Automatic landing system design via multivariable model reference adaptive control
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Abstract
The landing of a civil transport aircraft is one of the most critical phases due to parametric uncertainties and strong crosswind conditions. In this paper, separate controllers are designed for longitudinal and lateraldirectional channels for the landing phase, which is divided into the final approach, flare, and decrab. A multivariable model reference adaptive control scheme is implemented with state feedback for output tracking. The safety and flight performance of the autolanding control system are demonstrated through Monte Carlo simulations of a nonlinear civil transport aircraft model.
Keywords
Civil transport aircraft Autolanding design Adaptive control Output tracking Monte Carlo simulationsList of symbols
 \( D_{\text{LG}} \)
Distance to threshold
 \( H \)
Altitude
 \( H_{\text{LG}} \)
Landing gear height
 \( n = [n_{x} ,n_{y} ,n_{z} ] \)
Load factors
 \( ss_{\text{LG}} \)
Landing gear sideslip angle
 \( u = [\delta_{\text{th}} ,\delta_{\text{e}} ,\delta_{\text{a}} ,\delta_{\text{r}} ] \)
Control inputs (thrust, elevator, aileron, and rudder)
 \( V = [u,v,w] \)
Translational speeds
 \( V_{a} \)
True airspeed
 \( V_{c} \)
Calibrated airspeed
 \( V_{g} \)
Ground speed
 \( V_{Z} \)
Vertical airspeed
 \( V_{{Z_{{\rm {LG}}} }} \)
Landing gear vertical speed
 \( w = [w_{x} ,w_{y} ,w_{z} ] \)
Wind speeds
 \( X = [x,y,z] \)
Position of the center of gravity of the aircraft
 \( Y_{\text{LG}} \)
Deviation from runway axis
 \( \alpha \)
Angle of attack
 \( \beta \)
Aerodynamic sideslip angle
 \( \Delta = [\Delta_{\text{loc}} ,\Delta_{\text{gld}} ] \)
ILS noises (localizer noise and glide noise)
 \( \Delta y \)
Localizer deviation
 \( \Delta z \)
Glide deviation
 \( \chi \)
Flight path azimuth angle
 \( \varOmega = [p,q,r] \)
Angular rates
 \( \varPhi = [\phi ,\theta ,\psi ] \)
Attitude angles
1 Introduction
Today for a civil transport aircraft, most of the flight segments can be carried out by the autopilot, which guarantees the safety and stability of flights. However, the final approach and flare segments are still challenging tasks as high airworthiness standards have to be met in poor visibility conditions. In the aeronautical industry, the Certification Specifications for All Weather Operations (CSAWO) [1] taken by European Aviation Safety Agency (EASA) and the Advisory Circular (AC) 12028D [2] taken by the Federal Aviation Administration (FAA) provide acceptable means for obtaining approval of operations in Category III (CAT III) landing. With the help of CAT III instrument landing systems (ILS) that are now widely used in airports, automatic landing control laws have been proposed and are achieved by classical control techniques [3]. However, those automatic landing control laws are far from being robust to system uncertainties (e.g., mass, position of center of gravity (CG), etc.) or environmental phenomena (e.g., crosswinds, temperature variations, etc.). For this reason, ONERA, the French Aerospace Lab, and the AIRBUS Company have proposed a challenge aiming at inspiring new control systems that are able to improve the robustness. The challenge involves an ILS approach and flare from 1000 ft (304.8 m) above runway until touchdown [4].
Over the past two decades, there have been numerous research results of automatic landing control design for dealing with the civil transport aircraft landing problem. For instance, the linearquadraticgaussian with looptransfer recovery method was proposed by Ghalia and Alouani [5] to design an automatic landing controller for a typical commercial aircraft encountering a wind shear. A robust automatic landing controller was designed in Alpert [6] using a fixedorder \( H_{\infty } \) control method and was successfully applied to vertical speed tracking with the ground effect in consideration. An adaptive sliding mode control technique was used by Bouadi et al. [7] for flight path tracking, and the controller provided fault tolerance against aerodynamic parameter uncertainties, external disturbances, and modeling inaccuracies. Other control methods based on soft computing, such as fuzzy logic and neuro networks, can be found in Raj and Tattikota [8], Pashikar and Sundararajan et al. [9].
Model reference adaptive control (MRAC) is a fundamental adaptive control method, which is based on the state equation design and does not depend on the mathematical model of the controlled object. It has strong adaptive ability and robustness to timevarying system parameters and external disturbances. The multivariable MRAC design has been employed in many applications, such as flight control [10], faulttolerant control with parametric and structural uncertainties caused by damages [11].
The objective of this paper is to design an autopilot system with the integration of the MRAC method and classical control techniques to enable a correct landing despite parametric variations. The paper is organized as follows. In Sect. 2, the aircraft model and automatic landing segments are described. Then, the main theorem of multivariable MRAC method is introduced in Sect. 3. Based on this theorem, the detailed automatic landing controller design process is given in Sect. 4 and the control performance is validated through Monte Carlo simulations in Sect. 5. Finally, conclusions are drawn in Sect. 6.
2 Civilian aircraft landing control problem
The Civilian Aircraft Landing Challenge is a benchmark proposed by ONERA and AIRBUS. In this section, the aircraft model provided for the benchmark is first briefly described, followed by a description of the automatic landing segments.
2.1 The aircraft model
Characteristics of engines and actuators
Parameter  Timeconstant  Lowerbound  Upperbound  Ratelimit 

