CN113110428A - Carrier-based aircraft landing fixed time trajectory tracking method based on limited backstepping control - Google Patents

Carrier-based aircraft landing fixed time trajectory tracking method based on limited backstepping control Download PDF

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CN113110428A
CN113110428A CN202110356783.7A CN202110356783A CN113110428A CN 113110428 A CN113110428 A CN 113110428A CN 202110356783 A CN202110356783 A CN 202110356783A CN 113110428 A CN113110428 A CN 113110428A
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郑泽伟
吴宇轩
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Beihang University
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00—Control of position, course, altitude or attitude of land, water, air or space vehicles, e.g. using automatic pilots
    • G05D1/02—Control of position or course in two dimensions
    • G05D1/021—Control of position or course in two dimensions specially adapted to land vehicles
    • G05D1/0212—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory
    • G05D1/0223—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory involving speed control of the vehicle
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00—Control of position, course, altitude or attitude of land, water, air or space vehicles, e.g. using automatic pilots
    • G05D1/02—Control of position or course in two dimensions
    • G05D1/021—Control of position or course in two dimensions specially adapted to land vehicles
    • G05D1/0212—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory
    • G05D1/0221—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory involving a learning process

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Abstract

The invention provides a fixed-time trajectory tracking method for carrier-based aircraft landing based on limited backstepping control, provides a new trajectory tracking control method for carrier-based aircraft landing under the conditions of considering parameter uncertainty, output constraint and external interference, and belongs to the technical field of automatic control of carrier-based aircraft. The method is based on a backstepping method to design the autonomous landing trajectory tracking controller of the carrier-based aircraft, and a universal asymmetric obstacle Lyapunov function is adopted to solve the problems of state constraint and singular value. Meanwhile, the convergence time of the system is reduced by combining a fixed time control method, so that the track tracking error of a controlled object is converged to a small neighborhood of zero in fixed time, and uncertainty and external interference in a model are estimated and compensated by applying a novel adaptive estimation algorithm. The method reduces the influence of unknown interference on the carrier aircraft landing trajectory tracking accuracy, improves the convergence speed of the trajectory tracking error, and enhances the robustness and stability of the system.

Description

Carrier-based aircraft landing fixed time trajectory tracking method based on limited backstepping control
Technical Field
The invention provides a fixed time trajectory tracking method for carrier-based aircraft landing based on limited backstepping control, provides a new trajectory tracking control method for carrier-based aircraft landing under the condition of considering parameter uncertainty, output constraint and unknown interference, and belongs to the technical field of automatic control of carrier-based aircraft.
Background
In recent years, in order to enhance the overall operational capability of an aircraft carrier/carrier aircraft system, research and practical application of carrier aircraft landing trajectory tracking control are increasing. The carrier-based aircraft can not only carry out accurate target striking aiming at sea, land and air in the process of battle, but also can finish various accurate battle tasks such as detection, early warning, electronic countermeasure and the like, and is the main embodiment of the fighting capacity of the aircraft carrier. Meanwhile, the powerful cooperative combat capability of the aircraft carrier enables the aircraft carrier to become indispensable weapon equipment for protecting the national ocean territory. This requires good tracking performance of the carrier to efficiently complete the task, in which case many tracking control methods are in force. In practical application, model parameters of the carrier-based aircraft cannot be accurately known, the landing environment is complex and changeable, and the interference of the offshore complex atmospheric environment and the wake flow can bring great disturbance to the landing process of the carrier-based aircraft. Therefore, in order to enable the carrier-based aircraft to accurately track the reference trajectory in the complex airflow environment, it is necessary to constrain the position and the attitude of the carrier-based aircraft, and a flight control system of the carrier-based aircraft should have strong robustness and stability. At present, aiming at the research of a ship-based aircraft trajectory tracking control algorithm, the method mainly applied comprises sight guidance, a neural network, a fuzzy theory and the like. Most of the methods do not consider the problems of output constraint and fixed time convergence, and an important index for measuring the carrier landing performance of the carrier-based aircraft is the convergence time of the track tracking error of the carrier-based aircraft. Therefore, a carrier aircraft landing trajectory tracking control method with better performance and higher reliability needs to be provided.
