CN113110538A - Fixed-time fault-tolerant control method for carrier-based aircraft landing based on backstepping control - Google Patents

Abstract

The invention provides a fixed-time fault-tolerant control method for carrier-based aircraft landing based on backstepping control, provides a novel fault-tolerant control method for carrier-based aircraft landing under the condition of considering uncertain parameters, unknown interference and actuator faults, 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 fault-tolerant controller of the carrier-based aircraft, and utilizes a fixed time disturbance observer to carry out fault-tolerant control on faults of an actuator of the carrier-based aircraft and estimate and compensate uncertainty and external disturbance in a model. Meanwhile, the convergence time of the system is reduced by combining a fixed time control method, so that the control object converges the trajectory tracking error to a small neighborhood of zero within the fixed time. The method greatly reduces the influence of the actuator fault on the track tracking performance of the carrier-based aircraft, improves the convergence speed of the track tracking error, realizes that the carrier-based aircraft can continuously complete track tracking and safely land on the ship under the condition of the actuator fault, and enhances the robustness and the stability of the system.

Description

Fixed-time fault-tolerant control method for carrier-based aircraft landing based on backstepping control

Technical Field

The invention provides a fixed-time fault-tolerant control method for carrier-based aircraft landing based on backstepping control, provides a novel fault-tolerant control method for carrier-based aircraft landing under the condition of considering uncertain parameters, unknown interference and actuator faults, 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. The flight control system of the carrier-based aircraft converts instructions of a driver, an autopilot and other control units into electric signals, mechanical signals and hydraulic signals to control the position of a control surface of an actuator of the carrier-based aircraft so as to control the carrier-based aircraft to fly in a desired track. In the process of landing, in order to touch a ship in a proper posture, the carrier-based aircraft needs to slide down at a lower speed and maintain higher flight path control precision, so that safe landing is realized. However, in practical situations, the carrier-based aircraft has a lot of interference factors in the flight process, for example, the system performance is changed or even deteriorated due to external interference factors, such as gust and atmospheric turbulence, or due to unknown faults of actuators inside the carrier-based aircraft. For unknown interference factors, accurate measurement is difficult to perform only by using a sensor, and meanwhile, fault information has uncertainty and unknown property in time and place, so that the importance of the fault-tolerant control research for the shipboard aircraft is self-evident. By adding fault-tolerant control in the system, the carrier-based aircraft can still safely sail or land under the conditions of system failure and poor performance. A sliding mode disturbance observer and an extended observer are methods widely applied to unknown disturbance and fault estimation compensation, but the methods do not combine a fixed time control theory to reduce the system error convergence time, and an important index for measuring the carrier landing performance of a carrier-based aircraft is the convergence time of the carrier-based aircraft trajectory tracking error. Therefore, a carrier aircraft landing fault-tolerant control method with better performance, higher reliability and faster convergence time needs to be provided.

The invention discloses a fixed-time fault-tolerant control method for carrier-based aircraft landing based on backstepping control, which is based on the above problems, and provides a reliable control theory for solving the problems of uncertain parameters, external interference and fault tolerance of the carrier-based aircraft under the fault of an actuator. The problem of tracking an expected track under the fault condition is split into the problems of position tracking, attitude tracking and attack angle tracking through a six-degree-of-freedom model of the carrier-based aircraft under an inertial coordinate system. The method comprises the steps of estimating and compensating for external interference and actuator faults by using a fixed-time interference observer. Meanwhile, a fixed time control method is introduced to reduce the convergence time of the system, so that the carrier-based aircraft converges the track tracking error to a small neighborhood of zero within a fixed time. Through Lyapunov stability analysis and simulation, the designed controller is proved to have high fault-tolerant capability under the condition of actuator failure, the carrier-based aircraft can converge the trajectory tracking error to a small neighborhood of zero within a fixed time after the failure occurs, and the system is guaranteed to be globally and consistently bounded.

Disclosure of Invention

1. The purpose is as follows: the invention aims to provide a fixed-time fault-tolerant control method for carrier landing of a carrier-based aircraft based on backstepping control, and a control engineer can combine actual parameters and simultaneously realize the anti-disturbance and anti-actuator fault trajectory tracking control of the carrier-based aircraft according to the method.