Engines (EPR)  2 s  0.95  1.6  0.1 
Elevators  0.07 s  − 25 deg  25 deg  20 deg/s 
Ailerons  0.06 s  − 55 deg  55 deg  60 deg/s 
Rudder  0.2 s  − 30 deg  30 deg  30 deg/s 
2.2 Description of the landing phase

Final approach phase In this phase, the aircraft needs to track the glideslope and localizer path command signals generated by the ILS. Meanwhile, the calibrated airspeed is kept constant and the sideslip angle is close to zero.

Flare phase The flare controller replaces the final approach longitudinal controller when the height of the airplane landing gear \( H_{\text{LG}} \) is less than 15 m. In this phase, the throttle is set to idle, so the calibrated airspeed is no longer to be controlled and only the elevator is effective to reduce the vertical speed \( V_{z} \).

Alignment phase (or decrab mode) This phase replaces the final approach lateral outer control loop when the height of the airplane landing gear is less than 9 m. The objective of this phase is to minimize lateral effort at touchdown to meet airworthiness standards.
2.3 Overview of the autoland architecture
The longitudinal and lateral outer loops (lon outer loop and lat outer loop) generate the commanded signals \( (V_{cc} ,V_{zc} ) \) for the longitudinal axis and \( (n_{yc} ,\phi_{c} ) \) for the lateral axis, respectively, to inner loops (Lon Inner Loop and Lat Inner Loop). Along the longitudinal axis, when the airplane landing gear height \( (H_{\text{LG}} ) \) is less than 15 m above runway, the desired vertical speed signal \( V_{zc} \) is modified by Flare controller to ensure a soft landing and the same architecture is used along the lateral axis. When the height of the landing gear is less than 9 m, the desired lateral load factor \( n_{yc} \) and roll angle \( \phi_{c} \) signals are determined by Decrab controller.
3 Model reference adaptive control
In this section, the theoretical background of a multivariable MRAC method based on the state feedback and output tracking is introduced and more details can be found in Guo et al. [14].
3.1 Problem statement
To simplify the representation, the symbols of Laplace transformation and inverse Laplace transformation in the first expression are omitted without causing misunderstanding. \( \Delta r(t) \in R^{M} \) is a bounded external reference input signal and \( W_{m} (s) \) is the reference model transfer function matrix. \( d_{i} (s) \) is a monic stable polynomial of degree \( l_{i} \) with \( l_{i} = n  m \), where n and m are the degrees of denominator and numerator polynomials of system transfer function \( G(s) = C(sI  A)^{  1} B \).
3.2 State feedback control
3.3 Adaptive law
Guo et al. [19] proved through stability analysis that the above MRAC scheme with state feedback control law updated by the adaptive laws can guarantee the stability of the closedloop system. Meanwhile, closedloop signals can asymptotically track reference signals.
4 Automatic landing control design
In this section, the MRAC method is integrated with classical proportionalintegralderivative (PID) control to design an automatic landing control system. According to the control structure introduced in Sect. 2.3, the landing phase is divided into three segments, the final approach, flare, and decrab. The task of outer control loops is to provide the corresponding inner loops with appropriate reference signals to address the specific control objectives. On the other hand, the inner loops must track those signals despite perturbations and uncertainties. Note that the state signals are \( u,v,w,p,q,r,\phi ,\theta ,\psi \), all of which can be measured to apply the MRAC algorithm.
4.1 Longitudinal control architecture