The invention discloses a fixed-time carrier landing trajectory tracking method based on limited backstepping control, which is based on the above problems, and provides a reliable control theory for solving the carrier landing trajectory tracking problem of carrier-based aircraft under the conditions of uncertain parameters, output constraint and external interference. The trajectory tracking problem is divided into a position tracking problem, a posture tracking problem and an attack angle tracking problem through a six-degree-of-freedom model of the carrier-based aircraft under an inertial coordinate system. A novel self-adaptive estimation algorithm and a nonlinear disturbance observer are used for estimating and compensating external disturbance. Meanwhile, an obstacle Lyapunov function is introduced to solve the problem of output constraint, and the convergence time of the system is reduced by combining a fixed time control theory, so that the track tracking error of the carrier-based aircraft is converged to a small neighborhood of zero in fixed time. Through Lyapunov stability analysis and analog simulation, the designed controller is proved to be high in reliability, the carrier-based aircraft can track the reference track with high precision, the track tracking error is converged to a zero small neighborhood within a fixed time, and the system global consistency is guaranteed to be bounded.
Disclosure of Invention
1. The purpose is as follows: the invention aims to provide a carrier-based aircraft landing fixed time trajectory tracking method based on limited backstepping control, and a control engineer can realize the fixed time trajectory tracking control of anti-disturbance and anti-output constraint of carrier landing of a carrier-based aircraft according to the method while combining actual parameters.
2. The technical scheme is as follows: the invention relates to a fixed-time trajectory tracking method for carrier-based aircraft landing based on limited backstepping control, which mainly comprises the following steps: firstly, a six-degree-of-freedom model of the carrier-based aircraft under an inertial coordinate system is given, and then controller design is carried out according to the model. The method is divided into three parts of distance control, attitude control and automatic throttle control with constant attack angle according to effective input, so that the control law also correspondingly consists of three parts: distance control law, attitude control law and automatic throttle control law. The three control laws are designed based on an output constraint self-adaptive backstepping method and are combined with a fixed time control theory. The actual input control quantity obtained by calculation by the method is transmitted to actuating mechanisms such as a steering engine, an engine and the like, and the function of fixed time trajectory tracking of carrier-based aircraft landing can be realized.
The invention relates to a fixed time trajectory tracking method for carrier-based aircraft landing based on limited backstepping control, which comprises the following specific steps of:
step one, establishing a six-degree-of-freedom strict feedback nonlinear affine model of the carrier-based aircraft under an inertial coordinate system.
Step two, distance control design: and giving an expected track, calculating a position virtual control law according to the position error, further deducing a virtual input control law with output constraint for controlling a course angle and a climbing angle according to the virtual control law, and estimating and compensating external interference by using a self-adaptive control algorithm so as to reduce the distance difference between the carrier-based aircraft and the reference track.
Step three, angle control design: and calculating an angle error, calculating the angle error to obtain an angle virtual control law, further deriving an actual input control law with output constraints for controlling a pitch angle, a sideslip angle and a roll angular velocity from the virtual control law, and estimating and compensating external interference by using a self-adaptive control algorithm so as to reduce the angle difference between the shipboard aircraft and a reference track.
Step four, automatic throttle control design: and calculating an angle of attack error, calculating the angle of attack error to obtain an actual input control law, namely an automatic throttle control law, and estimating and compensating external interference by using an interference observer to reduce the angle of attack error.