An engineer can combine actual parameters and simultaneously realize the anti-disturbance and anti-actuator fault track tracking control of the carrier-based aircraft according to the method.

2. The technical scheme is as follows: the invention relates to a fixed-time fault-tolerant control method for carrier-based aircraft landing based on backstepping control, which mainly comprises the following steps:

firstly, a six-degree-of-freedom model of a carrier-based aircraft under an inertial coordinate system in consideration of external interference and actuator faults is given, and then a controller is designed according to the model. The method is divided into three parts of distance control, attitude control and automatic throttle control according to effective input, so that the control law correspondingly consists of three parts: distance control law, attitude control law and automatic throttle control law. All three control laws are designed based on a backstepping method. The actual input control quantity obtained by calculation by the method is transmitted to control surfaces, engines and other actuating mechanisms, and the fault-tolerant control function of the shipboard aircraft can be realized.

The invention relates to a fixed-time fault-tolerant control method for carrier-based aircraft landing based on 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 for controlling a course angle and a climbing angle according to the virtual control law, and estimating and compensating external interference by using a fixed time interference observer 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 deducing an actual input control law for controlling a pitch angle, a sideslip angle and a roll angular velocity from the virtual control law, and estimating and compensating external interference and actuator faults by using a fixed-time interference observer 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 a fixed-time 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 is_gx_gy_gIs an inertial coordinate system, O, established on the earth_bx_by_bz_bTo establish a coordinate system of the body on the carrier-based aircraft, O_px_py_pz_pRepresenting a track coordinate system. Under the coordinate system, the carrier-based aircraft strictly feeds back a nonlinear affine model of

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]^TWherein theta, beta and mu are respectively shown inYaw, roll and yaw angles, x₄＝[p,q,r]^TWherein p, q and r respectively represent the projection of each attitude angular velocity in the body coordinate system, u_act＝[δ_a,δ_e,δ_r]^TRepresenting the angle of deflection, delta, of the ailerons, elevators and rudder_pRepresenting the throttle control input of the engine, alpha being the angle of attack, V_kRepresenting the current flying speed of the carrier-based aircraft, d_f＝[d_χ,d_γ]^T，d_m＝[d_p,d_q,d_r]^TAnd d_αThe method represents the external unknown disturbance quantity caused by the wake flow, the sea wave and the like, the size of the disturbance quantity is unknown and bounded, and the unknown bound is represented as L₁、L₂And L₃. Definition of Δ₁＝b₄(ξ-I)u_act+b₄u_f+d_mFor actuator failure, ξ ═ diag ([ ξ [ ])₁,ξ₂,ξ₃]) In order to gain the damage to the actuator,

is an actuator addition fault, and f_i(i＝1,2,3,4,α)，b_iThe specific expression of the parameter (i ═ 1,2,3,4, α) is as follows:

f₄＝f₄(x₃,x₄,Q)

in the above formula, m is mass, σ represents mounting angle, T represents current thrust, and T represents thrust_maxMaximum thrust is indicated, l is span length, ρ is atmospheric density, S is wing area,

l, M, N respectively represent roll moment, pitch moment and yaw moment, Y, D, C respectively represent lift force, resistance force and lateral force, I_ii(i ═ x, y, z) represents each inertial parameter, coefficient, of the ship-borne aircraft

Representing the partial derivative of delta with respect to epsilon, i.e.

δ＝Y,D,C,L,M,N，ε＝α,β,δ_a,δ_e,δ_r,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 obtained_1d＝(y_d,z_d) The following error variables are thus defined:

ε₁＝x₁-x_1d，ε₂＝x₂-x_2d

in which the position error is epsilon₁Angle error of epsilon₂。

Selecting the Lyapunov function as

The following virtual control law x is designed_2dComprises the following steps:

the virtual control law v is as follows:

the fixed time disturbance observer is designed as follows:

wherein k is₁₁,k₁₂,k₂₁,k₂₂Greater than 0 is positive definite diagonal matrix, delta₁₀,δ₂₀Greater than 0 is a small constant and utilizes

This term eliminates chatter and prevents the occurrence of singularity problems, z₁,z₂As a quantity of state of disturbance observer, λ₁,λ₂,λ₃For gain in disturbance observer,/₁＝z₁-x₂And is and

λ₂＞0，λ₃＞4L₁. Wherein instruction filter estimation is applied

And

the design of the fixed time disturbance observer can accurately estimate unknown disturbance d in fixed time_fAnd the fixed time is

Wherein σ > 0 and

N₁＝λ₃+L₁，n₁＝λ₃-L₁and p > 1 is a controller parameter.

