An adaptive disturbance rejection algorithm is proposed for carrier landing system in the final-approach. The carrier-based aircraft dynamics and the linearized longitudinal model under turbulence conditions in the final-approach are analyzed. A stable adaptive control scheme is developed based on LDU decomposition of the high-frequency gain matrix, which ensures closed-loop stability and asymptotic output tracking. Finally, simulation studies of a linearized longitudinal-directional dynamics model are conducted to demonstrate the performance of the adaptive scheme.

The automatic carrier landing system requires that the aircraft arrives at the touchdown point in a proper sink speed and a small margin error for position. The key requirements of this problem are that the aircraft must remain within tight bounds on a three-dimensional flight path while approaching the ship and then touch down in a relatively small area with acceptable sink rate, angular attitudes, and speed. Further, this must be accomplished with limited control authority for varying conditions of wind turbulence and ship air wake.

During the past decades, research on the improvement of the automatic carrier landing system had received much attention. A vertical rate and vertical acceleration reference were used in the control law to reduce the turbulence effects and deck motion in [

Adaptive control has become one of the most popular designs for failures and disturbances compensation. An output tracking model reference adaptive control (MRAC) scheme was developed for single-input/single-output systems in [

In this paper, an adaptive control scheme is proposed to handle wind during carrier landing. The main contributions of this paper are described as follows:

With unmatched disturbance, the aircraft models in air-wake turbulence conditions during the carrier landing are analyzed. The longitudinal linearized model of a carrier-based aircraft dynamics is constructed on the final-approach.

Adaptive LDU decomposition-based state-feedback controller is designed to relax design conditions, including adaptive laws and stability analysis.

The proposed LDU decomposition-based disturbance rejection techniques are used to solve a typical carrier landing aircraft turbulence compensation problem. Extensive simulation results are obtained through a longitudinal aircraft dynamic model during aircraft landing.

The rest of this paper is organized as follows. In Section

The overall carrier landing task for a fixed-wing aircraft is shown in Figure

Procedures of carrier landing for the aircraft.

Final carrier landing phase.

Both of the bank and sideslip angles are zero; the decoupling longitudinal of the nonlinear equations is described in the calm circumstance. The longitudinal aircraft dynamics equations are presented as follows.

The force equations are

The kinematic equation is

The moment equation is

The navigation equation is

The identical equation is

The linear model of the longitudinal flight dynamics is constructed based on the small-perturbation equation. The linearized longitudinal flight dynamics is described as

The steady component of the carrier air wake is taken into account to provide some disturbances, as a basis of our simulations.

The steady component of the carrier air wake is taken into account to the simulation. The superstructure and deck/hull features of an aircraft carrier are known to generate turbulent airflow behind the carrier. This region of turbulent air has become known as the burble and it is often encountered by pilots immediately after an aircraft carrier. This turbulent region of air has adverse effects on landing aircraft and can cause pilots to bolter, missing the arresting wires and requiring another landing attempt.

The burble components are determined from look-up tables scheduled on the aircraft distance behind the ship in [

The linear model of the aircraft under the air-wake disturbance is addressed in [

In this section, to solve turbulence compensation problem, an adaptive disturbance rejection design is developed for multivariable systems with unmatched input disturbances.

Consider the linear time-invariant system as

The control objective is to design an adaptive state-feedback control signal

For any

Every

All zeros of

The leading principal minors of the high-frequency gain matrix

From plant (

The transfer matrix

Assumption

With the knowledge of the plant and disturbance parameters, the nominal state-feedback controller is

The matrix

Based on Lemma

For plant (

From plant (

Operate the interactor matrix (a polynomial matrix)

From (

For the disturbance vector

For model (

The parameter matrix and the disturbance signal components are

Hence, the disturbance

With

Next, the adaptive disturbance rejection design will be studied for the plant with uncertainties from the plant and unmatched disturbances.

Applying (

To deal with the uncertainty of the high-frequency gain matrix

Based on the error model (

To analyze the closed-loop system stability, we first establish some desired properties of the adaptive parameter update laws mentioned above.

The adaptive laws ensure that

Based on Lemma

For plant (

The proof of this stability theorem can be established through using a unified framework. Because the control input

The proposed multivariable adaptive disturbance rejection scheme is applied to a carrier landing system using LDU based decomposition. The aircraft longitudinal model defined in planted (

For the aircraft system, the transfer function,

The related gain parameters in adaptive laws (

For this simulations study, the initial state is chosen as

Final landing phase altitude for the aircraft.

Final landing phase tracking error for the aircraft.

Final landing phase altitude for the aircraft.

Final landing phase tracking error for the aircraft.

Final landing phase control signal.

In this paper, a multivariable disturbance rejection scheme is presented to solve the wind turbulence problem. The state-feedback output tracking MRAC scheme is designed based on the LDU decomposition of the high-frequency gain matrix. The aircraft carrier landing system under aircraft carrier air wake is analyzed. The proposed LDU decomposition-based disturbance rejection techniques are used to solve a typical carrier landing aircraft turbulence compensation problem. Finally, simulation results have been presented to show that MRAC-based disturbance rejection scheme is an effective method of the carrier landing system with the disturbances.

Aerodynamic drag derivative with respect to elevator deflection angle

Engine thrust, aerodynamic drag force, and aerodynamic lift force

Angle of attack, pitch, and flight-path slope

Altitude of aircraft

Gravitational acceleration

Mass of aircraft

Airspeed of aircraft

Pith rate

Moment of inertia in pitch

The pitch moment

Elevator deflection bias angle and engine throttle angle

Aerodynamic pitch moment and drag derivative with respect to airspeed

Thrust and aerodynamic lift derivative with respect to airspeed

Aerodynamic pitch moment and lift derivative with respect to

Turbulence velocity and body axis components of

The trim value of aircraft state

Aerodynamic pitch moment and drag derivative with respect to airspeed

Thrust and aerodynamic lift derivatives with respect to airspeed

Aerodynamic pitch moment and lift derivative with respect to elevator

Aerodynamic drag derivative with respect to

Aerodynamic drag due to

Aerodynamic pitch moment with respect to

Aerodynamic pitch moment with respect to

Benchmark aerodynamic thrust at the airspeed

Aerodynamic thrust derivatives with respect to the throttle

Aerodynamic lift derivative with respect to angle of attack and height.

The authors declare that they have no competing interests.