The six-degree-of-freedom strict feedback nonlinear affine model in the step one is as follows:
and (3) establishing a six-degree-of-freedom model of the carrier-based aircraft under an inertial coordinate system, as shown in the attached figure 1. O isgxgygIs an inertial coordinate system, O, established on the earthbxbybzbTo establish a coordinate system of the body on the carrier-based aircraft, OpxpypzpRepresenting a track coordinate system. Under the coordinate system, the carrier-based aircraft strictly feeds back a nonlinear affine model of
Figure BDA0003003619830000021
In the above equation, x1＝[y,z]TRepresenting position, x, in an inertial frame2＝[χ,γ]TWherein χ and γ represent a course angle and a climb angle, respectively, v ═ v1,ν2]T＝[sinμ,αcosμ]TAs a virtual control quantity, x3＝[θ,β,μ]TWhere θ, β and μ denote pitch, roll and yaw, respectively, and x4＝[p,q,r]TWherein p, q and r respectively represent the projection of each attitude angular velocity in the body coordinate system, uact＝[δa,δe,δr]TRepresenting the angle of deflection, delta, of the ailerons, elevators and rudderpRepresenting the throttle control input of the engine, alpha being the angle of attack, VkRepresenting the current flying speed of the carrier-based aircraft, df＝[dχ,dγ]T，dm＝[dp,dq,dr]TAnd dαThe method represents the external unknown disturbance quantity caused by the wake flow, the sea wave and the like, and the size of the external unknown disturbance quantity is unknown and bounded, and the unknown bound is expressed as
Figure BDA0003003619830000031
And
Figure BDA0003003619830000032
and f isi(i＝1,2,3,4,α)，biThe specific expression of the parameter (i ═ 1,2,3,4, α) is as follows:
Figure BDA0003003619830000033
Figure BDA0003003619830000034
Figure BDA0003003619830000035
Figure BDA0003003619830000036
Figure BDA0003003619830000037
Figure BDA0003003619830000038
f4＝f4(x3,x4,Q)
Figure BDA0003003619830000041
Figure BDA0003003619830000042
Figure BDA0003003619830000043
Figure BDA0003003619830000044
Figure BDA0003003619830000045
Figure BDA0003003619830000046
in the above formula, m is mass, σ represents mounting angle, T represents current thrust, and T represents thrustmaxMaximum thrust is indicated, l is span length, ρ is atmospheric density, S is wing area,
Figure BDA0003003619830000047
l, M, N respectively represent roll moment, pitch moment and yaw moment, Y, D, C respectively represent lift force, resistance force and lateral force, Iii(i ═ x, y, z) represents each inertial parameter, coefficient, of the ship-borne aircraft
Figure BDA0003003619830000048
Representing the partial derivative of delta with respect to epsilon, i.e.
Figure BDA0003003619830000049
δ＝Y,D,C,L,M,N，ε＝α,β,δa,δe,δr,p,q,r。
Wherein, in the distance control design in the step two, the method is as follows:
given a desired trajectory, a desired position coordinate x is obtained1d＝(yd,zd) The following error variables are thus defined:
z1＝x1-x1d，z2＝x2-α1
wherein the position error is z1Angle error of z2. Wherein, the range of the position error is required to be-omegabLj＜z1j(t)＜ΩbHj。
Selecting the Lyapunov function as
Figure BDA00030036198300000410
Figure BDA0003003619830000051
The following virtual control law α is designed1Comprises the following steps:
Figure BDA0003003619830000052
Figure BDA0003003619830000053
the virtual control law v is as follows:
Figure BDA0003003619830000054
Figure BDA0003003619830000055
the adaptive law is:
Figure BDA0003003619830000056
wherein k is11,k12,k21,k22Greater than 0 is a positive definite diagonal matrix, epsilon10,ε20Greater than 0 is a small constant and utilizes
Figure BDA0003003619830000057
This term eliminates chatter and prevents the occurrence of strangeness problems, m1,m2,n1,σ1The value of more than 0 is a constant value,
Figure BDA0003003619830000058
is L1Is determined by the estimated value of (c),
Figure BDA0003003619830000059
a vector is estimated for the error. Wherein instruction filter estimation is applied
Figure BDA00030036198300000510
And
Figure BDA00030036198300000511
the desired pitch angle θ can be determineddAngle of sideslip betadAnd the velocity roll angle mudComprises the following steps:
Figure BDA00030036198300000512
wherein, the angle control design method in step three is as follows:
obtaining the expected pitch angle theta from the second stepdAngle of sideslip betadAnd the velocity roll angle mudThe following error variables are thus defined:
