956700000113
step 4, combining a discrete fractional order theory and a backstepping control method, and designing a robust discrete fractional order controller by using the nonlinear discrete disturbance observer designed in the step 3 to enable the fixed-wing unmanned aerial vehicle system to track an expected reference signal on a flight track and an attitude angle; the method specifically comprises the following steps:
aiming at a longitudinal flight control system, designing a discrete fractional order controller based on the nonlinear discrete disturbance observer in the step 3 to enable the fixed-wing unmanned aerial vehicle system to track an expected flight trajectory reference signal, wherein the specific process is as follows:
in order to eliminate the interference caused by wind to the flying height of the unmanned aerial vehicle, a nonlinear discrete interference observer is designed based on the step 3, and the expression is as follows:
Figure FDA00027643956700000114
wherein k +1 and k respectively represent the k +1 th and k th time,
Figure FDA00027643956700000115
in order to discrete the state variable of the disturbance observer,
Figure FDA0002764395670000021
for the output of a discrete disturbance observer, ζzFor the control parameters of the design and satisfy ζz＞0，
Figure FDA0002764395670000022
Uz(k)＝Gz(k)uz(k)，
Figure FDA0002764395670000023
uz(k)＝sinγ(k)，
Figure FDA0002764395670000024
Figure FDA0002764395670000025
Is the fly height, at is the sampling period,
Figure FDA0002764395670000026
is the flight speed, γ is the track inclination;
the discrete fractional order height controller is designed to:
Figure FDA0002764395670000027
wherein the content of the first and second substances,
Figure FDA0002764395670000028
Figure FDA0002764395670000029
the order of the order is a fraction of the order,
Figure FDA00027643956700000210
expression representing a fractional order definition, λzAnd λ1zAs a constant of design, ez(k) For height tracking error, nz ═ j-1, andj-2, …, k +1 and
Figure FDA00027643956700000211
Figure FDA00027643956700000212
is a height reference signal;
in order to eliminate the interference caused by wind to the flight speed and the track inclination angle of the unmanned aerial vehicle, a nonlinear discrete interference observer is designed based on the step 3, and the expression is as follows:
Figure FDA00027643956700000213
wherein i0＝1,2，
Figure FDA00027643956700000214
In order to discrete the state variable of the disturbance observer,
Figure FDA00027643956700000215
being the ith of a discrete disturbance observer0The output of the first and second processors is,
Figure FDA00027643956700000216
for the designed control parameter to satisfy
Figure FDA00027643956700000217
Figure FDA00027643956700000218
Is FH(k) I th of (1)0The number of the variables is one,
Figure FDA00027643956700000219
Figure FDA00027643956700000220
is UH(k) Ith0Individual variable, UH(k)＝GH(k)uH(k)，uH(k) In order to control the law,
Figure FDA00027643956700000221
Figure FDA00027643956700000222
i of H (k)0The number of the variables is one,
Figure FDA00027643956700000223
m is the mass of the unmanned aerial vehicle, g is the acceleration of gravity;
the discrete fractional order velocity and track pitch controller is then designed to:
Figure FDA00027643956700000224
wherein the content of the first and second substances,
Figure FDA00027643956700000225
Figure FDA00027643956700000226
the order of the order is a fraction of the order,
Figure FDA0002764395670000031
expression representing a fractional order definition, λHAnd λ1HAs a constant of design, eH(k) For speed and track pitch angle error variables, nH is j-1, and j is 2, …, k +1 and
Figure FDA0002764395670000032
Figure FDA0002764395670000033
Figure FDA0002764395670000034
γd(k +1) are velocity, track inclination angle reference signals, respectively;
aiming at the attitude dynamics system, a discrete fractional order controller based on the nonlinear discrete disturbance observer in the step 3 is designed, so that the fixed wing unmanned aerial vehicle system is enabled to track an expected attitude angle reference signal, and the specific process is as follows:
in order to eliminate the interference caused by wind to the slow loop of the unmanned aerial vehicle attitude system, a nonlinear discrete interference observer is designed based on the step 3, and the expression is as follows:
Figure FDA0002764395670000035
wherein the content of the first and second substances,
Figure FDA0002764395670000036
in order to discrete the state variable of the disturbance observer,
Figure FDA0002764395670000037
is the ith output of the discrete disturbance observer, an
Figure FDA0002764395670000038
ζ1iFor the control parameters of the design and satisfy ζ1i＞0，
Figure FDA0002764395670000039
Is composed of
Figure FDA00027643956700000310
The (c) th variable of (a),
Figure FDA00027643956700000311
F1(x1(k) is a slow-loop nonlinear function, x, in the unmanned aerial vehicle attitude system1(k) Is the attitude angle of the unmanned aerial vehicle,
Figure FDA00027643956700000312
α (k) is the angle of attack, β (k) is the sideslip angle, μ (k) is the track roll angle, U1i(k) Is U1(k) The ith variable, and
Figure FDA00027643956700000313
G1(x1(k) for a slow loop control gain matrix in a drone attitude system,
Figure FDA00027643956700000314
x2(k) for the attitude of the drone, p (k) is the roll rate, q (k) is the pitch rate, r (k) is the yaw rate, x (k) is the yaw rate1i(k) Is x1(k) I ═ 1,2, 3;