The desired pitch angle θ can be determined_dAngle of sideslip beta_dAnd the velocity roll angle mu_dComprises the following steps:

wherein, the angle control design method in step three is as follows:

obtaining the expected pitch angle theta from the second step_dAngle of sideslip beta_dAnd the velocity roll angle mu_dThe following error variables are thus defined:

ε₃＝x₃-x_3d，ε₄＝x₄-x_4d

selecting the Lyapunov function as

The following virtual control law x is designed_4dComprises the following steps:

actual control law u_actComprises the following steps:

the fixed time disturbance observer is designed as follows:

wherein k is₃₁,k₃₂,k₄₁,k₄₂Greater than 0 is positive definite diagonal matrix, delta₃₀,δ₄₀Greater than 0 is a small constant and utilizes

This term eliminates chatter and prevents the occurrence of singularity problems, z₃,z₄As a quantity of state of disturbance observer, λ₄,λ₅,λ₆For gain in disturbance observer,/₂＝z₃-x₄And is and

λ₅＞0，λ₆＞4L₂. Wherein instruction filter estimation is applied

And

the design of the fixed-time interference observer can accurately estimate the unknown interference delta within fixed time₁And the fixed time is

Wherein σ₁Is greater than 0 and

N₂＝λ₆+L₂，n₂＝λ₆-L₂and p > 1 is a controller parameter.

The automatic throttle control design method in the fourth step is as follows:

given a desired angle of attack α_dThe following angle of attack error variables are thus defined:

ε₅＝α-α_d

selecting the Lyapunov function as

The following actual control law δ is designed_pComprises the following steps:

the fixed time disturbance observer is designed as follows:

wherein k is₅₁,k₅₂Greater than 0 is a constant, δ₅₀Greater than 0 is a small constant and utilizes

This term eliminates chatter and prevents the occurrence of singularity problems, z₅,z₆As a quantity of state of disturbance observer, λ₇,λ₈,λ₉For gain in disturbance observer,/₃＝z₅A, and λ₇h^-1(λ₇)＞N₃，λ₈＞0，λ₉＞L₃。

The design of the fixed time disturbance observer can accurately estimate unknown disturbance d in fixed time_αAnd the fixed time is

Wherein σ₂Is greater than 0 and

N₃＝λ₉+L₃，n₃＝λ₉-L₃p > 1 is controlThe machine parameters.

According to the designed carrier-based aircraft landing fixed-time fault-tolerant control method, each tracking error of the system can be converged to zero in a small neighborhood within fixed time T after an actuator fails, wherein T is

3. The advantages and effects are as follows:

compared with the prior art, the invention discloses a fixed-time fault-tolerant control method for carrier-based aircraft landing based on backstepping control, which has the advantages that:

1) the method can effectively solve the fault tolerance problem and greatly improve the control performance deterioration caused by the actuator fault.

2) The method adopts the fixed time interference observer to effectively estimate and compensate the model uncertainty, the external interference and the adverse effect of the actuator fault on the performance of the controller;

3) after the actuator fails, the errors of all state parameters of the system can be converged to a small neighborhood of zero in a fixed time.

4) The method can ensure the global consistency of the system to be bounded;

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]^Tfor carrier-borne aircraft under the coordinate system of the aircraft bodyProjecting each attitude angular velocity in a 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;

u_act u_act＝[δ_a,δ_e,δ_r]^Tthe deflection angles of the ailerons, the elevators and the rudders;

δ_p δ_pan engine throttle control parameter;

d_f,d_m,d_αthe external interference amount of the carrier-based aircraft;

Δ₁failure of the shipboard aircraft actuator;

L₁,L₂,L₃unknown upper-bound estimation values of the external interference quantity of the carrier-based aircraft;

x_1dthe expected position coordinates of the carrier-based aircraft;

x_3dan expected attitude variable of the shipboard aircraft;

ε₁position error of the carrier-based aircraft;

ε₂attitude errors of the carrier-based aircraft;