z3＝x3-x3d，z4＝x4-α2
wherein, the range of the error of the attitude angle is required to be-omegacLj＜z3j(t)＜ΩcHj。
Selecting the Lyapunov function as
Figure BDA0003003619830000061
Figure BDA0003003619830000062
The following virtual control law α is designed2Comprises the following steps:
Figure BDA0003003619830000063
Figure BDA0003003619830000064
actual control law uactComprises the following steps:
Figure BDA0003003619830000065
the adaptive law is:
Figure BDA0003003619830000066
wherein k is31,k32,k41,k42Greater than 0 is a positive definite diagonal matrix, epsilon30,ε40Greater than 0 is a small constant and utilizes
Figure BDA0003003619830000067
This term eliminates chatter and prevents the occurrence of strangeness problems, m3,m4,n2,σ2The value of more than 0 is a constant value,
Figure BDA0003003619830000068
is L2Is determined by the estimated value of (c),
Figure BDA0003003619830000069
for error estimationAnd (6) counting the vector quantity. Wherein instruction filter estimation is applied
Figure BDA00030036198300000610
And
Figure BDA00030036198300000611
the automatic throttle control design method in the fourth step is as follows:
given a desired angle of attack αdThe following angle of attack error variables are thus defined:
z5＝α-αd
wherein, the range of the error of the angle of attack is required to be-omegaaL＜z5＜ΩaH。
Selecting the Lyapunov function as
Figure BDA0003003619830000071
Figure BDA0003003619830000072
The following actual control law δ is designedpComprises the following steps:
Figure BDA0003003619830000073
using the error d estimated by the disturbance observerα
Figure BDA0003003619830000074
Wherein k is51,k52Greater than 0 is a constant, epsilon50Greater than 0 is a small constant and utilizes
Figure BDA0003003619830000075
This term eliminates chatter and prevents strangenessOccurrence of sexual problem, pα,lαThe value of more than 0 is a constant value,
Figure BDA0003003619830000076
is dαIs determined by the estimated value of (c),
Figure BDA0003003619830000077
to estimate the error.
The designed fixed-time trajectory tracking method for carrier landing of the carrier-based aircraft has the advantages that each tracking error can be converged to a small neighborhood of zero within the fixed time T, and T is
Figure BDA0003003619830000078
3. The advantages and effects are as follows:
compared with the prior art, the invention discloses a fixed time trajectory tracking method for carrier-based aircraft landing based on limited backstepping control, which has the advantages that:
1) the method can effectively solve the output constraint problem, and greatly improves the adverse effects on the design, tracking effect and performances of the controller caused by the sea condition environment limitation and the constraint problem in the design process of the controller;
2) the method adopts a self-adaptive algorithm and an interference observer to well inhibit model uncertainty, and effectively estimates and compensates the interference influence of external disturbance on the system;
3) and the convergence time of the system is reduced by using a fixed time control method, so that the track tracking error of the carrier-based aircraft is converged to a small neighborhood of zero in fixed time.
4) The method can ensure that the system is globally and consistently bounded, and the position error, the attitude error and the attack angle error are restricted within a specified range;
drawings
FIG. 1 is a schematic view of a coordinate system of the present invention;
FIG. 2 is a schematic diagram of a control system framework of the present invention;
the symbols are as follows:
x1 x1＝[y,z]Tthe current position of the carrier-based aircraft under an inertial coordinate system;
x2 x2＝[χ,γ]Tthe ship-borne aircraft is a course angle and a climbing angle under an inertial coordinate system;
x3 x3＝[θ,β,μ]Tthe pitch angle, the sideslip angle and the roll angle of the shipboard aircraft under an inertial coordinate system;
x4 x4＝[p,q,r]Tthe angular speed of each attitude angle under the body coordinate system of the carrier-borne aircraft is projected in the body coordinate system;
alpha is the current angle of attack of the carrier-based aircraft;
ν ν＝[sinμ,αcosμ]Tis a virtual control quantity in the position controller;