During the final approach, the trajectory of the aircraft must track the ILS beam as close as possible. This can be achieved by minimizing the glide deviation \( (\Delta z) \). Moreover, the nominal longitudinal slope trajectory is \( \gamma_{gld} =  3 \, \deg \) and the calibrated airspeed \( (V_{c} ) \) needs to be kept at \( 66{\text{ m/s}} \). Therefore, in this phase, the outer loop is to generate the reference vertical speed by feeding back the glide deviation \( (\Delta z) \) as \( \dot{\Delta }z \approx V_{z} \) and the inner loop is a vertical speed \( (V_{Z} ) \) and calibrated airspeed \( (V_{c} ) \) tracker.
Longitudinal outer control
Longitudinal inner control
4.2 Lateraldirectional control architecture
The aircraft is held level \( (\phi = 0) \) and the sideslip angle \( (\beta ) \) is controlled to be zero with the coordinated use of the ailerons and rudder during landing. During the final approach, the aircraft minimizes the localizer deviation \( (\Delta y) \) to track the ILS localizer beam and the bank angle \( \phi_{c} \) reference is provided by feeding back the localizer deviation \( (\Delta y) \). The reference for lateral load factor \( n_{y} \) which replaces the sideslip angle \( (\beta ) \) is zero.
Lateraldirectional outer control
Lateraldirectional inner control
4.3 Flare
4.4 Decrab
5 Simulation results
In this section, we apply the automated landing control law to the nonlinear transport aircraft model to assess its effectiveness. Two sets of simulations are conducted in MATLAB/Simulink, one under a nominal condition and the other with parametric variations. The preliminary simulation results verified that the control system designed in this paper can accomplish the landing task accurately and maintain the closedloop stability and robustness when the aircraft encounters some uncertainties (e.g., mass, CG position, and temperature variations).
5.1 Nominal condition
5.2 Monte Carlo assessment
Distributions for parameters affecting the landing performances
Parameter  Distribution  Min  Max 

Aircraft mass  Uniform  60 t  180 t 
Center of gravity  Uniform  15%  41% 
Temperature  Uniform  − 69 °C  + 40 °C 
Risks evaluation
Parameter  Average  Limit 

Longitudinal touchdown earlier than a point on the runway 60 m (200 ft) from the threshold. (HTP60)  \( 10^{  6} \)  \( 10^{  5} \) 
Lateral touchdown with the outboard landing gear greater than 21 m (70 ft) from the runway centreline, assuming a 45 m (150 ft) runway. (YTP)  \( 10^{  6} \)  \( 10^{  5} \) 
Bank angle such that wing tip touches ground before wheels. (PHI)  \( 10^{  8} \)  \( 10^{  7} \) 
Lateral velocity or slip angle for structural limit load. (SSTP)  \( 10^{  6} \)  \( 10^{  5} \) 
Distributions for parameters affecting the landing performances
Parameter  Mean (MRAC)  Variance (MRAC)  Mean (PID)  Variance (PID) 

HTP60 (m)  7.1968  2.1164  6.5022  6.5022 
YTP (m)  − 0.0096  0.0013  − 0.2225  − 0.2225 
PHI (deg)  − 6.6281e−04  2.9268e−08  0.1191  0.1191 
SSTP (deg)  0.0016  6.9623e−07  0.1242  0.1242 
6 Conclusion
This paper presents an automated landing system, in which the landing phase is divided into the final approach, flare, and decrab phases. Separate controllers are designed for longitudinal and lateraldirectional channels by integrating the PID control method and state feedback output tracking multivariable MRAC scheme. The performance is demonstrated through Monte Carlo nonlinear simulations with uncertainties taken into account. In addition, the proposed control scheme is compared with the traditional PID control method. The Monte Carlo assessment results show that the MRAC method is better than the traditional PID method in the presence of uncertainties.
Notes
Acknowledgments
This research was sponsored by the National Natural Science Foundation of China under the Grant #61473186.
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