ε₃,ε₄angle error and angular velocity error of the carrier-based aircraft;

ε₅angle of attack error of the shipboard aircraft;

x_2d,x_4da virtual control law;

k₁₁,k₁₂,k₂₁,k₂₂,k₃₁,k₃₂designing parameters of a virtual control law;

k₄₁,k₄₂,k₅₁,k₅₂actual control law design parameters;

z₁,z₂,z₃,z₄,z₅,z₆a fixed time disturbance observer state parameter;

λ₁,λ₂,λ₃,λ₄,λ₅,λ₆,λ₇,λ₈,λ₉fixing deviceTiming the observer-shaped gain of the disturbance;

l₁,l₂,l₃fixed time disturbance observer error;

T₁,T₂,T₃estimation error d of fixed time disturbance observer_f,Δ₁,d_αA fixed time of (d);

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 fault-tolerant control method for carrier-based aircraft landing based on backstepping control, which comprises the following specific steps of:

the method comprises the following steps: establishing six-degree-of-freedom strict feedback nonlinear affine model of shipboard aircraft under inertial coordinate system

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 is_gx_gy_gIs an inertial coordinate system, O, established on the earth_bx_by_bz_bTo establish a coordinate system of the body on the carrier-based aircraft, O_px_py_pz_pRepresenting a track coordinate system. Under the coordinate system, the carrier-based aircraft strictly feeds back a nonlinear affine model of

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, u_act＝[δ_a,δ_e,δ_r]^TRepresenting the angle of deflection, delta, of the ailerons, elevators and rudder_pRepresenting the throttle control input of the engine, alpha being the angle of attack, V_kRepresenting the current flying speed of the carrier-based aircraft, d_f＝[d_χ,d_γ]^T，d_m＝[d_p,d_q,d_r]^TAnd d_αThe method represents the external unknown disturbance quantity caused by the wake flow, the sea wave and the like, the size of the disturbance quantity is unknown and bounded, and the unknown bound is represented as L₁、L₂And L₃. Definition of Δ₁＝b₄(ξ-I)u_act+b₄u_f+d_mFor actuator failure, ξ ═ diag ([ ξ [ ])₁,ξ₂,ξ₃]) In order to gain the damage to the actuator,

is an actuator addition fault, and f_i(i＝1,2,3,4,α)，b_iThe specific expression of the parameter (i ═ 1,2,3,4, α) is as follows:

f₄＝f₄(x₃,x₄,Q)

in the above formula, m is mass, σ represents mounting angle, T represents current thrust, and T represents thrust_maxMaximum thrust is indicated, l is span length, ρ is atmospheric density, S is wing area,

l, M, N respectively represent roll moment, pitch moment and yaw moment, Y, D, C respectively represent lift force, resistance force and lateral force, I_ii(i ═ x, y, z) represents each inertial parameter, coefficient, of the ship-borne aircraft

Representing the partial derivative of delta with respect to epsilon, i.e.

δ＝Y,D,C,L,M,N，ε＝α,β,δ_a,δ_e,δ_r,p,q,r。

Step two: distance control design

Given a desired trajectory, a desired position coordinate x is obtained_1d＝(y_d,z_d) The following error variables are thus defined:

ε₁＝x₁-x_1d，ε₂＝x₂-x_2d

in which the position error is epsilon₁Angle error of epsilon₂。

Selecting the Lyapunov function as

The following virtual control law x is designed_2dComprises the following steps:

the virtual control law v is as follows:

the fixed time disturbance observer is designed as follows:

wherein k is₁₁,k₁₂,k₂₁,k₂₂Greater than 0 is positive definite diagonal matrix, delta₁₀,δ₂₀Greater than 0 is a small constant and utilizes

This term eliminates chatter and prevents the occurrence of singularity problems, z₁,z₂As a quantity of state of disturbance observer, λ₁,λ₂,λ₃For gain in disturbance observer,/₁＝z₁-x₂And is and

λ₂＞0，λ₃＞4L₁. Wherein instruction filter estimation is applied

And

the design of the fixed time disturbance observer can accurately estimate unknown disturbance d in fixed time_fAnd the fixed time is

Wherein σ > 0 and

N₁＝λ₃+L₁，n₁＝λ₃-L₁and p > 1 is a controller parameter.