uact uact＝[δa,δe,δr]Tthe deflection angles of the ailerons, the elevators and the rudders;
δp δpan engine throttle control parameter;
df,dm,dαthe external interference amount of the carrier-based aircraft;
Figure BDA0003003619830000081
unknown upper-bound estimation values of the external interference quantity of the carrier-based aircraft;
x1dthe expected position coordinates of the carrier-based aircraft;
x3dan expected attitude variable of the shipboard aircraft;
z1position error of the carrier-based aircraft;
z2attitude errors of the carrier-based aircraft;
z3,z4angle error and angular velocity error of the carrier-based aircraft;
z5angle of attack error of the shipboard aircraft;
tan h (·) custom function;
ΩbL,ΩbHshipboard aircraftLimiting upper and lower limits of position error;
ΩcL,ΩcHrestraining upper and lower limit values of the angle error of the shipboard aircraft;
ΩaL,ΩaHconstraining upper and lower limit values of an attack angle error of the shipboard aircraft;
α1,α2a virtual control law;
Figure BDA0003003619830000091
unknown vector estimation values of the ship-borne aircraft system model;
Figure BDA0003003619830000092
estimating an error value by an unknown vector of a ship-borne aircraft system model;
k11,k12,k21,k22,k31,k32designing parameters of a virtual control law;
k41,k42,k51,k52actual control law design parameters;
t, fixing time of carrier aircraft landing system error convergence;
Detailed Description
The design method of each part in the invention is further explained as follows:
the invention relates to a fixed time trajectory tracking method for carrier-based aircraft landing based on limited backstepping control, which comprises the following specific steps of:
the method comprises the following steps: establishment of six-freedom-degree strict feedback nonlinear affine model
And (3) establishing a six-degree-of-freedom model of the carrier-based aircraft under an inertial coordinate system, as shown in the attached figure 1. O isgxgygIs an inertial coordinate system, O, established on the earthbxbybzbTo establish a coordinate system of the body on the carrier-based aircraft, OpxpypzpRepresenting a track coordinate system. Under the coordinate system, the carrier-based aircraft strictly feeds back a nonlinear affine model of
Figure BDA0003003619830000093
In the above equation, x1＝[y,z]TRepresenting position, x, in an inertial frame2＝[χ,γ]TWherein χ and γ represent a course angle and a climb angle, respectively, v ═ v1,ν2]T＝[sinμ,αcosμ]TAs a virtual control quantity, x3＝[θ,β,μ]TWhere θ, β and μ denote pitch, roll and yaw, respectively, and x4＝[p,q,r]TWherein p, q and r respectively represent the projection of each attitude angular velocity in the body coordinate system, uact＝[δa,δe,δr]TRepresenting the angle of deflection, delta, of the ailerons, elevators and rudderpRepresenting the throttle control input of the engine, alpha being the angle of attack, VkRepresenting the current flying speed of the carrier-based aircraft, df＝[dχ,dγ]T，dm＝[dp,dq,dr]TAnd dαThe method represents the external unknown disturbance quantity caused by the wake flow, the sea wave and the like, and the size of the external unknown disturbance quantity is unknown and bounded, and the unknown bound is expressed as
Figure BDA0003003619830000094
And
Figure BDA0003003619830000095
and f isi(i＝1,2,3,4,α)，biThe specific expression of the parameter (i ═ 1,2,3,4, α) is as follows:
Figure BDA0003003619830000101
Figure BDA0003003619830000102
Figure BDA0003003619830000103
Figure BDA0003003619830000104
Figure BDA0003003619830000105
Figure BDA0003003619830000106
f4＝f4(x3,x4,Q)
Figure BDA0003003619830000107
Figure BDA0003003619830000108
Figure BDA0003003619830000111
Figure BDA0003003619830000112
Figure BDA0003003619830000113
Figure BDA0003003619830000114
in the above formula, m is mass, σ represents mounting angle, T represents current thrust, and T represents thrustmaxIndicating maximum thrust, | indicating wingSpanwise length, ρ is the atmospheric density, S is the wing area,
Figure BDA0003003619830000115
l, M, N respectively represent roll moment, pitch moment and yaw moment, Y, D, C respectively represent lift force, resistance force and lateral force, Iii(i ═ x, y, z) represents each inertial parameter, coefficient, of the ship-borne aircraft
Figure BDA0003003619830000116
Representing the partial derivative of delta with respect to epsilon, i.e.