then the design of unmanned aerial vehicle attitude system virtual controller is:
Figure FDA00027643956700000315
wherein x isvd(k) Being a virtual controller, x1dFor the desired attitude angle tracking signal, N1＝diag[N11,N12,N13]And N is1iAs a constant of design, e1(k) In order to track the error, the tracking error is,
Figure FDA00027643956700000316
state variable of tracking differentiator in discrete form, h11Is a designed constant;
in order to eliminate the interference caused by wind to the fast loop of the unmanned aerial vehicle attitude system, a nonlinear discrete interference observer is designed based on the step 3, and the expression is as follows:
Figure FDA0002764395670000041
wherein the content of the first and second substances,
Figure FDA0002764395670000042
in order to discrete the state variable of the disturbance observer,
Figure FDA0002764395670000043
is the ith output of the discrete disturbance observer, an
Figure FDA0002764395670000044
ζ2iFor the control parameters of the design and satisfy ζ2i＞0，
Figure FDA0002764395670000045
Is composed of
Figure FDA0002764395670000046
The (c) th variable of (a),
Figure FDA0002764395670000047
F2(x (k)) is a fast-loop nonlinear function, U, in the unmanned aerial vehicle attitude system2i(k) Is U2(k) The ith variable, and
Figure FDA0002764395670000048
G2(x (k)) is a fast loop control gain matrix, x, in the unmanned aerial vehicle attitude system2i(k) Is x2(k) I ═ 1,2, 3;
the discrete fractional attitude system controller is designed to:
Figure FDA0002764395670000049
wherein the content of the first and second substances,
Figure FDA00027643956700000410
in a discrete form tracking the state variables of the differentiator,
Figure FDA00027643956700000411
Figure FDA00027643956700000412
the order of the order is a fraction of the order,
Figure FDA00027643956700000413
expressions representing fractional order definitions, λ and λ1Constant of design, h01As a constant of design, e2(k) For tracking error, n is j-1, and j is 2, …, k +1 and
Figure FDA00027643956700000414
2. the robust discrete fractional order control method for the fixed-wing unmanned aerial vehicle considering the external wind interference according to claim 1, wherein the model of the longitudinal flight control system and the attitude dynamics system of the fixed-wing unmanned aerial vehicle under the external wind interference in the step 1 is:
Figure FDA0002764395670000051
Figure FDA0002764395670000052
Figure FDA0002764395670000053
Figure FDA0002764395670000054
Figure FDA0002764395670000055
Figure FDA0002764395670000056
Figure FDA0002764395670000057
Figure FDA0002764395670000058
Figure FDA0002764395670000059
wherein M is the mass of the drone, g is the acceleration of gravity,
Figure FDA00027643956700000510
is the flight level of the aircraft,
Figure FDA00027643956700000511
is the flight speed, gamma is the track pitch angle,
Figure FDA00027643956700000512
is the resistance force of the water-bearing material,
Figure FDA00027643956700000513
is the engine thrust, alpha is the angle of attack, beta is the sideslip angle, mu is the track roll angle,
Figure FDA00027643956700000514
is lift, p is roll rate, q is pitch rate, r is yaw rate,
Figure FDA00027643956700000515
and
Figure FDA00027643956700000516
is the component of the thrust vector in the body coordinate system,
Figure FDA00027643956700000517
is aerodynamic, Ixx、IyyAnd IzzIs moment of inertia, IxzIs the product of inertia,/Δ0、nΔ0And mΔ0Is a function of p, q and r, Δ lΔ、ΔnΔAnd Δ mΔIs an uncertainty term caused by wind gradients, dz、dv、dγ、dα、dβAnd dμThe interference caused by wind to the unmanned aerial vehicle is shown as follows:
dz＝wWg
Figure FDA0002764395670000061
Figure FDA0002764395670000062
Figure FDA0002764395670000063
Figure FDA0002764395670000064
Figure FDA0002764395670000065
wherein, wWg、uWgAnd vWgIs the external wind speed and χ is the azimuth angle between the air flow coordinate system and the ground coordinate system.
3. The robust discrete fractional order control method for fixed-wing drones considering external wind interference according to claim 2, wherein the discrete form drone nonlinear model with external wind interference in step 2 is:
Figure FDA0002764395670000066
Figure FDA0002764395670000067
Figure FDA0002764395670000068
Figure FDA0002764395670000069
Figure FDA00027643956700000610
y(k)＝x1(k)
where Δ T is the sampling period, k +1 and k are the k +1 and k times, respectively,
Figure FDA00027643956700000611
Figure FDA00027643956700000612
uz(k)＝sinγ(k)，
Figure FDA00027643956700000613
Figure FDA00027643956700000614
Figure FDA00027643956700000615
Figure FDA00027643956700000616
F1(x1(k) ) is a slow-loop non-linear function in the unmanned aerial vehicle attitude system,
Figure FDA00027643956700000617
G1(x1(k) for a slow loop control gain matrix in a drone attitude system,
Figure FDA00027643956700000618
F2(x (k)) is a fast loop non-linear function in the unmanned aerial vehicle attitude system,
Figure FDA00027643956700000619
G2(x (k)) is a fast loop control gain matrix in the unmanned aerial vehicle attitude system, and is defined
Figure FDA00027643956700000620
Figure FDA00027643956700000621
Figure FDA0002764395670000071
Then there is
Figure FDA0002764395670000072
Figure FDA0002764395670000073
Figure FDA0002764395670000074
Figure FDA0002764395670000075
Figure FDA0002764395670000076
Figure FDA0002764395670000077
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