The desired pitch angle θ can be determined_dAngle of sideslip beta_dAnd the velocity roll angle mu_dComprises the following steps:

step three: angle control design

Obtaining the expected pitch angle theta from the second step_dAngle of sideslip beta_dAnd the velocity roll angle mu_dThe following error variables are thus defined:

ε₃＝x₃-x_3d，ε₄＝x₄-x_4d

selecting the Lyapunov function as

The following virtual control law x is designed_4dComprises the following steps:

actual control law u_actComprises the following steps:

the fixed time disturbance observer is designed as follows:

wherein k is₃₁,k₃₂,k₄₁,k₄₂Greater than 0 is positive definite diagonal matrix, delta₃₀,δ₄₀Greater than 0 is a small constant and utilizes

This term eliminates chatter and prevents the occurrence of singularity problems, z₃,z₄As a quantity of state of disturbance observer, λ₄,λ₅,λ₆For gain in disturbance observer,/₂＝z₃-x₄And is and

λ₅＞0，λ₆＞4L₂. Wherein instruction filter estimation is applied

And

the design of the fixed-time interference observer can accurately estimate the unknown interference delta within fixed time₁And the fixed time is

Wherein σ₁Is greater than 0 and

N₂＝λ₆+L₂，n₂＝λ₆-L₂and p > 1 is a controller parameter.

Step four: automatic throttle control design

Given a desired angle of attack α_dThe following angle of attack error variables are thus defined:

ε₅＝α-α_d

selecting the Lyapunov function as

The following actual control law δ is designed_pComprises the following steps:

the fixed time disturbance observer is designed as follows:

wherein k is₅₁,k₅₂Greater than 0 is a constant, δ₅₀Greater than 0 is a small constant and utilizes

This term eliminates chatter and prevents the occurrence of singularity problems, z₅,z₆As a quantity of state of disturbance observer, λ₇,λ₈,λ₉For gain in disturbance observer,/₃＝z₅A, and λ₇h^-1(λ₇)＞N₃，λ₈＞0，λ₉＞L₃。

The design of the fixed time disturbance observer can accurately estimate unknown disturbance d in fixed time_αAnd the fixed time is

Wherein σ₂Is greater than 0 and

N₃＝λ₉+L₃，n₃＝λ₉-L₃and p > 1 is a controller parameter.

According to the designed carrier-based aircraft landing fixed-time fault-tolerant control method, each tracking error of the system can be converged to zero in a small neighborhood within fixed time T after an actuator fails, wherein T is

Claims (4)

1. A fixed-time fault-tolerant control method for carrier-based aircraft landing based on 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 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 for controlling a course angle and a climbing angle according to the virtual control law, and estimating and compensating external interference by using a fixed time interference observer so as to reduce the distance difference between the carrier-based aircraft and the 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 a fixed-time 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 is_gx_gy_gIs an inertial coordinate system, O, established on the earth_bx_by_bz_bTo establish a coordinate system of the body on the carrier-based aircraft, O_px_py_pz_pRepresenting a track coordinate system. Under the coordinate system, the carrier-based aircraft strictly feeds back a nonlinear affine model of

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, u_act＝[δ_a,δ_e,δ_r]^TRepresenting the angle of deflection, delta, of the ailerons, elevators and rudder_pRepresenting the throttle control input of the engine, alpha being the angle of attack, V_kRepresenting the current flying speed of the carrier-based aircraft, d_f＝[d_χ,d_γ]^T，d_m＝[d_p,d_q,d_r]^TAnd d_αThe method represents the external unknown disturbance quantity caused by the wake flow, the sea wave and the like, the size of the disturbance quantity is unknown and bounded, and the unknown bound is represented as L₁、L₂And L₃. Definition of Δ₁＝b₄(ξ-I)u_act+b₄u_f+d_mFor actuator failure, ξ ═ diag ([ ξ [ ])₁,ξ₂,ξ₃]) In order to gain the damage to the actuator,

is an actuator addition fault, and f_i(i＝1,2,3,4,α)，b_iThe specific expression of the parameter (i ═ 1,2,3,4, α) is as follows:

f₄＝f₄(x₃,x₄,Q)

in the above formula, m is mass, σ represents mounting angle, T represents current thrust, and T represents thrust_maxMaximum thrust is indicated, l is span length, ρ is atmospheric density, S is wing area,

l, M, N respectively represent roll moment, pitch moment and yaw moment, Y, D, C respectively represent lift force, resistance force and lateral force, I_ii(i ═ x, y, z) represents each inertial parameter, coefficient, of the ship-borne aircraft

Representing the partial derivative of delta with respect to epsilon, i.e.