Figure BDA0003003619830000117
δ＝Y,D,C,L,M,N，ε＝α,β,δa,δe,δr,p,q,r。
Step two: distance control design
Given a desired trajectory, a desired position coordinate x is obtained1d＝(yd,zd) The following error variables are thus defined:
z1＝x1-x1d，z2＝x2-α1
wherein the position error is z1Angle error of z2. Wherein, the range of the position error is required to be-omegabLj＜z1j(t)＜ΩbHj。
Selecting the Lyapunov function as
Figure BDA0003003619830000118
Figure BDA0003003619830000119
The following virtual control law α is designed1Comprises the following steps:
Figure BDA0003003619830000121
Figure BDA0003003619830000122
the virtual control law v is as follows:
Figure BDA0003003619830000123
Figure BDA0003003619830000124
the adaptive law is:
Figure BDA0003003619830000125
wherein k is11,k12,k21,k22Greater than 0 is a positive definite diagonal matrix, epsilon10,ε20Greater than 0 is a small constant and utilizes
Figure BDA0003003619830000126
This term eliminates chatter and prevents the occurrence of strangeness problems, m1,m2,n1,σ1The value of more than 0 is a constant value,
Figure BDA0003003619830000127
is L1Is determined by the estimated value of (c),
Figure BDA0003003619830000128
a vector is estimated for the error. Wherein instruction filter estimation is applied
Figure BDA0003003619830000129
And
Figure BDA00030036198300001210
the desired pitch angle θ can be determineddAngle of sideslip betadAnd the velocity roll angle mudComprises the following steps:
Figure BDA00030036198300001211
step three: angle control design
Obtaining the expected pitch angle theta from the second stepdAngle of sideslip betadAnd the velocity roll angle mudThe following error variables are thus defined:
z3＝x3-x3d，z4＝x4-α2
wherein, the range of the error of the attitude angle is required to be-omegacLj＜z3j(t)＜ΩcHj。
Selecting the Lyapunov function as
Figure BDA0003003619830000131
Figure BDA0003003619830000132
The following virtual control law α is designed2Comprises the following steps:
Figure BDA0003003619830000133
Figure BDA0003003619830000134
actual control law uactComprises the following steps:
Figure BDA0003003619830000135
the adaptive law is:
Figure BDA0003003619830000136
wherein k is31,k32,k41,k42Greater than 0 is a positive definite diagonal matrix, epsilon30,ε40Greater than 0 is a small constant and utilizes
Figure BDA0003003619830000137
This term eliminates chatter and prevents the occurrence of strangeness problems, m3,m4,n2,σ2The value of more than 0 is a constant value,
Figure BDA0003003619830000138
is L2Is determined by the estimated value of (c),
Figure BDA0003003619830000139
a vector is estimated for the error. Wherein instruction filter estimation is applied
Figure BDA00030036198300001310
And
Figure BDA00030036198300001311
step four: automatic throttle control design
Given a desired angle of attack αdThe following angle of attack error variables are thus defined:
z5＝α-αd
wherein, the range of the error of the angle of attack is required to be-omegaaL＜z5＜ΩaH。
Selecting the Lyapunov function as
Figure BDA0003003619830000141
Figure BDA0003003619830000142
The following actual control law δ is designedpComprises the following steps:
Figure BDA0003003619830000143
using the error d estimated by the disturbance observerα
Figure BDA0003003619830000144
Wherein k is51,k52Greater than 0 is a constant, epsilon50Greater than 0 is a small constant and utilizes
Figure BDA0003003619830000145
This term eliminates chatter and prevents the occurrence of singularity problems, pα,lαThe value of more than 0 is a constant value,
Figure BDA0003003619830000146
is dαIs determined by the estimated value of (c),
Figure BDA0003003619830000147
to estimate the error.
The designed fixed-time trajectory tracking method for carrier landing of the carrier-based aircraft has the advantages that each tracking error can be converged to a small neighborhood of zero within the fixed time T, and T is
Figure BDA0003003619830000148

Claims (4)

1. A fixed time trajectory tracking method for carrier-based aircraft landing based on limited backstepping control is characterized by comprising the following specific steps:
step one, establishing a six-degree-of-freedom strict feedback nonlinear affine model of the carrier-based aircraft under an inertial coordinate system. (ii) a
Step two, distance control design: and giving an expected track, calculating a position virtual control law according to the position error, further deducing a virtual input control law with output constraint for controlling a course angle and a climbing angle according to the virtual control law, and estimating and compensating external interference by using a self-adaptive control algorithm so as to reduce the distance difference between the carrier-based aircraft and the reference track.
Step three-angle control design: and calculating an angle error, calculating the angle error to obtain an angle virtual control law, further deriving an actual input control law with output constraints for controlling a pitch angle, a sideslip angle and a roll angular velocity from the virtual control law, and estimating and compensating external interference by using a self-adaptive control algorithm so as to reduce the angle difference between the shipboard aircraft and a reference track.
Step four, automatic throttle control design: and calculating an angle of attack error, calculating the angle of attack error to obtain an actual input control law, namely an automatic throttle control law, and estimating and compensating external interference by using an interference observer to reduce the angle of attack error.
The establishment process of the six-degree-of-freedom strict feedback nonlinear affine model in the first step is as follows:
and (3) establishing a six-degree-of-freedom model of the carrier-based aircraft under an inertial coordinate system, as shown in the attached figure 1. O isgxgygIs an inertial coordinate system, O, established on the earthbxbybzbTo establish a coordinate system of the body on the carrier-based aircraft, OpxpypzpRepresenting a track coordinate system. Under the coordinate system, the carrier-based aircraft strictly feeds back a nonlinear affine model of
Figure FDA0003003619820000011
In the above equation, x1＝[y,z]TRepresenting position, x, in an inertial frame2＝[χ,γ]TWherein χ and γ represent a course angle and a climb angle, respectively, v ═ v1,ν2]T＝[sinμ,αcosμ]TAs a virtual control quantity, x3＝[θ,β,μ]TWhere θ, β and μ denote pitch, roll and yaw, respectively, and x4＝[p,q,r]TWherein p, q and r respectively represent the projection of each attitude angular velocity in the body coordinate system, uact＝[δa,δe,δr]TRepresenting the angle of deflection, delta, of the ailerons, elevators and rudderpRepresenting the throttle control input of the engine, alpha being the angle of attack, VkRepresenting the current flying speed of the carrier-based aircraft, df＝[dχ,dγ]T，dm＝[dp,dq,dr]TAnd dαThe method represents the external unknown disturbance quantity caused by the wake flow, the sea wave and the like, and the size of the external unknown disturbance quantity is unknown and bounded, and the unknown bound is expressed as
Figure FDA0003003619820000012
Figure FDA0003003619820000013
And
Figure FDA0003003619820000014
and f isi(i＝1,2,3,4,α)，biThe specific expression of the parameter (i ═ 1,2,3,4, α) is as follows:
Figure FDA0003003619820000021
Figure FDA0003003619820000022
Figure FDA0003003619820000023
Figure FDA0003003619820000024
Figure FDA0003003619820000025
Figure FDA0003003619820000026
f4＝f4(x3,x4,Q)
Figure FDA0003003619820000027
Figure FDA0003003619820000028
Figure FDA0003003619820000029
Figure FDA0003003619820000031
Figure FDA0003003619820000032
Figure FDA0003003619820000033
in the above formula, m is mass, σ represents mounting angle, T represents current thrust, and T represents thrustmaxMaximum thrust is indicated, l is span length, ρ is atmospheric density, S is wing area,
Figure FDA0003003619820000034
l, M, N respectively represent roll moment, pitch moment and yaw moment, Y, D, C respectively represent lift force, resistance force and lateral force, Iii(i ═ x, y, z) represents each inertial parameter, coefficient, of the ship-borne aircraft
Figure FDA0003003619820000035
Representing the partial derivative of delta with respect to epsilon, i.e.