δ＝Y,D,C,L,M,N，ε＝α,β,δ_a,δ_e,δ_r,p,q,r。

2. The fixed-time fault-tolerant control method for carrier-based aircraft landing based on 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 obtained_1d＝(y_d,z_d) The following error variables are thus defined:

ε₁＝x₁-x_1d，ε₂＝x₂-x_2d

in which the position error is epsilon₁Angle error of epsilon₂。

Selecting the Lyapunov function as

The following virtual control law x is designed_2dComprises the following steps:

the virtual control law v is as follows:

the fixed time disturbance observer is designed as follows:

wherein k is₁₁,k₁₂,k₂₁,k₂₂Greater than 0 is positive definite diagonal matrix, delta₁₀,δ₂₀Greater than 0 is a small constant and utilizes

This term eliminates chatter and prevents the occurrence of singularity problems, z₁,z₂As a quantity of state of disturbance observer, λ₁,λ₂,λ₃In order to disturb the gain in the observer,

and is

λ₂＞0，λ₃＞4L₁. Wherein instruction filter estimation is applied

And

the design of the fixed time disturbance observer can accurately estimate unknown disturbance d in fixed time_fAnd the fixed time is

Wherein σ > 0 and

N₁＝λ₃+L₁，n₁＝λ₃-L₁and p > 1 is a controller parameter.

The desired pitch angle θ can be determined_dAngle of sideslip beta_dAnd the velocity roll angle mu_dComprises the following steps:

3. the fixed-time fault-tolerant control method for carrier-based aircraft landing based on 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 step_dAngle of sideslip beta_dAnd the velocity roll angle mu_dThe following error variables are thus defined:

ε₃＝x₃-x_3d，ε₄＝x₄-x_4d

selecting the Lyapunov function as

The following virtual control law x is designed_4dComprises the following steps:

actual control law u_actComprises the following steps:

the fixed time disturbance observer is designed as follows:

wherein k is₃₁,k₃₂,k₄₁,k₄₂Greater than 0 is positive definite diagonal matrix, delta₃₀,δ₄₀Greater than 0 is a small constant and utilizes

This term eliminates chatter and prevents the occurrence of singularity problems, z₃,z₄As a quantity of state of disturbance observer, λ₄,λ₅,λ₆For gain in disturbance observer,/₂＝z₃-x₄And is and

λ₅＞0，λ₆＞4L₂. Wherein instruction filter estimation is applied

And

the design of the fixed-time interference observer can accurately estimate the unknown interference delta within fixed time₁And the fixed time is

Wherein σ₁Is greater than 0 and

N₂＝λ₆+L₂，n₂＝λ₆-L₂and p > 1 is a controller parameter.

4. The fixed-time fault-tolerant control method for carrier-based aircraft landing based on 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 α_dThe following angle of attack error variables are thus defined:

ε₅＝α-α_d

selecting the Lyapunov function as

The following actual control law δ is designed_pComprises the following steps:

the fixed time disturbance observer is designed as follows:

wherein k is₅₁,k₅₂Greater than 0 is a constant, δ₅₀Greater than 0 is a small constant and utilizes

This term eliminates chatter and prevents the occurrence of singularity problems, z₅,z₆As a quantity of state of disturbance observer, λ₇,λ₈,λ₉In order to disturb the gain in the observer,

and lambda₇h^-1(λ₇)＞N₃，λ₈＞0，λ₉＞L₃。

The design of the fixed time disturbance observer can accurately estimate unknown disturbance d in fixed time_αAnd the fixed time is

Wherein σ₂Is greater than 0 and

N₃＝λ₉+L₃，n₃＝λ₉-L₃and p > 1 is a controller parameter.

According to the designed carrier-based aircraft landing fixed-time fault-tolerant control method, each tracking error of the system can be converged to zero in a small neighborhood within fixed time T after an actuator fails, wherein T is

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