Figure FDA0003003619820000036
δ＝Y,D,C,L,M,N，ε＝α,β,δa,δe,δr,p,q,r。
2. The carrier-based aircraft landing fixed time trajectory tracking method based on limited backstepping control according to claim 1, characterized in that: the distance control design in the step two specifically comprises the following steps:
given a desired trajectory, a desired position coordinate x is obtained1d＝(yd,zd) The following error variables are thus defined:
z1＝x1-x1d，z2＝x2-α1
wherein the position error is z1Angle error of z2. Wherein, the range of the position error is required to be-omegabLj＜z1j(t)＜ΩbHj。
Selecting the Lyapunov function as
Figure FDA0003003619820000037
Figure FDA0003003619820000038
The following virtual control law α is designed1Comprises the following steps:
Figure FDA0003003619820000039
Figure FDA0003003619820000041
the virtual control law v is as follows:
Figure FDA0003003619820000042
Figure FDA0003003619820000043
the adaptive law is:
Figure FDA0003003619820000044
wherein k is11,k12,k21,k22Greater than 0 is a positive definite diagonal matrix, epsilon10,ε20Greater than 0 is a small constant and utilizes
Figure FDA0003003619820000045
This term eliminates chatter and prevents the occurrence of strangeness problems, m1,m2,n1,σ1The value of more than 0 is a constant value,
Figure FDA0003003619820000046
is L1Is determined by the estimated value of (c),
Figure FDA0003003619820000047
a vector is estimated for the error. Wherein instruction filter estimation is applied
Figure FDA0003003619820000048
And
Figure FDA0003003619820000049
the desired pitch angle θ can be determineddAngle of sideslip betadAnd the velocity roll angle mudComprises the following steps:
Figure FDA00030036198200000410
3. the carrier-based aircraft landing fixed time trajectory tracking method based on limited backstepping control according to claim 1, characterized in that: the angle control design method in step three is as follows:
obtaining the expected pitch angle theta from the second stepdAngle of sideslip betadAnd the velocity roll angle mudThe following error variables are thus defined:
z3＝x3-x3d，z4＝x4-α2
wherein, the range of the error of the attitude angle is required to be-omegacLj＜z3j(t)＜ΩcHj。
Selecting the Lyapunov function as
Figure FDA00030036198200000411
Figure FDA0003003619820000051
The following virtual control law α is designed2Comprises the following steps:
Figure FDA0003003619820000052
Figure FDA0003003619820000053
actual control law uactComprises the following steps:
Figure FDA0003003619820000054
the adaptive law is:
Figure FDA0003003619820000055
wherein k is31,k32,k41,k42Greater than 0 is a positive definite diagonal matrix, epsilon30,ε40Greater than 0 is a small constant and utilizes
Figure FDA0003003619820000056
This term eliminates chatter and prevents the occurrence of strangeness problems, m3,m4,n2,σ2The value of more than 0 is a constant value,
Figure FDA0003003619820000057
is L2Is determined by the estimated value of (c),
Figure FDA0003003619820000058
a vector is estimated for the error. Wherein instruction filter estimation is applied
Figure FDA0003003619820000059
And
Figure FDA00030036198200000510
4. the carrier-based aircraft landing fixed time trajectory tracking method based on limited backstepping control according to claim 1, characterized in that: the automatic throttle control design method in the fourth step is as follows:
given a desired angle of attack αdThe following angle of attack error variables are thus defined:
z5＝α-αd
wherein, the range of the error of the angle of attack is required to be-omegaaL＜z5＜ΩaH。
Selecting the Lyapunov function as
Figure FDA00030036198200000511
Figure FDA0003003619820000061
The following actual control law δ is designedpComprises the following steps:
Figure FDA0003003619820000062
using the error d estimated by the disturbance observerα
Figure FDA0003003619820000063
Wherein k is51,k52Greater than 0 is a constant, epsilon50Greater than 0 is a small constant and utilizes
Figure FDA0003003619820000064
This term eliminates chatter and prevents the occurrence of singularity problems, pα,lαThe value of more than 0 is a constant value,
Figure FDA0003003619820000065
is dαIs determined by the estimated value of (c),
Figure FDA0003003619820000066
to estimate the error.
The designed fixed-time trajectory tracking method for carrier landing of the carrier-based aircraft has the advantages that each tracking error can be converged to a small neighborhood of zero within the fixed time T, and T is
Figure FDA0003003619820000067
CN202110356783.7A 2021-04-01 2021-04-01 Carrier-based aircraft landing fixed time trajectory tracking method based on limited backstepping control Pending CN113110428A (en)

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Publication number Priority date Publication date Assignee Title
CN117369471A (en) * 2023-11-06 2024-01-09 大连海事大学 Unmanned ship data driving fuzzy heading control method with preset performance

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117369471A (en) * 2023-11-06 2024-01-09 大连海事大学 Unmanned ship data driving fuzzy heading control method with preset performance
CN117369471B (en) * 2023-11-06 2024-05-28 大连海事大学 Unmanned ship data driving fuzzy heading control method with preset performance

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